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9 LIBRARY
59% Michigan State
, University

This is to certify that the
thesis entitled

DESIGN OPTIMIZATION OF SUSTAINABLE PANEL SYSTEMS
USING HYBRID NATURAL/SYNTHETIC FIBER REINFORCED
POLYMER COMPOSITES

presented by

JANELLE C. RIEMERSMA MUSCH

has been accepted towards fulfillment
of the requirements for the

MASTERS degree in CIVIL ENGINEERING

 

 

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3/24/03

Date

MSU is an affirmative-action, equal-opportunity employer

 

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DESIGN OPTIMIZATION OF SUSTAINABLE PANEL SYSTEMS USING
HYBRID NATURAL/SYNTHETIC FIBER REINFORCED POLYMER
COMPOSITES
By

Janelle C. Riemersma Musch

A THESIS
Submitted to
Michigan State University
In partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Civil Engineering

Department of Civil and Environmental Engineering

2008

ABSTRACT
DESIGN OPTIMIZATION OF SUSTAINABLE PANEL SYSTEMS USING
HYBRID NATURAL/SYNTHETIC FIBERE REINFORCED POLYMER
COMPOSITES
By
Janelle C. Riemersma Musch

Natural fiber reinforced composites are an attractive alternative to traditional
synthetic fiber reinforced composites because of their environmental benefits and low
cost. However, the addition of natural fibers to a composite results in a lower stiffness
material. A viable compromise between the higher material properties of synthetic fibers
and the environmental benefits of natural fibers is found by utilizing both synthetic and
natural fibers to create a hybrid fiber reinforced composite system. Material properties
are also improved by efficient arrangement of the structural members. The use of hybrid
neutral/synthetic fiber reinforced composites for structural applications has been shown
to be a feasible alternative to traditional synthetic building materials.

The strength and environmental performance of natural and synthetic fiber
composites was studied by considering a floorboardl panel application. The floorboard
was optimized by altering the geometry of the cross sectional frame and the fiber material
chosen for each ply of the composite. The frame was then optimized to minimize volume
while meeting constraints on allowable strain, deflection and an environmental quota
based on a life cycle assessment of each constituent material. The enviromnental
constraint was altered to produce a range of optimized floorboard designs that will allow
a designer to consider both strength and environmental requirements in a structural

member design.

 

 

   
  
 
   

To my husband; Ryan
To my parents; Leonard and Yvonne
, ‘ invite]! give- ne strength, your encouragement which gives me

‘Iopeandyonrlovewhichinaptresme

 

ACKNOWLEDGEMENTS

I am most grateful to my advisor, Dr. Rigoberto Burguefio, for his insight,
patience, support, and encouragement throughout this work and during my time at MSU.
His time and guidance have been invaluable during my research and studies. The topic
and ideas presented throughout this thesis were proposed by him.

I would also like to thank the members of my advisory committee, Dr. Ronald
Harichandran and Dr. Ronald Averill for their interest and insight.

Lastly, I am gratefiil for the support of my friends and colleagues. A special word
of thanks to Mahmoodul Haq who was a source of support both for the topic studied in

this thesis and for his valuable advice and assistance in all things MSU.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TABLE OF CONTENTS

ACKNOWLEDGEMENTS v
TABLE OF CONTENTS vi
LIST OF TAB].FS iv
LIST OF FIGURES 1r
1 INTRODUCTION 1
1.1 Overview 1
1.2 General Research Objective 2
1.3 Synthetic Fiber Composites 3
1.4 Natural Fiber C ' 3
1.5 Design Prt ’ " 4
1.6 Environmental Ratings of Mater-ink S
1.7 Objective and Scope 5

2 OPTIMIZATION THEORY, COMPOSITE THEORY AND
ENVIRONEMENTAL DESIGN ASPECTS OF BUILDING MATERIALS .............. 8
2.1 Overview R
2.2 Fiber Reinforced Polymer Composites Background 9
2.2.1 Overview 9
2.2.2 Overview of Composite Theory 12
2.2.2.1 Properties of Continuous Fiber Composites: Lamina Properties 14
2.2.2.2 Properties of Continuous Fiber Composites: Laminate Properties .17
2.2.2.3 Strain Computations in a Laminate Frame 7?
2.2.2.4 Properties of Randomly Oriented Short Fiber Composites ............. 25
2.2.3 Classical Lamination Theory for use with Beam Elements ...................... 26
2.2.4 Conclusions 33
2.3 Bi r " 33
2.3.1 Overview 33
2.3.2 Benefits of l" r " 34
2.3.3 Challenges of Biocomposites 35
2.3.4 Bio Composite Applications- State of the Art 36
2. 3 ..4 1 Automotive‘. ‘ 36
2. 3 ..4 2 Civil/Construction Applications 39
2.3.4.3 Commodities Applications 41
2.3.5 Conclusions 42
2.4 Optimization Background 42

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2.4.1 Overview 42
2.4.2 Structural Optimization 43
2.4.2.1 Variables 43
2.4.2.2 Objectives 44
2.4.2.3 Constraints 45
2.4.3 Conclusions 46
2.5 Optimization Techniques and Optimization with HEEDS .............................. 46
2.5.1 Overview 46
2.5.2 Optimization T L ' , 47
2.5.2.1 Genetic Algorithms 47
2.5.2.2 Gradient Based “ “' 4 57
2.5.2.3 Simulated Annealing 55
2.5.2.4 Response Surface Methodology 56
2.5.3 HEEDS Procedures and Terminology 57
2.5.4 Conclusions 59
2.6 Environmental Aspects of Building Material Design 59
2.6.1 Overview 59
2.6.2 Natural R 59
2.6.3 Energy I keg? 61
2.6.4 Life Cycle Assessment 61
2.6.5 LEED Ratings and Industry Interest 63
2.6.6 Conclusions 55
2.7 Summary 65
3 DEVELOPMENT AND IMPLEMENTATION OF STRUCTURAL AND
ENVIRONMENTAL PERFORMANCE OPTIMIZATION TECHNIQUE ............. 66
3.1 Overview ‘5
3.2 Optimization of Floor Panel Case Study: Problem " “ ’L' 66
3.2.1 Flooring Systems 66
3.2.2 Loading 73
3.2.3 Materials 75
3.2.4 Construction Issues 77
3.2.5 Modeling Issues 79
3.3 Optimization of Floor Panel Case Study: Optimization Problem Formulation
84
3.3.1 Optimization Objectives 84
3.3.2 Design Variables R4
3.3.3 Constraints 95
3.3.4 Optimization Problem “‘ ‘ ‘ 89
3.3.5 Optimization Method 91
3.4 Optimization of Floor Panel Case Study: Environmental Performance ........ 91
3.4.1 Environmental Goals for Design 91
3.4.2 Life Cycle Ratings for Composite Materialq 91
3.4.3 Environmental Ratings for Optimization Problem 94
3.5 Mathematical Modeling 95

vii

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3.6 C ‘ ' 97
4 DISCUSSION AND RESULTS 98
4.1 Overview 98
4.2 Design and Optimization Process 08
4.2.1 Optimization Design Process Description 93
4.2.2 Optimization Outputs 104
4.3 Optimization Results and “' ' 107
4.4 Validation 1 19
4.5 Industry Applicability 121
4.5.1 User Defined Environmental Performance 121
4.5.2 Applicability to Current Industry Practice 121
4.6 C ‘ ' 124
5 CONCLUSIONS AND RECOMMENDATIONS 125
5.1 C ' ‘ 125
5.2 Recommendations for Future Work 126
5.2.1 Increased Complexity of the Optimization Problem ............................... 126
5.2.2 Expansion of the Library of Final Designs 127
5.2.3 Computational PFC ' y 128
5.2.4 Laboratory Manufacturing and Testing 128
REFERENCES 129

 

viii

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LIST OF TABLES
Table 2.1 Properties of Natural and Synthetic Fibers 34
Table 2.2 LEED for New Construction (NC) Point Levels 64
Table 2.3 LEED for New Construction (NC) Category Possible Points ........................... 64
Table 3.1 Reinforcing Fiber and Matrix Material Properties 76
Table 3.2. Illustration of Nodal Symmetry 85
Table 3.3. Multiplier Values by Load State 22
Table 3.4. Ultimate Strains RR
Table 3.5. Maximum Allowable Strains 89
Table 3.6. Life Cycle Composite Environmental Ratings 93
Table 4.1 Variable Node Delta x Selection 99
Table 4.2 Example Material Types and Layer Thicknesses 101
Table 4.3 Material Percentages and Environmental Rating 103
Table 4.4. Fiber Material Costs 1 10
Table 4.5. Comparison to Commercial Panel 117
Table 4.6 LEED Materials and Resources Points by Sectinn 123

 

 

 

LIST OF FIGURES

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 2.1 Composite Material Phases 10
Figure 2.2 Specific Strength and Stiffness Values for Composites and Traditional

Materials 11
Figure 2.3 Unidirectional Lamina and Principal Coordinate Axes ................................... 13
Figure 2.4 Transformation Angle 16
Figure 2.5 Force and Moment P " ‘ 17
Figure 2.6 Laminate Thickness Coordinates 18
Figure 2.7. Simply Supported 2D Beam with Central Folded Layer ................................ 19
Figure 2.8 One Dimensional Element Subject to Axial Forces 70
Figure 2.9 Two Dimensional Flemmt 71
Figure 2.10 Local Element End Forces 74
Figure 2.11. Frame Element 76
Figure 2.12. Laminated Beam in Pure Bending 77
Figure 2.13. Four-Layer Laminate 30
Figure 2.14. A Population, Genes, and CL 48
Figure 2.15. Probability of Selection based on Fitness Values 49
Figure 2.16. Crossover One Cut Method 50
Figure 2.17. Crossover Two Cut Method 50
Figure 2.18. Mutation Operator 51
Figure 2.19. Plot ofFunction f(x) = —2x3 +5).2 +3x—2 5:
Figure 2.20. HEEDS Optimization Process 58
Figure 3.1 Floor System ° L " 67
Figure 3.2 Floorboard and Structural Panel Materials 68

x

 

 

 

 

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I‘

 

Figure 3.3. Floor Panel System and Loading 60

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 3.4. General Simply Supported Plate 70
Figure 3.5. Simply Supported Plate with Central Folded Layer ....................................... 71
Figure 3.6. Simply Supported 3D Beam with Central Folded Layer ................................ 71
Figure 3.7. Simply Supported 2D Beam with Central Folded Layer ................................ 72
Figure 3.8. Frame and Loading Layout 72
Figure 3.9 Possible Vertical Member Arrangements 73
Figure 3.10 Simple Truss Load Paths 74
Figure 3.11. Building Block Layer An g ‘ 78
Figure 3.12. Building Block Composite Layer Cross Serums 79
Figure 3.13 Idealized Truss Nodal C " 80
Figure 3.14. Non-idealized Truss Nodal Connection 80
Figure 3.15 Proposed Truss Nodal Connections 87
Figure 3.16. Frame Node 1" L ing 85
Figure 3.17. Equivalent Nodal Loads 96
Figure 4.1. Optimization Procedure, Steps 1 and 2 99
Figure 4.2 Delta x 111 L " 100
Figure 4.3 Material Types and Layer Thicknesses, Blocks 1-3 ...................................... 101
Figure 4.4. Optimization Procedure, Steps 3 and 4 102
Figure 4.5. Member Strain Illustration 103
Figure 4.6. Optimization Procedure, Step 5 104
Figure 4.7. Volume Values over Course of Cr " ° " 105
Figure 4.8. HEEDS Progress to Environmental Rating 107

 

 

 

 

 

 

 

 

 

 

Figure 4.9. Environmental Rating v Volume 109
Figure 4.10 Enviromnental Rating v Cost 110
Figure 4.11 Cost v. Material Percentage 11 1
Figure 4.12 Environmental Rating v Material 1‘ ‘ a 112
Figme 4.13 Environmental Rating v Material Percentages: Trends ............................... 113
Figure 4.14. Environmental Rating v. Material Percentages: Hemp and Carbon ........... 114
Figure 4.15 Environmental Rating v Performance Measure 116
Figure 4.16 Performance Measure v Material Percentage 116
Figure 4.17. Durashield Panel (Strongwell 2008) 1 17
Figure 4.18 Allowable Pressure (psi) of 3” Panels 118
Figure 4.19 Hemp BioPanel with Top and Bottom Woven Jute Fabric .......................... 118
Figure 4.20. Member Strain Ill ‘ " 120

 

Figure 4.21 DuraSpan Deck Panel Cross-Section Schematic (Martin Marietta 2008) 120

xii

 

 

1 INTRODUCTION

1.1 Overview

The world’s supply of natural resources is decreasing and the demand for
sustainable and renewable raw materials continues to rise (Mohanty, Misra, and Drzal
2005). Interest in environmental sustainability of materials has also recently gained
significant interest through the standardization of green building practices through
programs such as the United States Green Building Council’s Leadership in Energy and
Environmental Design (LEED) program. The use of rapidly renewable materials has been
recognized by industry as an important contributor to green building (U SGBC 2006).

Composite materials combine the properties of two or more constituent materials
to achieve a final product that out performs the constituent materials acting alone (Daniel
and Ishai 2006). Fiber reinforced polymer (FRP) composite materials, which consist of
polymer matrices reinforced with micron-size fibers, are valued for their high strength
and stiffness to weight ratios and are used in a wide variety of applications fi'om weight
critical applications such as aeronautic and automotive paneling to specialized
applications such as structural reinforcement for earthquake loads. Traditional fiber
reinforced composites utilize synthetic constituent materials such as glass or carbon
fibers as reinforcement and epoxy or polyester polymers as a matrix. In an effort to
improve the sustainability of fiber-reinforced composites, the use of natural fibers and
polymers materials become of high interest. In an effort to improve the sustainability of
fiber-reinforced composites, the use of natural constituent materials has been investigated.

This thesis focuses on the development and use of fiber reinforced composites that are

 

 

 

 

constructed of natural fibers, such as hemp and jute, and a traditional synthetic matrix.
These fiber-reinforced composites are referred to as natural fiber composites in this thesis.

Recent efforts have shown that natural fiber composites can compete with glass
fiber composites (Mohanty et a1. 2002). However, the use of natural fiber composites has
been largely limited to non-structural applications due to the reduction in strength that is
seen when synthetic fibers are replaced with natural fibers, making them more suitable to
low strength applications. It has been shown that strategic arrangement of material can
help overcome this disadvantage and make the use of natural fiber composites feasible
for load bearing applications (Burguefio et a1. 2005). Ideal strategic arrangement is
achieved through structural optimization and it has been demonstrated that improved
designs can be achieved through structural sizing optimization (Isaac 2005, Sharma 2005).

The topics introduced thus far are studied through a design problem that considers
the use of a natural fiber reinforced composite for a load bearing application while
incorporating environmental impact as a design consideration. The research objective is
defined and the fimdamental topics of interest present in this topic will be expanded in
the remaining sections of this chapter. Fundamental topics include synthetic and natural

fiber composites, material optimization and environmental ratings of materials.

1.2 General Research Objective

The objective of this research was to develop innovative designs for hybrid
mural/synthetic fiber reinforced composites for sustainable construction. Sustainability
was defined as the ability to balance performance and environmental constraints. The

approach was to develop such designs through structural optimization. Structural

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performance was controlled by changing the distribution of hybrid material designs to
achieve the most beneficial arrangement for a given loading. Environmental performance
was achieved by controlling the ratio of synthetic to natural materials in the structure.

Details on the specific research objectives are presented at the end of this section.

1.3 Synthetic Fiber Composites

Modern synthetic fiber reinforced composites were initially developed for the
space industry where reduction of weight has a critical impact on performance and
system energy usage. A structural composite generally consists of two distinct phases; a
discontinuous, stiffer and stronger reinforcement phase and a continuous, weaker matrix
phase. The properties of the composite depend on the properties of the reinforcement, the
matrix and the proportion of each. As mentioned previously, the main advantage of fiber-
reinforced composites is their high strength and stifliress and low weight. Fiber
reinforced composites are also valued for their high degree of confonnability to different
geometric and practical applications. Other benefits include corrosion resistance, wear
resistance, seamless construction, environmental stability, thermal insulation and
conductivity and acoustic insulation (Daniel and Ishai 2006). Disadvantages include high
initial costs and negative environmental impact due to the use of oil based constituent

materials and the high degree of processing required to create the composite.

L4 Natural Fiber Composites
Natural fiber composites are fiber-reinforced composites that are composed of a

traditional synthetic matrix material, but replace traditional synthetic fibers with natural

 

fibers. Natural fibers are fibers that are readily available in nature. The two main
components of these fibers are cellulose and lignin, which provide the structural stiffness
in plant cell walls. Common examples of natural fibers that are used as composite
reinforcement are bamboo, hemp, jute and cotton fibers. The tensile strengths and
Yormg’s modulus values for natural fibers tend to be lower than synthetic fibers, but the
density of natural fibers is often less than the synthetics. Thus the specific strength of a
natural fiber composite is comparable to a glass fiber composite (Mohanty, Misra, and
Drzal 2005). Natural fiber composites are generally less expensive than synthetics, more
readily available and use less energy. Nonetheless, natural fiber composites have several
disadvantages over synthetic fiber composites including increased susceptibility to
environmental degradation, decreased mechanical properties and low tolerance of high

temperatures experienced during manufacture.

1.5 Design Optimization

A research objective is to obtain the most beneficial arrangement of materials
while balancing performance and environmental constraints. This objective is reached
through the use of structural design optimization. Structural design optimization
generally involves sizing of a component to meet strength or performance requirements
such as maximum allowed deflection while simultaneously minimizing weight or volume.
Basic optimization includes an objective function, such as minimum weight, variables,
such as beam flange thickness or member length, and constraints such as maximum
allowed deflection or maximum allowed strain. Optimization is the process of

maximizing the performance of a system by varying design inputs. Mathematical

 

optimization techniques have been developed to facilitate and expedite the design process
when the design is too complex to be optimized according to designer experience or a
trial and error process alone. An adaptive hybrid algorithm, which employs a unique
combination of optimization search methods, is used in this thesis. Several of these basic
methods are defined including gradient based methods and genetic algorithms. Gradient-
based methods rely on the ability to compute a gradient or slope of the optimization
and/or constraint functions. Gradient-based methods represent some of the fastest
optimization methods. Genetic algorithms are based on the theory of genetic evolution
and rely on a system of evaluating the goodness of members of a population and ranking
these members so that good designs are more likely to be carried through to subsequent
generations. The optimization techniques utilized in this thesis are discussed in detail in

Chapter2.

1.6 Environmental Ratings of Materials

The use of material in a design represents an environmental burden. This
enviromnental burden can be lessened by minimizing the amount of material needed, by
minimizing the amount of energy needed, or by choosing a material that is more
renewable. It is difficult at first glance to quantify what the environmental impact of a
material is. For instance, if a car door panel material is being chosen, the energy usage of
that material could be defined in two ways. First, energy could be defined as the amount
of energy required to create the car door panel. In this instance, one would select a
material that requires very little processing, thus saving energy. Second, energy could be

defined as the amormt of energy used during the lifetime of the vehicle due to the weight

 

of the car door panel. In this instance, one would select a material with a very low density,
thus saving firel costs over the life of the vehicle. It is easily conceivable that a low-
dcnsity material might require greater processing energy initially, but that this energy
usage would be recouped over the lifetime of the vehicle. Thus, it is necessary to define
the factors that will contribute to the environmental evaluation of materials. The
environmental rating metric used in this thesis is derived from a technique known as Life
Cycle Assessment. Life cycle assessment considers energy usage of a material over its
entire life, often fi‘om material extraction to material disposal or recycle, or fi'om “cradle
to grave.” Materials are evaluated based on defined environmental impact categories such
as water use, smog, and materials extraction. Societal impact categories such as
wonomical impacts may also be considered. Life cycle assessment is a method that
contains variability depending on the initial choices made. Initial choices include the
portion of the life cycle considered in the analysis, the environmental and societal impact
categories that were defined as well as the relative importance assigned to each impact
category. Life cycle assessment is used in this thesis to quantify the environmental impact
of constituent materials so that they may be incorporated into an optimization process.

Further discussion on environmental ratings of materials is contained in Chapter 2.

1.7 Objective and Scope

The objective of this thesis is to demonstrate that the design of a fiber reinforced
polymer composite panel system can be optimized for mechanical and environmental
performance. The structural system chosen for this evaluation is a floorboard panel. It is

expected that a system that contains a balance of synthetic and natural fibers will yield

 

the desired strength and environmental performance depending on the requirement and
values of the designer. It is a goal of this optimization process to demonstrate the use of
environmental performance as a design constraint and to compare a range of choices
available to the designer. The final result of this process will demonstrate that through
desigi optimization, a designer can specify not only the mechanical performance metrics
that are traditionally used in a structural design, but also the environmental metrics that
are becoming increasingly important in today’s atmosphere.

This thesis procwds as follows: A literature review and discussion of topics
necessary to perform the evaluation of the composite floor panel is first carried out. This
is followed by an introduction to the specific structural system and problem parameters
are defined. The optimization of the system is carried out, and results are discussed.
Finally, conclusions and recommendations are provided.

The chapters of this thesis are organized in the following order:

0 Chapter 2: Optimization Theory, Composite Theory and Environmental
Design Aspects of Building Materials

0 Chapter 3: Development and Implementation of Structural and
Environmental Optimization Technique

0 Chapter 4: Discussion and Results

0 Chapter 5: Conclusions and Recommendations

 

2 OPTIMIZATION THEORY, COMPOSITE THEORY AND

ENVIRONEMENT AL DESIGN ASPECTS OF BUILDING MATERIALS

2.] Overview

This chapter presents background on the three main topics addressed in this thesis:
fiber reinforced composites, optimization, and environmental design of building materials.

Fiber reinforced polymer (FRP) composites are materials composed of a micro-
sized fibrous material and a polymer matrix and are valued for their high mechanical
properties and low weight. The types of F RP composites and the fundamental methods to
define the properties of continuous and short fiber composites are presented. Natural fiber
composites are fiber-reinforced composites that replace traditional synthetic fibrous
reinforcement, such as glass or carbon fibers, with natural rapidly renewable fibrous
reinforcement, such as hemp or jute fibers. Natural fiber composites mechanical
properties and challenges are presented, then, state of the art applications of natural fiber
composites in automotive, construction and commodities are discussed.

Design optimization is the process of finding the best solution to a mathematical
or design problem that simultaneously meets all imposed constraints. The optimization
sofiware package HEEDS (Red Cedar Technology 2005) was used in this thesis. An
overview of structural optimization is presented and several of the optimization methods
utilized by HEEDS, including gradient-based methods, and genetic algorithms, are
discussed.

Increased environmental awareness and the rising cost of building materials and

building energy usage has prompted the growth of environmentally fiiendly building

 

materials and methods. Methods to quantify building material energy usage are discussed.
The widely used environmental rating system for buildings called Leadership in Energy
and Environmental Design (LEED) (U SGBC 2006) is introduced and industry interest in

environmental building methods is discussed.

2.2 Fiber Reinforced Polymer Composites Background
2.2.1 Overview

A composite is a material consisting of two or more macroscopic materials whose
mechanical performance and properties are superior to that of the independent constituent
materials (Daniel and Ishai 2006). Fiber reinforced polymer (FRP) composites are
commonly composed of two main material phases: fibrous reinforcement and a polymer
matrix (see Figure 2.1). The fibrous reinforcement phase is discontinuous, stiff and strong.
It provides much of the strength and stiffness for the composite. Commonly used fibrous
reinforcement materials include glass and carbon fibers. The polymer matrix phase is
continuous, and is less stiff and strong than the fibrous phase. The matrix protects the
fibers, transfers load to the fibers and gives the composite its shape. Commonly used

matrix materials include epoxy and polyester.

FIBROUS
. : WREINFORCEMENT

  

Figure 2.1 Composite Material Phases

FRP composites are valued for their high strength to weight ratios and high
degree of adaptability in many design situations. FRP composites can be formed to suit
the demands of the designer and are thus useful in a wide range of applications.
Composites are also valued for their corrosion resistance, wear resistance, environmental
stability, and insulating ability (Daniel and Ishai 2006). The specific strength (ratio of
strength to density) and specific stiffness (ratio of stiffiiess to density) values of several
composite materials are compared to traditional construction materials in Figure 2.2.
Composite materials have a significant advantage over traditional materials in terms of
these properties. This is why composites are favored over traditional homogenous
materials in weight sensitive applications (Daniel and Ishai, 2006, Riley, Sturges and

Morris 1999).

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Materials

The general concept of fiber reinforced composites has been used since ancient
times. For example, the use of straw reinforced clay bricks in ancient Egypt is recorded in
the Bible (Exodus 5:7). The growth of the aeronautical and space industries in the 19503
and 19608 spurred the development of modern fiber reinforced composites as engineers
realized the tremendous potential of this class of materials that was not only stiff and
strong but also lightweight. The coupling of weight reduction and ability to cast exterior
pieces in one form, thus reducing bolted connections and drag, led to significant
improvements in aircraft performance (Gibson 1994). Composite applications became
more widespread in the late 1970s. Today, composites are used commonly in aircraft,
marine, automotive, sporting goods, armor and biomedical applications (Daniel and Ishai

2006). FRP composites have also more recently gained significance in the field of civil

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infrastructure. Composites are used to reinforce structural members against earthquakes,
to reinforce highway road surfaces, to produce structural flooring systems, and to produce
structtn'al shapes for buildings and bridges (Daniel and Ishai 2006, Ehsani 1999, Bank

LC. 2006, Strongwe112008).

2.2.2 Overview of Composite Theory

The properties of fiber reinforced composite materials can be determined using a
mechanics of materials approach. The equations presented below describe the necessary
formulas to determine the needed composite material properties. Equations are first
presented for continuous fiber composites and then for randomly orientated short fiber
composites. A discussion on the use of laminated beam theory and laminated plate theory
is included in this section. Composite properties presented here are necessary for the
evaluation of composite materials in this thesis and thus are presented below. An
introduction to continuous fiber and short fiber composites is presented next.

A single layer of a composite is called a lamina. A composite may have one or
more lamina. A composite composed of several layers is called a laminate. A
mprssentative unidirectional lamina is shown in Figure 2.3. Fiber reinforcement and

matrix materials are labeled in the figure.

 

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Figure 2.3 Unidirectional Lamina and Principal Coordinate Axes

 

Fibrous reinforcement can be continuous or discontinuous. Continuous fibers are
long and continuous over the length of the composite shape. Laminated composite theory
is based on the computation of continuous fiber composites, as they are the easiest to
compute. Continuous fibers may be arranged parallel to one another, oriented at right

angles, or arranged in several directions. Discontinuous fiber reinforcement is composed

of short fibers that may still be long compared to their diameter. Short fibers may be

oriented parallel to one another or may have a random orientation. Short fiber

reinforcement generally does not provide the same level of strength as continuous fiber

reinforcement, but short fiber composite properties are nearly isotropic and are easier to

construct due to the random orientation of the fibers. Fiber reinforcement is continuous

for the lamina shown in Figure 2.3. The next sections describe mechanics of materials

equations for continuous fiber and short fiber composites.

l3

 

 

 

2.2.2.1 Properties of Continuous Fiber Composites: Lamina Properties

Composite properties depend on both the matrix and fiber material properties.
Properties are computed for each lamina in a composite and for the laminate as a whole.
Important continuous fiber composite properties and their corresponding mechanics of

materials equations are described below.

Fiber volume fraction, Vf, is an important characterizing measure of a composite.
The fiber volume fi'action gives the ratio of the volume or fibers to the volume of the
composite. A larger Vf value usually results in higher strength and stiffness for the
composite. Vm is the matrix volume fi'action and is computed as follows assuming no
voids:

V," =1— V, (1)

The axial modulus, denoted E1, is the modulus of elasticity in the longitudinal or
1 direction (see Figure 2.3). It is computed by a rule of mixtures equation.

E1=Vf*E1f+Vm*Em (2)

The transverse modulus, E2, is the modulus of elasticity in the transverse or 2

direction (see Figure 2.3). Its computation is shown in equation 3.

V ---1
E2 = _f_ + V_m (3)
Ezf Em

The shear modulus, Glz, relates the shear stress and the shear strain in the 1-2

plane (see Figure 2.3). Its computation is shown in equation 4.

l4

 

 

 

 

—1
V
612 = [_f_+V_m] (4)

The Poisson’s ratio, v12, is the ratio associated with loading in the 1-direction and

strain in the 2-direction. The transverse Poisson’s ratio, v21, is the ratio associated with

loading the 2-direction and strain in the l-direction. Computations are shown in equations

5and6.
012=Vf*vf+Vm*vm (5)
Vf V _1
Of Um

The stiffness matrix, Q, relates the in-plane stress components with the in-plane

strain components along the principal material axes for a thin, unidirectional lamina. Q is

computedasfollows:
-1
L fl 0
El E1
-012 1
= _ _ o 7
Q E1 E2 ( )
o 0 L
G12

Lamina stiffiiess matrices are computed according to the local coordinate system
(axes numbered 1, 2, and 3) as shown in Figure 2.3. When one desires to compute the
properties of a laminate composed of lamina that do not all share the same local

coordinate system, the Q stiffness matrix as computed in equation 7 must be transformed

15

to a global coordinate system (axes labeled X, Y, and Z), Qba, (see Figure 2.4). This

doneinequations 8, 9, and 10.

 

 

 

 

 

1 .

1 o o

R: o 1 o (8)
_o o 1
-c2 32 2sc

T: 32 c2 —2.sc c=cos(0), s=sin(0) (9)
"SC SC 62—82

Qbar=T‘1*Q*R*T*R’1 (10)

16

 

 

 

 

 

 

2.2.2.2 Properties of Continuous Fiber Composites: Laminate Properties
The general expression relating in-plane forces and moments in a laminate to

reference plane strains and curvatures according to classical lamination theory is shown

[3H2 SHE] 0‘)

Where N is a vector of normal forces per unit length, M is a vector of moments

below.

per unit length, a is a vector of strains, and K is a vector of curvatures (see Figure 2.5).

 

Figure 2.5 Force and Moment Resultants

The stifliiess matrix is made up of laminate stiffness matrices A, B and D, which
are functions of the geometry, material properties, and stacking sequence of the
individual plies. The A stiffness matrix components are extensional stifi'nesses, or in-
plane moduli. They relate in-plane loads to in-plane strains. The B stiffiiess matrix
components are the coupling stiffiiesses. They relate in-plane loads to curvatures, and

17

 

 

 

 

moments to in—plane strains. The D stiffness matrix components are the bending or
flexmal laminate stifinesses and relate moments to curvatures (Daniel and Ishai 2006).
Figure 2.6 shows the cross section of a typical laminate and the laminate thickness

coordinates that are used to compute the A, B and D stiffness matrices.

 

Figure 2.6 Laminate Thickness Coordinates

The computation of laminate stiffness matrices A, B and D is accomplished using
equations 12, 13, and 14. The laminate thickness coordinate terms h(k+l) and h(k) are
defined in Figure 2.6.

A = inar(h(k + 1) — h(k)) (12)
k=l

B=§ZQI>ar<<h<k+m2 —(h(k»2) (13)
k=l

=§ZQbar((h(k+l))3 —(h(k))3) (14)
k=l

 

 

 

The floorpanel considered in this thesis was assumed to consist of a cellular truss—
like structure composed of two parallel outside plates and a central folded plate acting as
a web. For ease of calculation, the folded central plate was modeled as a series of straight
inclined plate sections much like an accordion configuration. It was assumed that during
bending plane sections remain plane and that the fiber layer orientations were all at 0
degrees with respect to the longitudinal axis of the panel. Thus, each plate is dominated
by axial behavior and transverse bending. These assumptions allowed the system to be

simplified to a two dimensional analytical model as that shown in Figure 2.7.

I Z

 

‘
r

x A

figure 2.7. Simply Supported 2D Beam with Central Folded Layer

Each member of the frame shown in Figure 2.7 is composed of a six-layer
laminate. It is thus desirable to obtain the effective laminate stiffness for each laminate
fi'ame member so that the frame can be analyzed according using one-dimensional frame
elements. Laminated plate theory equations were used to determine the laminate stiffness
and effective stiffnesses of the equivalent frame members. Two-dimensional laminate
models can be described by a simplification of laminated plate theory termed laminated
beam theory. Modeling assumptions and a discussion of laminated plate theory versus
laminated beam theory are discussed later in this section. The stiffness matrix for a
standard six-degree of fi'eedom two-node linear elastic frame element is presented in

equation 15. Stifi‘ness depends on the length, L, of the frame member, the cross sectional

l9

 

area, A, of the member, the moment of inertia, I, of the cross section of the member, and

the modulus of elasticity, E of the frame member.

fl 0 0 __A£ 0 0
L L
1251 6E1 1251 6E1
° ‘3— T ‘—3 —2
L L L L
651 451 6E1 251
o —2 L o ——2 L
K = AE L AE L (15)
—— o o — 0 0
L L
1251 6E1 1251 651
o —— —— o —— ~—
3 L2 3 2
6E1 251 6E1 451
o —— — o —— —
_ L2 L L2 L _

 

 

The modulus of elasticity of homogenous material like steel is the same in all
directions. The modulus of elasticity of a composite is different depending on the
orientation of fibers in the member. Thus, two effective moduli were defined for a
composite material for use in the stiffness matrix shown in equation 15.

The stifl‘hess matrix of equation 15 is composed of two kinds of terms, the axial
aimless terms and the bending stiffiiess terms. Consider a one-dimensional element
subjected to axial forces only (see Figure 2.8). The element will stretch in the direction of

the force some distance AL.

 

P <—— +> P B—A
L dLL—

 

 

 

 

Figure 2.8 One Dimensional Element Subject to Axial Forces

20

The stiifiiess of the member can be derived using Hooke’s law and is stated in

equation (16).

K=— (16)

 

This term is the axial stiffness term and the modulus value, E, to be used in this
term should therefore be a measure of the axial stiffness of the composite. Effective axial
in plane stiffiiess, Ex, for a composite is computed as follows:

1

= ht * As(l,1) (17)

Ex

ht = total laminate thickness, As = [A]'1

This equation is equally valid for symmetric and asymmetric laminates (Daniel
and Ishai 2006).

Consider next a two-dimensional element subject to bending for which the

degrees of fieedom corresponding to vertical and bending deformations are shown

‘ P in

L

(Figure 2.9).

 

 

 

 

 

 

 

Figure 2.9 Two Dimensional Element

The stiffness terms of this beam element can be determined using conjugate beam

method and the resulting beam element stiffiress matrix is shown in equation 18.

21

 

 

 

—E£ £12 _% 9’2
L3 L2 3 2
9!! 4_E£ -9fl El
2 L 2 L
K: _@ “651 rm -251 “8)
L3 L2 L3 L2
.6131 E _E’_ 2
L2 L L2 L

 

These terms are the flexural stiffness terms and the modulus value for use in these
terms is the effective flexural stiffness of the composite laminate. The effective flexural
stiffness, Exf, for laminates is:

= __3 12 (19)
ht *Ds(1,l)

ht = total laminate thickness, Ds = [D]—1

This equation is equally valid for symmetric and asymmetric laminates (Daniel
and Ishai 2006).

2.2.2.3 Strain Computations in a Laminate Frame

A We similar to the simple fiame shown in Figure 2.7 is considered in this
thesis. Each member of the frame is composed of a laminate. The modulus values for
«ch fi'ame member/laminate are obtained using equations 17 and 19. The general
stiffness matrix for the flame is then obtained using equation 15 where the axial modulus
Values are as found using equation 17 and the flexural modulus values are as found using
equation 19. It is next desirable to compute the strain in each member assuming that the

frame is loaded. This computation begins with the calculation of nodal displacements in

22

 

 

 

the frame. The global stiffness matrix for the frame is assembled from the local stiffness

matrices.

 

La..-

Nodal displacements, vg, are computed according to equation 20.

1
ivgl= [Kglobal]— {F} (20)
Where K3101“ is the global stiffness matrix

Strain in a composite plate is computed using the relationships in equations (1 l)

and (21).

a 53:0 [or
.y = 63,0 + z ky (21)
m m0 kxy

z = through-the-thickness coordinate of a point in the cross section

so = midplane strains

k = midplane curvatures

Strain computation is completed for each member using equations 22 and 23.

Local element end forces are computed with equation 22 by multiplying the local
Stiffiiess matrix by the transformed global nodal displacements. Equation 22 is a beam
flieory equation and thus generates axial, shear, and moment values at the end of a beam

element as shown in Figure 2.10.

23

 

lmJ

 

N1[f/ // // // JN2

 

v1|// // // // J v2

MI W M2

Figure 2.10 Local Element End Forces

Equation 23 is a laminated plate theory equation and thus requires inputs for
forces in the X and Y directions as shown in Figure 2.5. Due to the two dimensional
nature of the frame considered in Figure 2.7, only the forces in the X direction are
considered. These forces are computed with equation 22 and the axial and maximum
moment components of the local element end forces are entered as shown in equation 23.

Element forces in the Y direction are assumed to be zero.

N1
V1
fL = :2 = [kiLitingi (22)
V2
M2
Nx N1
Ny N2
[N] Nz 0
= = (23)
M M Max(Ml,M2)
My 0
1112 O

24

 

 

 

Equation 11 is rearranged and used with the result of equation 23 to solve for the

mid-plane strains and curvatures (see equation 24).

—l
A B N
6" = * (24)
k B D M
The maximum strain, h(k) is the distance to the outside ply from the center of the

composite. This is computed using equation 25.

{e}=[eo]+(h(k»*[k] (25)

2.2.2.4 Properties of Randomly Oriented Short Fiber Composites

Properties or randomly oriented short fiber composites are based on the properties
of tmidirectional continuous fiber composites of the same fiber and matrix material types.
Unidirectional continuous fiber lamina properties must first be computed as described in
Section 2.2.2.1, then equivalent properties are found for the short fiber composite. The
elastic constants for a short fiber composite are based on the invariant properties of an

equivalent unidirectional continuous fiber composite (Jones 1999). The invariant terms

are shown below.
U1 = (3er + 3Q22 + 2Q12 + 4Q66)/8 (26)
U5 = (er +sz "2912 +4Q66)/8 (27)

Equations for the elastic constants of the randomly oriented short fiber composite

are shown below (Halpin and Pagano 1969).

5 = 4U5(Ul — U5)/Ul (28)
v = (Ul — 2U5)/U1 (29)
G = US ~ (30)

25

 

The Q stiffness matrix for a randomly oriented short fiber material is re-computed
with the numbers found above. Equivalent stiffness properties are computed as described

in section 2.2.2.1.

2.2.3 Classical Lamination Theory for use with Beam Elements

The composite floor panel considered in this thesis was reduced to a two-
dimensional frame as discussed in Section 3.2.1 and shown in Figure 3.8. This simplifies
computations and allows the structure to be evaluated as a flame. The stiffiiess of the
flame is computed according to the stiffness method as discussed in Section 2.2.2. The
stiffiress method is based on standard six-degree of freedom two-node linear elastic frame

elements as shown in Figure 2.11.

 

2 ~\ 5

 

 

 

 

 

Figure 2.11. Frame Element

Composite computations can be similarly simplified to a laminated beam, which

is subject to pure bending as shown in Figure 2.12.

26

 

 

Z
Z

    

L

Figure 2.12. Laminated Beam in Pure Bending

Laminated beam theory dictates that plane sections initially normal to the
longitudinal axis remain plane and normal, that the beam has both geometric and material
property symmetry about the neutral surface, that there is no shear coupling or ply
orientations are either 0° or 90°, that the plies are perfectly bonded and no slip occurs,

and finally that the only stress components are ax and In (Gibson 1994). The

geometric and material properties of the floor panel developed in this thesis were not
constrained to be symmetric about the neutral axis. Also, the floor cross section elements
are intended to behave like folded plates, thus it was more appropriate to utilize classical
lamination theory for the analysis of composites.

Classical lamination theory is an expansion of laminated beam theory and is based
on a laminated plate as shown in Figure 2.5. Classical lamination theory considers
coupling effects of material behavior in the X and Y directions. Classical lamination

theory is used to generate the A, B and D matrices and thus the effective axial in-plane
stiffiiess, Ex, and the effective flexural stiffness, Exf, values, for each floor panel cross
section member as outlined in Section 2.2.2.2. These values are then used to generate the

frame element stifl‘ness matrix for the floor panel cross section. However, the floor panel

27

 

 

L

cross-section stiffness matrix is computed for a two-dimensional frame that is based on
the initial assumption that no coupling of material properties in the X and Y direction
occurs. Thus, the use of classical lamination theory in conjunction with the analysis of a
two-dimensional fi'ame introduces an error in computations due to this mismatch. The use
of laminated beam theory in conjunction with the two-dimensional fiame analysis would
eliminate this mismatch, however, classical lamination theory was deemed more

appropriate for this analysis as stated above. To quantify the mismatch error, the
computation of the effective flexural stiffiress, Exf, by way of the classical lamination

theory and the laminated beam theory are compared.

Effective flexural stiffness is computed as shown in equation 19, which is restated

here.
12
W = 3—-— (19)
ht *Ds(1,l)
where Ds = [D]"1 and ht is the total height of the composite cross section.
The coupling stiffiress matrix, D, is computed as shown in equation 14, which is
restated here.
1 h 3 3
D =329bar((h(k+1» —(h(k») (14)
k=l
The laminated beam equation for effective flexural stiffness is shown in equation
30 (Gibson 1994).
Egg = 2((h(k +1)) - (h(k)) ) h—3El (30)
k=l
28

. -p
o:"\ .
..u nu

I“

r.

n‘.-
a“.

N

 

 

 

Qbar is the transformed stiffness matrix as computed in section 2.2.2.1 above. If
the fiber orientation of a given lamina is 0°, or a multiple of 90°, then the transformation

matrix and therefore the Qbm. matrix are not fully populated. For example, if

1.322 0.107 0
Q = 11:106 0.107 0.353 0 (31)
0 0 0.323

and the fiber orientation of the given layer is 0°, then

1.322 0.107 0
Qba,=lx106 0.107 0.353 0 (32)
o o 0.323

Likewise, if the fiber orientation of the given layer is 90°, then

0.353 0.107 0
Q,,,,,=rxro6 0.107 1.322 0 (33)
o o 0.323

Neither matrix is fully populated, i.e. the 1-6 and 2-6 terms are zero, therefore

there is no shear coupling.

If the fiber orientation of a given lamina is not 0° or 90°, then the transformation

matrix and therefore the Qt,ar matrix becomes fully populated due to shear coupling

efieas. For example if the fiber orientation of a given lamina is 45° and Q is the same as

Shown above, then

6.338 3.105 4.847
Q,,,,,=1x105 3.105 6.338 4.847 (34)
2.423 2.423 7.311

This matrix is fully populated due to the interaction of the material properties in

the X and Y directions. The term

29

.‘ 2".
It

 

 

 

 

 

----htfiZ---

 

 

Figure 2.13. Four-Layer Laminate

 

(35)

(36)

iljh.

 

Rug-s.

7‘s“.

 

The term shown in equation 35 is computed as follows for this four-layer laminate:

[1
2w: +1113 - (h(k)?) =
k:

ate)—t—%+afl+[t—%+~T(an“ziltt—awtszl

3
— h (37)

3
Thus, D =¥-2—Qbar (38) for a laminate of a single material, and

12 12 7.3 1 1
h3Ds(1,1) I13 12 Ds(1,1) Ds(1,l)

h
For a laminate of multiple materials, the Z:((h(k+l))3 —(h(k))3) term
k=1

essentially weights the Qbars of each layer according to their distance from the neutral

axis, giving more weight to Qba, values that are farther from the neutral axis, but Exf is

still essentially Exf =

 

1
Ds(1,l) '

IfQ=Qbab then

31

 

— — 0
El E1
1
D -D 1: s = —”12 — 0
s l 1 51 52 (40)
0 0 L
012
and
Ds(11)-i
’ E1 (41)
thus,Exf= E1 (42)

Therefore, if the laminate is composed of multiple materials and all laminate
material angles are equal to zero, the Exf is equal to a weighted average of the E1 values.
Ifthe laminate is composed of lamina layers that are not all oriented at zero degrees, then
Q does not equal Qbar and the D matrix terms will also be determined by the interaction
of the composite properties in the X and Y directions and the Exf term will also be

influenced by this interaction. Composite beam theory assumes that all fiber orientation

angles are either zero of ninety degrees to avoid the complication of considering the

interaction of the E1 and E2 terms. Therefore if the assumption is made that all fiber

orientation angles are zero, then the value computed for Exf will be the same as that for

laminated beam theory as demonstrated above. Thus the use of classical laminated theory

32

 

is valid for this application due to the assumption that all fiber orientation angles are zero

degrees and will not introduce any error into the calculations.

2.2.4 Conclusions

An overview of fiber reinforced composite theory was presented in this section.
Mechanics of material equations and theory necessary for the computation of composite
properties for both continuous fiber and short fiber composites in this thesis were
presented. The section was completed with a discussion of laminated plate and laminated

beam theory use in this thesis.

2.3 Biocomposites
2.3.1 Overview

Recently, due to increased environmental awareness, users of fiber-reinforced
polymer composites are realizing the need for more environmentally fiiendly alternatives
to traditional synthetic composites. Researchers have responded with the development of
biocomposites and natural fiber composites. Natural fiber composites are composites that
replace traditional synthetic reinforcement fibers such as glass and carbon with natural
fibers such as hemp and kenaf. Biocomposites are a more general classification as they
may utilize natural fibers and/or replace traditional synthetic petroleum based resins, such
as polyester and epoxy, with natural plant based resins such as soybean oil and corn
ethanol. The term biocomposites will be used throughout this section as composites
utilizing natural fibers in synthetic or natural resins. Biocomposites offer many

advantages over synthetic composites, but present challenges as well. Uses and demand

33

 

for biocomposites continue to increase. The benefits and challenges of biocomposites as

well as current and future uses (state of the art) will be discussed in the following sections.

2.3.2 Benefits of Biocomposites

Natural fiber reinforced polymer composites typically result in lower mechanical
properties due to the lower performance of natural fibers compare to synthetic fibers.
However, because of their low density, the specific properties of natural fibers can
compete with synthetic E glass. Table 2.1 compares key mechanical properties of several
natural fiber and synthetic fibers. Mechanical properties of biocomposites can also be
increased by strategic arrangement of materials to maximize material usage (Burguefio et
al. 2005), treatment of fibers to enhance bonding ability (Liu et al. 2005), and careful
balance of natural fiber to synthetic materials (Mohanty, Misra, and Drzal 2005). These
methods enhance the performance of biocomposites and enable them to compete with

synthetic materials in real world applications.

Material

 

Table 2.1 Properties of Natural and Synthetic Fibers

34

In spite of the limitations and challenges noted above, the use of biocomposites is
of interest because they are environmentally fiiendly, readily available, and offer energy
savings over synthetic materials. Interest in enviromnentally fiiendly materials has
swelled in recent years due to overburdening of landfills, the depletion of natural
resources and the ever-increasing price of crude oil. Governmental legislation and
consumer interest both drive the effort to discover new materials and new ways of using
materials (Mohanty, Misra, and Drzal 2005). In addition, plant based fibers are readily
available in most parts of the world (Mohanty, Misra, and Drzal 2005). The use of rapidly
renewable materials (those materials that are harvested within 12 months of planting)
offer the additional benefit of low energy consumption during their lifetime and ability to
provide raw materials at a rate that is sustainable even with high usage.

Other advantages of natural fibers and biocomposites over traditional synthetic
fibers include, low cost, high toughness, acceptable specific strength, reduced tool wear,
reduced dermal and respiratory irritation, good thermal properties, ease of separation, and

biodegradability (Mohanty, Misra and Hinrichsen 2000, Nickel and Reidel 2003).

2.3.3 Challenges of Biocomposites

The previous section discussed the problem of lower mechanical properties and
ways that this is overcome. Other disadvantages of biocomposites include the hydrophilic
nature of natural fibers which lowers compatibility with hydrophobic polymeric matrices,
and relatively low processing temperatures required to not degrade properties during
manufacture (Mohanty Misra and Hinrichsen 2000). Natural fiber and biocomposites are

also more susceptible to biologic degradation, UV degradation, lower bond strength and

35

higher than acceptable moisture absorption (Mohanty Misra and Hinrichsen 2000,
Mohanty, Misra, and Drzal 2005).

Natural fibers are susceptible to degradation because organisms interact with
carbohydrates in the natural fibers and break them down (Mohanty, Misra, and
Hinrichsen 2000). Photochemical (UV) degradation takes place when some natural fibers
are exposed to outside light (Mohanty, Misra and Hinrichsen 2000). Natural composites
must be surface treated to avoid these forms of degradation.

Bonding in biocomposites can be improved by treating the natural fibers with an
alkali solution. This process increases the interaction between fibers and matrix, which,
in turn, improves mechanical properties (Liu 2004). Moisture absorption of the finished
product is also a downside to biocomposites. Researchers have found success by treating

the finished composite with a commercial water sealer in the same way one would treat

wood (Dweib et al 2006).

2.3.4 Bio Composite Applications - State of the Art
Bio composite applications have expanded in recent years. The use of
biocomposites in the automotive industry, in the civil and construction industries and in

various commodity applications is summarized in the following sections.

2.3.4.1 Automotive Applications
The automotive industry was the first industry to use biocomposites in place of
synthetic composites on a large scale. Automobile manufacturers rely heavily on

composites for body panels, seating and interior trim among other uses. Composites are

36

vital to modern automobiles because they are strong, durable, and lightweight. The
automotive industry is also increasingly under pressure from government and society to
extend fuel economy and improve the environmental performance of their products. Thus,
the use of biocomposites in place of synthetic composites was a desirable application as it
would decrease the use of petroleum based products, decrease the amount of energy
needed to create vehicle raw materials, and decrease finished product total weight, thus
increasing fuel economy.

European automakers in the early 19905 began using biocomposites in automotive
interiors. A flax-sisal-epoxy composite was first used in the Mercedes E class door panels
in the early 19903 (Brosius 2006).

In North America, the demand for biocomposites for automotive use has
encouraged the growth of several bio composite manufacturers, for example Kafus
Biocomposites/Flexform Technologies of Elkhart Indiana. Kafus
Biocomposites/Flexform Technologies produces several blends of natural fiber composite
mat, which are used to manufacture finished automotive interior trim components in cars
and trucks. Currently this product is used for full door panels, truck lines, door trims,
headliners and related components. The natural fiber composite mats are a blend of
natural fibers such as kenaf, hemp and sisal, with polymers to create a high strength, low
weight moldable material. They are less likely to shatter upon impact and reduce molding
time for components while lowering the emissions of volatile organic compounds
(V OCs). Kafus Biocomposites/Flexforrn Technologies products are used in General
Motors, Ford, and other Tier 1 vehicles including Chrysler Sebring, Ford Expedition, and

the Mercedes M class SUV (Brosius 2006, Business Wire 1999, Fowler et al. 2006).

37

Ford has been one of the most active researchers in plant based automotive
applications. The company has been looking for ways to “integrate soy into everything
fi'om seat foam to fenders” (Sloan 2008). The founder of Ford Motor Company, Henry
Ford, encouraged the use of hemp and soy in manufacturing concepts as early as the
19308 (Holberry and Houston 2006). Visteon Automotive systems, an enterprise of Ford
Motor Company, are a dedicated research facility that is actively investigating ways to
develop better natural fiber composites for automotive use. The 2003 Model U concept
car used a glass fiber reinforced soy based resin in the tailgate and natural fiber
composites from Kafus Biocomposites/Flexform Technologies have been incorporated in
production vehicles since 2000 (Fowler et al. 2006, Sloan 2008, Brosius 2006, Business
Wire 1999).

A related application of biocomposites is the use of bio composite panels in John
Deere tractors. John Deere approached Ashland Performance Materials out of Columbus
Ohio with a novel marketing concept: develop a soybean oil and corn ethanol resin for
use in body panels on tractors and combines that are used to harvest soybeans and corn.
The concept was to identify and promote new agricultural markets while at the same time
improving the environmental performance of their product. This seems particularly
relevant when the intended consumer (farmer) is so heavily invested in the rapidly
renewable crop that is used to promote environmental performance. Ashland deve10ped a
resin product they call ENVIREZ 1807 that is 13% soybean oil, and 12% com ethanol.
John Deere used this resin to manufacture sheet molding compound (SMC) composite

panels that they used in their 2001-2003 model year 9750 John Deere Havestor Combines

38

and other tractors. Performance of the material was good and it had the dual benefit of
promoting non-food uses for farming products (Sloan 2008).

Biocomposites used in automotive applications are currently limited to a mixture
of biological and synthetic materials or a non-biodegradable bio composite. Researchers
are working to develop a completely biodegradable bio composite that is stable during its
lifetime and then can be triggered to biodegrade. This would be a huge benefit to the
automotive industry as 10-11 million automobiles are discarded each year in the U. S.
After these vehicles are processed, about 25% by weight of the vehicle remains as waste
(Mohanty et al. 2002). A completely biodegradable bio composite would solve this

problem.

2.3.4.2 Civil/Construction Applications

Fiber reinforced polymers (FRP)s have recently gained acceptance in several civil
infrastructure applications. FRP wraps are used to strengthen and better confine concrete
columns against earthquake loads. FRPs compose entire bridge decks where they have
the advantage of lower weight and increased durability over traditional materials. FRPs
are used in coastal and marine structures such as oil drilling wells where composites
immune to corrosion and environmental degradation are a highly desirable. The FRPs
used in these applications are almost exclusively synthetic composites and they have
proven to be effective in each of the above performance categories. The replacement of
synthetic composites with biocomposites for civil infiastructure applications is hampered
by several factors. First, natural materials absorb water and are thus problematic in

applications where they are exposed to the environment. Second, biocomposites can

39

compete with glass fiber reinforced composites in terms of strength, but cannot yet
compete with higher strength composites such as carbon and aramid that are used in more
demanding applications. Further research and development of biocomposites will allow
additional applications in this field.

Current application of biological material and biocomposites in civil
infrastructure include various composite designs for use as structural paneling. Three
examples are highlighted below.

A research project focused on incorporating bamboo flakes and fibers from oil
palm tree fronds into a cement composite for use in housing and building industries.
Cement replacement materials and chemical admixtures must be added to the cement to
counteract the adverse effects on the hydration characteristic of the cement. The resulting
products were a cement particleboard for use in housing applications (Sudin and Swamy
2006).

The use of a green hemp and polyester composite for load bearing applications
was made plausible by arranging the materials in a hierarchical cellular fashion. This
arrangement maximizes the capacity of the composite plate and makes it possible for the
composite to compete with commercial E glass/vinylester composite panels (Burguefio R.
et al 2005).

Research has also shown that large-scale bio based composite sandwich panels
are suitable for residential housing applications. A bio based composite sandwich panel
was constructed of structural foam wrapped with cellulose fiber (recycled cardboard) and
infiltrated with a soy oil based resin. The resulting composite sandwich showed good

mechanical performance and also eliminated the need for traditional rafter and shingle

40

construction as the sandwich roofing is cast and installed in one piece (Dweib MA. et al

2006).

2.3.4.3 Commodities Applications

Biocomposites are increasingly being used in applications were synthetic
composites or other materials were formerly the material of choice. Several innovative
examples are presented below.

Germany’s aerospace research center, DLR Institute of Structural Mechanics,
developed a hardhat that as well as meeting all strength requirements for German safety
equipment, was also composed of 85% renewable resources. The hardhat was composed
of a bio composite and also achieved a weight reduction of 5 to 10% over synthetic hard
hats. The DLR also developed and installed bio composite panels for air columns and
seats in five Hamburg Hochbahn trains. The paneling achieved a 30% weight savings and
also achieved the highest levels of flame protections when treated with a flame retardant
(Nickel and Reidel 2003).

Commercially available natural fiber and recycled material composite fencing has
found success in recent years. Praire F enceTM is a composite fencing system made
primarily of recycled HDPE and wheat straw. Besides the environmental benefit of using
recycled and waste biological materials, this fencing system offers long term durability
and lower maintenance than traditional wood, wood composite and vinyl fencing.

Decking and furniture applications are also increasingly common. JER Envirotech
manufactures a variety of thermoplastic natural fiber composite pellets and sheeting for

use in a wide variety of applications. The bio composite pellets are composed of organic

41

cellulose fibers in a thermoplastic matrix such as polystyrene. JER Envirotech products
are used in many applications from decking and flooring, to children’s toys (JER
Envirotech 2008). In the USA, Environ Biocomposites LLC uses wheat straw in its
Biofiber composites and sunflower hills in its Dakota Burl composites. These composites
are intended for indoor flooring and decorative uses.

Phenix Biocomposites manufactures a composite board, EnvironTM made of
wastepaper and soy flour for use in furniture, cabinetry and architectural non-structural

applications. Environ is also fully degradable (Fowler PA. 2006).

2.3.5 Conclusions

The use of biocomposites in automotive, civil infiastructure and commodities
applications will continue to increase due to environmental demands and government
pressures. The need for biocomposites that are increasingly environmentally friendly
while also providing adequate strength and performance for various applications is also

expected to continue. It is therefore vital that research in this important field continues.

2.4 Optimization Background
2.4.1 Overview

Optimization is the process of finding the best solution to a mathematical or
design problem that simultaneously meets all imposed constraints. Conventional
engineering design normally involves several iterations before a final design is reached.
Conventional engineering design relies on the engineer’s intuition, experience and skill to

find a satisfactory final design that meets all requirements and is efficient and cost

42

effective. The human element to this design method can sometimes lead to erroneous
results. In contrast, optimum design requires the engineer to explicitly identify a set of
design variables, the objective function to be optimized, and the constraint functions for
the system (Arora 2004). Optimum design methods can then be used to find the best
solution in a more efficient manner than the traditional iterative process.

The competitive atmosphere of modern engineering and business environments
necessitates the use of efficient optimization techniques as opposed to costly human-

driven trial and error. The basics of structural optimization are presented next.

2.4.2 Structural Optimization

Structural optimization usually involves sizing of members to meet minimum
strength and performance requirements while also minimizing the weight or size of the
members used. This can be accomplished through several optimization techniques, which
will be presented and discussed in the proceeding sections. The basic elements of an

optimization problem are described next in preparation for this discussion.

2.4.2.1 Variables
Most optimization problems have more than one variable. The standard vector

notation for problem variables where X, are the variables is shown below.
{x} = (x1,x2,...,x,,) (43)
Variables can be either continuous or discrete. Continuous variables can take on
any value within given bounds.

3<x1_<_10 (44)

43

These bounds are known as simple bounds and act as constraints in the
optimization problem. In standard mathematical form, all constraints are written in the
“less than” format. This form is shown below.

x1 $10 and — x1 5 3 (45)

Discrete variables can only take on discrete values from a given set of numbers.
For example, the web thickness of a beam can be restricted to only take on standard

available thickness values. This notation is shown below.

x1 =(l,l,§,l,£,3,l,l) (46)
8 4 8 2 8 4 8

The solution to a problem with discrete variables is more difficult to formulate
mathematically than a problem that only has continuous variables. An objective function
with discrete variables is not continuous, and thus cannot be differentiated. Therefore,
discrete valued variables are often treated as continuous variables to solve the
optimization problem. Then, a discrete value close to the optimum solution is selected
and rechecked for validity.

The set of values that an objective function can take that satisfy all constraints and

simple bounds is known as the feasible set.

2.4.2.2 Objectives

A general optimization problem has one or more objectives, such as the minimum
weight of a structure or maximum profit of a given process. The objective function is
known as the cost function and in standard form, it is always transcribed so that the goal
is to minimize the function. The standard notation for a single objective function is

shown below.

Objective: Minimize f (x) = f (x1,x2,...,x,,) (47)

When there is more than one objective function, the minimum value of one
objective function is not usually the minimum objective of the other. One method of
considering two objective functions is to weight the objective function and combine the
weighted sum into a single objective function. This requires the user to assign value-
based weights to the objective functions. A second method of considering multiple
objectives is Pareto optimization where objectives are treated independently and trade-
offs between the objectives are obtained to determine how to best improve each objective
without negatively affecting any other. A point in a design space is Pareto optimal if there
is no other point that reduces at least one objective function without increasing another

(Arora 2004).

2.4.2.3 Constraints

Constraints limit the feasible set of design variable values. Typical constraints in a
structural optimization problem include maximum allowed stress or maximum allowed
deflection. There are two basic types of constraints: equality and inequality constraints.
Equality constraints specify that variables or combinations of variables are equal to a
given value. Equality constraints are formulated so that the given function of variables is
equal to zero. An example of an equality constraint is shown below.

h, (x) - 3 = o (48)

45

Inequality constraints specify that a variable or combination of variables must be
greater than or less than a given value. Inequality constraints are formulated in a “less

than” format in standard notation.

$00 5 0 (49)

2.4.3 Conclusions

Optimization was introduced and the basic elements of an optimization problem
were defined in preparation for a more detailed discussion of specific optimization
techniques. A commercial software package (HEEDS, (Red Cedar Technology 2005))
was used utilized to perform the task of optimization in this thesis. This software package

and the main optimization methods employed by it are discussed in the next section.

2.5 Optimization Techniques and Optimization with HEEDS
2.5.1 Overview

Methods of optimization are presented including genetic algorithm, gradient
based methods, response surface methodology and simulated annealing. The commercial
software package HEEDS (Hierarchical Evolutionary Engineering Design System) is
capable of optimizing a wide variety of problems via a combination of optimization
techniques. The HEEDS proprietary search method is termed SHERPA (Systematic
Hybrid Exploration that is Robust, Progressive and Adaptive). HEEDS uses the elements
of multiple search methods including Genetic algorithm, response surface methodology
(design of experiments), simulated annealing, and gradient-based methods,

simultaneously to take advantage of the best attributes of each method. Internal tuning

46

parameters are automatically updated throughout the optimization process and the
relative contribution of each method is also adjusted based on information gained from

the modeling space during optimization (Red Cedar Technology 2008). HEEDS

procedure and terminology are introduced.

2.5.2 Optimization Techniques
2.5.2.1 Genetic Algorithms

A genetic algorithm (GA) is a mathematical technique based on the principles of
natural selection and genetic recombination (Holland 1975). The vocabulary of the
technique is also taken from natural selection theory, and the terms familiar to natural
selection will next be defrned in terms of the genetic algorithm.

A population is a set of design points at a given iteration value. Each member of
the population represents a possible solution of the optimization problem. These members
are called chromosomes. Each chromosome is a specific combination of variable values
or genes. A gene is a specific value for a particular design variable. Just as in biology, a
gene represents the value for a certain trait. Genes and chromosomes making up a

population are shown in Figure 2.14.

47

POPULATION

 

 

 

 

 

 

 

T T 71—
c f e
b b f
c a E] GENE
a d b
i a [it
CHROMOSOME

Figure 2.14. A Population, Genes, and Chromosomes

The goal of the GA process is to generate a new population from the current
population such that the average fitness of the new population is improved. New
populations are generated until a stopping criterion is met or a specified number of
iterations (populations) have been met (Arora 2004). The fitness of each member of a
population is rated according to a fitness function. The fitness function rates how well an
individual member meets the established objective function. A simple way to represent
the fitness function to a minimization problem is through a cost function:

F.- =8... -f.- (50)

High cost function values correspond to better designs. The fitness of each
member is used to weight good designs so that they are more likely to pass on traits to the
next generation. The probability that a member will be selected to recombine for the next
generation is illustrated through the use of a pie chart in Figure 2.15. Members with
higher fitness values have corresponding higher probabilities of selection and thus a

larger area of the pie chart.

48

43

Figure 2.15. Probability of Selection based on Fitness Values

New populations are created through the use of three basic genetic operators,
reproduction, crossover, and mutation. Reproduction is the process of selecting a set of
chromosomes from the current population and copying them into the new population.
Chromosomes may be selected more than once for the new generation or may not be
selected at all. Chromosomes with high fitness function values are more likely to be
selected, thus each successive population should improve upon its predecessor. Crossover
is the process of varying gene combinations within chromosomes to create new designs
thus increasing genetic diversity and further exploring the design space. Crossover is
carried out after reproduction has taken place. Two chromosomes are randomly selected
and their genes are combined to create two new chromosomes. Two common methods of
crossover are illustrated in Figures 2.16 and 2.17. In the one cut method, a “cut” position
is selected in a string of genes of each chromosome. The chromosomes are separated and
the chromosome halves are switched to create two new chromosomes. The two out

method employs a similar procedure with two out locations as shown in Figure 2.17.

49

 

 

C1 C2 C1' C2‘
"a? T T H
c f CUT L .9.
7,“ b LOCATION b b
c a CROSSOVER c a
a d > a d
_f. .2. _f_ .5:

 

 

 

 

 

 

 

 

Figure 2.16. Crossover One Cut Method

 

 

C1 C2 C1' C2'
"—21— T T _af
0 f CUT f c
*3 b LOCATIONS j j
3. .i‘. CROSSOVER i i
a d = .d- a
.1. .2. .2. _f_

 

 

 

 

 

 

 

 

Figure 2.17. Crossover Two Cut Method

Mutation is a second process used to introduce genetic diversity into a population.
In mutation, certain genes on a chromosome are randomly selected and their values are
changed to another randomly generated gene value. This process is shown in Figure 2.18.
The mutation operator is used to prevent the loss of valuable genetic information and to

keep the design from converging upon a local minimum value.

50

C

p—s

SELECTED
GENES

 

a)» . creme

 

 

 

 

a

C

b

MUTATION c
> a

d

C

Figure 2.18. Mutation Operator

Constrained optimization problems can be handled by imposing penalties on
designs that do not meet constraints. Penalties must be carefully chosen as a penalty
value that is too small may result in an infeasible final solution, while a penalty that is tOO
large will force designs away from the active constraint boundaries (Lagaros et al. 2002).
The penalty can be applied to the fitness function as shown below.

Fi=fmax+P*Vi011—fi (51)

The convergence of a genetic algorithm is affected by several factors including
fitness function scaling, population size, reproduction rate, crossover rate, mutation rate,
and stopping criteria. The fitness function rates members for relative fitness. Ifthe ratings
are scaled so that there is a large difference between fit and unfit designs, then
convergence will progress more rapidly. The population size is the number Of design
considered in any given generation. Large populations contain more possibility for
diversity and larger exploration of the design space in a given iteration, but also slow
convergence. The reproduction rate controls what percentage of the Old population is
replaced to create a new population. The crossover rate describes the probability that

crossover will occur. Likewise, the mutation rate describes the rate at which mutation

51

will occur. Crossover and mutation Operators create greater diversity within a population
thus decreasing the possibility that the Optimization will converge prematurely. However,
greater diversity also increasing processing time and slows convergence. Stopping
criteria include maximum number Of iterations and user defined performance measures.
Stopping criteria can be altered to define when convergence has been met.

Genetic algorithms belong to a class Of optimization methods that are based on
random number generation (Arora 2004). The algorithm evaluates fimction values at each
step in the search process without the need for gradient computation. GAs are therefore
well suited for discrete valued problems, problems where the gradient Of the function is
difficult to obtain or problems where the gradient Of the function cannot be calculated.
Genetic algorithms are also less likely to get “stuck” on local minimums because they
explore the design space in a broader fashion. GAs are applicable to wide range of
problems and are generally easier to program than problems involving gradient
computation. Two significant drawbacks to GAs include the relatively large amount Of
computation necessary to solve even a simple Optimization problem and there is also no

guarantee that the absolute minimum or maximum value has been obtained.

2.5.2.2 Gradient Based Methods

Gradient-based methods of optimization are based on the concepts Of slope and
concavity of a continuous function. A sample function is shown in Figure 2.19. The
minimums and maximums occur where the slope of the function, i.e. its first derivative is

equal to zero.

52

 

 

 

 

 

‘ Figure 2.19. Plot of Function f(x) = —2x3 + 5x2 + 3x — 2

The first derivative, set equal to zero.

f(x) = —6x2 +10x+ 3 = o (52)
The solutions of this function:

x1 = —0.26 (maximum in Figure 2.16)

x2 = 1.926 (minimum in Figure 2.16)

The second derivative is computed to test for concavity and determine if the point

is a maximum or minimum.
f"(x) = —le+10 (53)
f"(xl)=—-12(—0.26)+10=13.12 > 0 (54)
Equation 36 is concave up, therefore x1 is a minimum.

f"(xz) = —12(1.926)+10 = —13.11< o (55)

53

Equation 37 is concave down, therefore x2 is a maximum.

When there is more than one variable, as in the Objective function shown in
equation 56, the first derivative will be a vector called a gradient (see equation 58) and

the second derivative will be a matrix called a Hessian (see equation 59).

 

 

f(x*) = x2 + 2xy + 4 y2 objective function (56)
{x *} = {x y} design variables (57)
6f (15*) 2 2
' _ dx _ x+ y
f (x"') — afO‘") _ {2x + 8y} (58)
dy
"azf 62f _
.. _ dxz dxay _ 2 2
f (I*) — 62 f 02 f — [2 8] (59)
-dya" dyz _

 

 

Many Optimization techniques are based on the basic gradient method presented
above. Two of the most basic methods are the steepest descent method and Newton’s
Method. These two methods are firrther described to expand the concept of gradient
methods utilized by HEEDS.

The steepest descent method uses only first derivatives in its search for the
minimum point. A starting point is guessed, and the first derivatives or gradient is
computed. The direction of steepest descent will be the opposite Of this gradient value. A
step size along the steepest descent path is calculated that minimizes the function. This

process is repeated until the steepest descent is equal to or close to zero (Arora 2004).

54

Newton’s Method uses gradients and Hessians in its search for the minimum point.
Newton’s method uses a second order Taylor series expansion that includes the values Of
the gradient and Hessians at each approximated point. These values are used to determine
the descent direction. Optimization with Newton’s method proceeds at a quadratic rate

and thus converges faster than the steepest descent method.

2.5.2.3 Simulated Annealing

Simulated annealing (SA) is a stochastic approach that simulates the statistical
process of growing crystals using the annealing process to reach its absolute (global)
minimum internal energy configuration (Arora 2004). During annealing, the temperature
is lowered slowly so that crystals have time to form. If the temperature drops too quickly,
crystals may not have time to form and the process will become “trapped” in a local

minimum energy state for the internal energy. SA emulates this process. The basic steps

Of SA are outlined below.

1. A value is chosen for the initial temperature, Ti, (expected global

minimum for the Objective function) and a feasible value is chosen for
the variables to generate an initial design. A maximum number Of
iterations, L, and a coefficient r (where r < l) are also chosen.

2. A new design point, i.e. values for all design variables, is randomly
generated in the neighborhood of the current design. If this point does
not result in a feasible design, a new point is generated until a feasible

design is found.

55

The Objective function at the feasible design, f(xo) is compared tO the

Objective function at the current design, f(xl). If it is less (read better)

than the current design, this design replaces the current best design. If it
is greater than (read worse) than the current design, the probability

density function (see equation 60)
p(Af) = exp(f(xl);f(x0)] (60)

is compared tO a randomly generated number 2 in the range [0,1]. If 2 <

 

p(Af), then this design replaces the current best design, otherwise, one
returns to step 2.
If the maximum number Of iterations, L, has not been met, one returns
to step 2. If L has been met, proceed to step 5.
The temperature is lowered to a new temperature as follows

7i: = ’7}
and the process repeats until a preset stopping criteria such as a

maximum number Of total iterations is met.

2.5.2.4 Response Surface Methodology

Response Surface Methodology is a method, which uses a set of designed

experiments to obtain an Optimal result. A first-degree polynomial model of the

Optimization problem is implemented to determine the relationship between several

explanatory variables and one or more response variables. When, by experiments, the

significant explanatory variables have been determined (the variables that have the most

56

effect on the response variable), the second order polynomial model is approximated
through statistical methods such as central composite design. This second order
polynomial can then be used to find optimal solutions through gradient-based methods.
Response surface methodology basically estimates gradients of a function and uses

gradient methods and steepest descent to find the Optimum value (Box and Wilson 1951).

2.5.3 HEEDS Procedures and Terminology

The Optimization package HEEDS Offers the flexibility to solve a wide variety of
problems and can be used in conjunction with virtually any analytical engineering
software like ABAQUS (Simulia 2008) or MATLAB (The Mathworks Inc, 2008). The
basic HEEDS problem evaluation setup is depicted schematically in Figure 2.14. The
user must first establish the design objective, variables and constraints. The user then
establishes a baseline design by selecting default values for all design variables and
evaluating the design. During the Optimization process, values are selected for all design
variables according to the design method or methods currently being employed, the
design is evaluated using the same analytical software that was originally used to
evaluate the problem and the performance of the resulting design is judged. Designs are
evaluated by judging the value returned for the Obj ective firnction(s) and the extent to
which the constraints are met. If a design does not meet a constraint it is considered an
infeasible design. Designs that violate constraints are penalized, but are allowed to
remain in the population of designs. This allows the optimization process to consider both
feasible and infeasible designs in its search for the Optimum solution. Large penalties are

assigned to designs with large violations and small penalties to designs with small

57

violations. Once a design meets a constraint, designs are mainly compared by how well
they meet their objective functions. Each iterative design is compared to the benchmark
design. Each time a better design is found, this design is saved as the current best design.

Optimization ends when the user specified number of iterations has been reached.

 

Step 1: Establish Baseline Design

 

 

 

 

e

 

 

Step 2: Select Value for Variables

 

 

 

 

Step 3: Evaluate Design

 

 

 

 

 

Step 4: Judge Design, Establish Design Performance
4a: Evaluate Constraints
Assign penalties to violated constraints

4b: Evaluate Objective Function

 

 

 

 

 

Step 5: Compare to Baseline Design: Higher Performance?

 

 

 

 

 

 

 

 

 

 

 

 

 

_JL _JL_
Yes No
Replace Baseline Design

 

 

 

 

Figure 2.20. HEEDS Optimization Process

58

2.5.4 Conclusions

The fundamental concepts behind design Optimization were introduced and
discussed. Four main optimization techniques including genetic algorithms, gradient-
based methods, simulated annealing and response surface methodology were introduced
and discussed as the main optimization techniques employed by the optimization
software HEEDS. HEEDS was used to perform the optimization problem presented in
this thesis and thus the general approach in which HEEDS carried out the optimization

problem was also discussed

2.6 Environmental Aspects of Building Material Design
2.6.1 Overview

The objective of this thesis is to optimize a material for both mechanical
performance and environmental performance. For the second task, the enviromnental
performance of a material must be quantified. Environmental measures and ways to
quantify them are discussed. Life cycle assessment is discussed as a tool for
environmental quantification. The section is concluded with a discussion of a current
ratings system (LEED) used to define the degree of environmentally sound measures
taken in construction. LEED ratings are introduced as they are applied to the final design

developed in this thesis.

2.6.2 Natural Resources
The design of any building or infrastructure project will naturally include the

simple optimization concept that the project should be completed with the lowest

59

plausible amount of material. Any reduction in the amount of material used will naturally
lower costs and construction time. This simple optimization also benefits the environment
as less use of resources translates into a smaller project carbon footprint. What is not
always considered in design is the choice of the material itself. Time and experience have
narrowed the field of core civil engineering materials, such as steel and concrete, to a
relatively short list of options that are typically used. While science continues to
investigate ways to improve these materials and to find new and better materials, changes
occur slowly. Thus, a designer chooses a particular kind of structural steel for the design
of a building, and then optimizes the design to use as little of the steel as possible, but
does not typically reconsider the original choice of steel. Environmental awareness has
become more critical in recent years, and thus the environmental optimization of any
project should include more than just minimizing material use. The environmental impact
of the material must also be examined.

The two environmental objectives that must be considered are thus 1) to reduce
the amount of material used in a design, and 2) to choose a material with the lowest
possible environmental impact. The environmental impact of a material must be
quantified to do this, and this will be discussed further in the following sections. One
must realize that these two objectives will often be at odds with one another. An
environmentally friendly material is often not as strong as a less environmentally friendly
material, thus more of the weaker material is necessary to meet strength requirements.
Thus, there must be some balance between the level of environmental benefit and amount

of material used.

60

2.6.3 Energy Usage

The environmental impact of a building material must be quantified in order to
achieve an environmental design. One way to measure the environmental impact of a
material is through its energy use. A typical starting point is to measure the energy that it
takes to create the building product fiom its raw material. Another energy measure might
also include the energy required to maintain the material throughout its useful lifetime.
The most complete measure of energy usage of a material is its energy usage from
“cradle to grave” or if the material is recycled from “cradle to cradle.” This method
quantifies total energy expended by the material from its conception to its disposal. This

method is knows as life cycle assessment.

2.6.4 Life Cycle Assessment

Life cycle assessment (LCA) is the evaluation of a product’s sustainability. A
frequently quoted definition for sustainable development is “development that meets the
needs of present without compromising the needs of future generations to meet their own
needs” (U .N. Brundtland Commission 1987). LCA is an environmental management tool
that enables quantification of environmental burdens and their potential impacts over the
whole life cycle of a product, process or activity (Azapagic 1999). An LCA quantifies a
product’s sustainability by evaluating its performance according to a large number of
environmental indicators. Typical environmental indicators include climate change, fossil
fuel depletion, human toxicity to air and water, ecotoxicity, and eutrophication. Societal
impacts such as risk and remuneration may also be considered (BRE and Netcomposites

2004, Mohanty, Misra, and Drzal 2005). LCA includes four basic steps: goal definition

61

and scoping, inventory analysis, impact assessment and improvement assessment
(Azapagic 1999). Goal definition and scoping require definition of the system and system
purpose. In LCA it is stressed that the definition of the system should include not only the
physical location of the plant or manufacturing site, but also the surrounding environment
that is effected by the site. This definition helps users avoid short sited enviromnental
practices that may, for instance, limit total energy use at the plant site, but increase
environmental impacts further down the line. In the second step, material and energy
balances are performed and environmental burdens are classified. The third step further
defines the environmental burdens by classifying them into selected categories such as
fossil fuel depletion and water extraction. Value based weights are assigned to the
enviromnental categories to rank the level of importance. Experts usually assign these
weights, but there is unavoidable subjectivity in this state. In the final step, opportunities
for improvement are identified. LCA quantifies energy usage and impacts from material
extraction to material disposal, or fiom cradle to grave. It is meant to be a holistic
assessment of the total impact of a product or process. This quantification of
environmental impacts is ofien used to evaluate and improve an existing process or
product. LCA results could also be used dming the design process to minimize
environmental impacts of a product or process. Environmental aspects are more easily
incorporated at the concept stage of design than at some point later in life, thus LCA

performed at the design stage has a large potential for positive impact.

62

2.6.5 LEED Ratings and Industry Interest

The building industry has become increasingly aware of the environmental impact
of building construction and daily building energy use. The United States Green Building
Counsel has created the Leadership in Energy and Environmental Design (LEED) rating
system and oversees the certification of buildings as LEED certified. This is the only
commercial building rating system in the United States, but other counties have similar
ratings systems in place such as LEED Canada, which is overseen by the Canadian Green
Building Council, and the Building Research Establishment Environmental Assessment
Method (BREEAM) standard in the United Kingdom, which is overseen by a non-profit
group in the UK LEED is a ratings system that rewards points for environmentally
fiiendly measures that builders, owners, and developers seek to obtain. The program
seeks to accelerate the adoption of green building practices through a universally
accepted and understood ratings system. LEED certification can be obtained on a wide
variety of projects. There are currently separate LEED rating systems for New
Construction, Existing Buildings, Commercial Interiors, Core and Shell, Schools, Retail,
Healthcare, Homes, and Neighborhood Development. There are also additional ratings
systems being developed (U SGBC 2008). LEED certification is obtained by earning
points according to the LEED ratings system appropriate to the development. There are
four levels of LEED certification: Certified, Silver, Gold and Platinum. The necessary
points required for each certification level are shown in Table 2.2 (USGBC 2006). Points
are earned in five categories as well as an additional category for innovation and design.
The categories and possible point totals for LEED NC is shown in Table 2.3 (USGBC

2006).

63

LEED NC Point Levels

Rating Points
Platinum 52-69
Gold 39-51
Silver 33-38

Certified 26-32

Table 2.2 LEED for New Construction (NC) Point Levels

 

 

LEED NC

Category Possible Points

Sustainable Sites 14
Water Efficiency 5
Energy and Atmosphere 17
Materials and Resources 13
Indoor Environmental Quality 15
Innovation and Desigfirocess 5
Total 69

Table 2.3 LEED for New Construction (NC) Category Possible Points

According to the LEED manual “buildings annually consume more than 30% of
the total energy and more than 60% of the electricity used in the US. Each day five
billion gallons of potable water is used solely to flush toilets. A typical North American
commercial construction project generates up to 2.5 pounds of solid waste per square foot
of completed floor space” (U SGBC 2006). Green building practices reduce or eliminate
these negative environmental impacts. They also reduce daily operating costs, enhance
building marketability, and increase worker productivity.

The demand for environmentally sound design and LEED certification in the US
continues to rapidly increase. The growth of certified LEED for new construction

projects from 2000 to 2004 was 160%. From 2004 to 2006 the number of certified LEED

64

for new construction projects increased an additional 315%. LEED involvement from
2000-2004 was mainly comprised of government, school and nonprofit projects. Since
the beginning of 2005, the private sector has discovered the “business case” for green
building and is driving the growth of this market in all LEED categories. Green building
as an industry is expected to continue to grow at this rapid pace and thus what has been a
trend will become a full-fledged, green building revolution (Judelson 2007).

LEED design includes materials and resources as one the five main certification
categories. Therefore, the development and use of sustainable materials has a direct

impact on currently used green building practices.

2.6.6 Conclusions

Environmental aspects of building material design include such factors as the use
of natural resources and energy usage. Two methods of quantifying the environmental
properties of a building material were discussed. These methods are life cycle assessment

and LEED. Environmental aspects of a specific design are considered in the next chapter.

2.7 Summary

This thesis deals with the topic of structural optimization of a fiber reinforced
polymer composite structure for both its mechanical and environmental performance.
Introductory topics were discussed in this chapter including design optimization, fiber
reinforced composite theory and environmental design of building materials. These

concepts will be applied to a specific design problem in the proceeding chapter.

65

3 DEVELOPMENT AND IMPLEMENTATION OF STRUCTURAL AND

ENVIRONMENTAL PERFORMANCE OPTIMIZATION TECHNIQUE

3.1 Overview

Synthetic fiber reinforced composites are currently preferred over natural fiber
reinforced composites because of their higher strength and stiffiress properties. However,
society has increasingly recognized the need for more environmentally fiiendly building
materials and practices. The development of a fiber reinforced composite floorboard
panel will be used to investigate the design of a load-bearing member for both structural
and environmental performance. This chapter begins with an outline of the floor panel
basic dimensions, loading, materials and modeling and construction issues. The floor
panel is then presented as an optimization problem and objectives, variables and
constraints are defined. Next, the environmental performance of the floor beam is
discussed and life cycle ratings of materials are used to compute an overall environmental
rating for any given floor beam design. Mathematical composite modeling issues are
discussed including the computation of strains and the use of laminated plate theory in
conjunction with standard six-degree of fi‘eedom two-node linear elastic frame elements.

Finally, the design and optimization method for the floor panel is outlined.

3.2 Optimization of Floor Panel Case Study: Problem Definition
3.2.1 Flooring Systems
A typical flooring system consists of a floorboard panel, which is supported by a

system of joists and girders (see Figure 3.1). The floorboard panel is directly supported

66

by joists (for example member AD in Figure 3.1), which in turn are supported by the
girders (members AB and DC). Floorboard panels are traditionally thin, relatively
lightweight members that support the loads imposed on a given floor. They are supported
by a series of joists that are closely spaced to minimize mid span deflections and thus

minimize the required thickness of the floorboard panel.

 

 

Figure 3.1 Floor System Schematic

A floorboard panel is considered in this study to investigate the strength and
environmental performance of a load-bearing member. Cross sectional and plan views of

typical floorboard panel and structural panel materials are shown in Figure 3.2.

67

 

(a) Corrugated Fiberboard (b) Plywood

 

(c) OSB (d) Composite Floor Panel

Figure 3.2 Floorboard and Structural Panel Materials

Plywood and OSB are considered “engineered woods”. Plywood (Figure 3.2b) is
constructed by arranging thin layers or veneers of wood so that their grains are at ninety-
degree angles to one another to create a laminate. Plywood is usually constructed of an
odd number of veneers so that the finished product in symmetric. Layers are held
together with adhesive and are compressed and heat-treated. Oriented Strand Board (OSB,
Figure 3.2c) is constructed by layering small flakes of wood into cross-oriented directions
and bonding the layers together with resin or adhesive. Engineered woods are ofien more
resistant to warping and cracking than natural woods because of their symmetric
construction. The composite floor panel shown (Figure 3.2d) is constructed of recycled
plastic grocery bags and reclaimed wood. This composite is intended for outdoor use and

also incorporates an environmentally friendly aspect by utilizing recyclable materials.

68

Corrugated fiberboard (Figure 3.2a) is a very common material that is used in light
structural applications such as packaging. It is constructed of at least two face sheets and
a corrugated core sheet or sheets. All sheets are made of thick paper based boards. The
center-corrugated sheet provides flexural stiffness to the material by separating the face
sheets. It also transfers out-of-plane loads to the location of supports just as loads are
transferred in a truss. Further discussion on truss load transfer is included in the next
section. Notice the truss-like configuration of the corrugated cardboard.

The general configuration of the flooring system investigated in this thesis is
shown in Figure 3.3. The loading shown is the design live load for an office building

application (ASCE 2003), which is considered a typical loading for a floor panel for this

 

 

 

 

 

thesis.
q=100 psf
COMPOSITE SANDWICH PANEL i i i
g; / SUPPORT MEMBER
f/ .
L . wfio$vvb
~ 10' >1

 

 

Figure 3.3. Floor Panel System and Loading

The floor panel system spans 10 feet between supports. This is a typical spacing
between girders in a raised floor system (Southern Pine Council 2008). This floor system

is intended to behave as a typical floor panel and joist system. The total depth of the floor

69

panel is three inches. The floor panel thickness was chosen so the resulting panel would
be similar in dimension and thus competitive with commercially available panels. The
three-inch depth was chosen based on commercially available fiberglass paneling
thiclcnesses (Strongwell 2008). A general simply supported plate in shown in Figure 3.4.
The plate is stiffer in the Y direction than in the X direction due to the orientation of the
supports. Thus, the design of such a plate is focused on the performance of the less stiff X
direction. The plate analysis can be simplified to a strip that is oriented parallel to the X

direction (see the highlighted portion of Figure 3.4).

 

 

Figure 3.4. General Simply Supported Plate

A simply supported plate with a top, bottom, and folded middle layer in shown in
Figure 3.5. The folded middle layer is similar to the corrugated fiberboard layout shown
in Figure 3.2a and provides additional stiffness and separation between top and bottom

layers.

70

 

 

Figure 3.5. Simply Supported Plate with Central Folded Layer

The plate analysis can be simplified to a strip that is oriented parallel to the X
direction (see the highlighted portion of Figure 3.5), just as in Figure 3.4. This
highlighted strip is shown alone in Figure 3.6. The performance of the strip in the X
direction is the critical performance that must be considered. Thus the strip shown in
Figure 3.6 is analyzed as a beam. The depth of the beam in the Y direction was chosen to
be a unit 1 foot. It is assumed that plane sections remain plane in the Y direction, thus the
beam is further simplified to a two-dimensional simply supported frame as shown in

Figure 3.7.

 

 

 

 

Figure 3.6. Simply Supported 3D Beam with Central Folded Layer

71

 

 

 

 

A Ex

Figure 3.7. Simply Supported 2D Beam with Central Folded Layer

The two-dimensional simply supported beam considered in this thesis is intended
to have a folded central layer as shown in Figure 3.7. To simplify the analysis of the
beam, the folded central layer is modeled as a series of short vertical and inclined
members that roughly mimic a truss configuration as shown in Figure 3.7. The shape of
the folded interior layer is a variable in the floor panel development, thus the default
position of all interior members is vertical. This default position as well as the

dimensions and loading for the two-dimensional beam element considered in this thesis is

 

shown in Figure 3.8.
AIA
.7.
/_w=8.33lb/in |
riiiiii HHHHHI [HHHW [l HHH

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2 3 4 5 6 7 8 91011121314151617181920

 

 

 

 

 

 

—a—+~3"—-—

 

l‘_
i
:5,

 

 

 

 

I
120"

Figure 3.8. Frame and Loading Layout

This cross section will be analyzed as a frame, but it is intended that the vertical

frame members as shown in Figure 3.8 can be arranged in an inclined fashion to allow for

72

truss- like load transfer. There are twenty-one vertical members in the considered frame.
The open windows between vertical members are numbered in Figure 3.8. The frame is
constrained to be symmetric about its centerline. An example of a possible arrangement
of vertical members is shown in Figure 3.9. Predeterrnined vertical members were
allowed to move as shown in Figure 3.9. More detail concerning this design variable is

contained in section 3.3.

 

 

 

 

 

 

 

l—LLxmaix = :I: 5" (typ)

Figure 3.9 Possible Vertical Member Arrangements

3.2.2 Loading

The loading considered for the frame is the design live load for an office building
application (ASCE 2003). The loading is expected to be uniform across the depth of the
floorboard member, thus the member is simplified to the two-dimensional frame problem
as shown in Figure 3.8. A unit one-foot depth is considered for the frame problem. This
dimension is necessary for loading calculations as well as stiffness computations for the
member. The equivalent loading in Figure 3.8 is computed below.

Floor Joist Load per Linear foot: = (100 psf)(l ft) = 100 lb/ft

= 8.333 lb/in

73

It is intended that the frame will transfer loads to its supports in the same manner
that loads are transferred in a truss. A brief description of this load transfer process
follows.

A simple truss and central point loading are shown in Figure 3.10.

/— LOAD PATH

 

A A

(a)

 

LOAD PATH

 

 

 

 

 

(b)

Figure 3.10 Simple Truss Load Paths

Load is transferred from the point of application to the supports by way of the
inclined members. The inclined members have a vertical component and thus the sum of
the vertical components will be equal to the total vertical loading to maintain equilibrium.
The simplest example of this load transfer is depicted in Figure 3.10a. Load transfer is
depicted with arrows. The truss in Figure 3.10b has a longer span than the truss in Figure
3.10a, thus the vertical load is more efficiently carried by a series of vertical and inclined
members than by a single inclined member. This is true when the horizontal dimension
and thus horizontal component of load become larger than the vertical component. The

74

horizontal loads will control the loading and needed bar diameter. It is thus more efficient
to use a series of smaller diameter bars to transfer the load.

The frame shown in Figure 3.8 does not have any inclined members and thus will
not be able to transfer loading as efficiently as a truss arrangement such as those shown in
Figure 3.10. It is thus desirable to allow the vertical members to move during this
investigation as it is expected that they will assume a more truss-like arrangement that

will transfer loads efficiently.

3.2.3 Materials

Typical floor systems are built with steel or wood girders and an engineered wood
floor panel. Two engineered wood products are shown in Figure 3.2. Synthetic fiber
reinforced composites such as the fiberglass flooring composite shown in Figure 3.2 or
the fiberglass composite panels Durashield made by Strongwell (Strongwell 2008) are
also commercially available and are used for a wide variety of flooring and paneling
applications. Increased interest in sustainability and green building programs such as
LEED (U SGBC 2006) has encouraged the use of more environmentally fiiendly building
products. The use of fiber-reinforced composites in industry is well documented. The
push to replace synthetic fiber reinforced composites, which rely on petroleum based
constituent materials, with natural fibers and natural resins is a direct response to the
recent increased environmental awareness and green building movement. The use of
fiber-reinforced composites for load-bearing applications was investigated in this thesis

while simultaneously considering the environmental impact of the constituent materials.

75

The material chosen for the composition of the frame shown in Figure 3.8 is a
fiber-reinforced composite that is composed of a polyester resin and one of four selected
reinforcing fibers. The four reinforcing fibers considered were two common synthetic
fibers; carbon and e-glass, and two common natural fibers; jute and hemp. The carbon, e-
glass and jute fibers are applied in long continuous strands, while the hemp used is short,
randomly oriented pieces. Reinforcing fibers, resin matrix, and associated properties

considered in this study are listed in Table 3.1.

 

 

 

 

 

 

Material E1 (psi) E2 (psi) G12 (psi) v (poisson)
Jute 2.90E+06 2.90E+06 4.30E+06 0.23
Eglass 1.05E+07 1.05E+07 4.30E+06 0.23
Carbon 3.40E+07 2.20E+06 4.00E+06 0.20
Hemp 1.02E+07 1.02E+07 4.30E+06 0.23
Polyester 2.17E+05 2.17E+05 2.00E+05 0.35

 

 

 

 

 

 

 

Table 3.1 Reinforcing Fiber and Matrix Material Properties

It can be seen from Table 3.1 that hemp and e-glass have similar modulus (E1 and
E2) values, while the properties of carbon are noticeably higher and the properties of jute
are noticeably lower.

Each member of the frame shown in Figure 3.8 is composed of a fiber-reinforced
composite. It is desirable to study the effects of combining several different reinforcing
fibers in the same member, thus it was determined that each member would be composed

of six lamina layers with each layer allowed to contain any one of the four reinforcing

fibers.

76

3.2.4 Construction Issues

Ease of construction of the final design was considered in the conceptual stage of
the frame. To assist with the assembly of dozens of six-layer laminates into the final
frame shape, it was determined that the flame should be constructed by first assembling
foam building blocks the size and shape of the windows (see Figure 3.8), wrapping these
foam blocks with the appropriate fiber layers, and finally infiltrating the system with
resin. The construction method proposed is similar to that documented by others (Dweib
et al. 2004, 2006). The foam blocks provide the shape of the frame and contribute
significantly to thermal and sound insulation. They do not contribute significantly to the
strength and stiffness of the member (Dweib et al. 2004). It has also been demonstrated
that frames built by wrapping the fibers around the foam blocks provide higher strength
and stiffness performance than frames manufactured with a web separate from the top
and bottom face sheets (Dweib et al. 2006).

Foam building blocks (see Figure 3.11) the size and shape of each window in the
frame are each wrapped with three fiber layers. A three-layer face sheet is also placed on
the top, bottom, and sides of the frame. Frame members are thus comprised of the layers
of the adjacent building blocks or building block and outside face sheet (see Figure 3.11

and Figure 3.12).

77

 

 

 

Q A.
FOAM
BUILDING
BLOCK

 

 

 

 

 

 

 

FOAM
BUILDING

 

 

 

~ ' a: Arm/MN /W

 

I CORE LAYER

El FACESHEET LAYER

Figure 3.11. Building Block Layer Arrangement

78

 

 

OP FACE SHEET FIBER LAYER. I,

.ZTOP FACE SHEET FIBER LAYERS. '1 .1"
BUILDING BLOCK- FIBBR' LAYERS: ': '.

BUILDING BLOCK FIBER LAYERS :

g
5
a
if:
a:
I?
E;

‘ JUTE GLASS CARBON ORIHEM? "

a
g:
0.
a.
.43
w}
L?

WWW-N ORHE r3

 

(b) Section 2. Cross Section of Frame Member (typ).

Figure 3.12. Building Block Composite Layer Cross Sections

3.2.5 Modeling Issues
Several modeling issues for the proposed frame are considered in this section.
These include the connection detail at the nodes, joint stresses, hygrothermal behavior,

and curing strains.

79

Truss member nodal connections are often idealized to consider all members
intersecting at a node. This idealization is shown in Figure 3.13. The physical width of

each member is assumed to be small or is neglected in this approximation.

Figure 3.13 Idealized Truss Nodal Connection

If the width of the members is not small, the width of the members can cause
difficulties during construction. A non-idealized nodal connection is shown in Figure
3.14. The location where the center of each inclined member meets the top member is
marked. These two points do not intersect as in the idealized case because the members

are not allowed to overlap and have a nominal thickness.

 

 

 

Figure 3.14. N on-idealized Truss Nodal Connection

80

The construction method of the proposed frame may result in a joint detail as
shown in Figures 3.15a and b. In Figure 3.15a, the left and right fiber members are
allowed to overlap near the node, thus pushing the center fiber layers down so that the top
node of the center fibers are no longer coincident with the idealized node location. In
Figure 3.15b, members do not overlap near the node, and thus the center fiber layers top

node is more nearly coincident with the idealized node location.

81

/— TOP FIBERS
1

a

CENTER FIBERS

 

 

 

(a)

/— TOP FIBERS
1
I

 

 

 

LEFT FIBERS c RIGHT FIBERS

  

 

 

 

 

 

 

 

(b)

Figure 3.15 Proposed Truss Nodal Connections

The proposed fi'ame was evaluated according to the stiffness method. The
stiffness matrix for each frame member was constructed, then transformed to the correct
global coordinate system and assembled into the total stiffness matrix. The layers for
each member are determined by the layer composition of the two adjacent building

blocks. If the inclined members are allowed to overlap, as shown in Figure 3.15a, then

82

the inclined members could potentially have a different layer makeup near the joint than
away from the joint due to the intersection of multiple members at that joint. To avoid
this complication, inclined members were not allowed to overlap, and all joints more
nearly approximated Figure 3.15b.

Members may fail due to stresses experienced at joints before they reach full
capacity. Joints must be carefully detailed to avoid failures of this type and allow the
structure to reach its full strength. It is expected that the constructed joints as shown in
Figure 3.15b may exhibit reduced strength due to un-reinforced resin areas caused by the
radius of the building block. If this radius is reduced too much, stress concentrations will
also occur at the resulting comer. This phenomenon was not modeled mathematically and
is a topic for future investigations.

Each member was composed of six layers of fiber materials. These six layers
could be any arrangement of the four possible fiber materials listed in Table 3.1.
Different fiber types will develop different bonds with the matrix material. In addition, it
has been observed that adjacent lamina layers with differing components cure at different
rates. This causes strains to develop between layers during the curing process. These
strains were not modeled mathematically and are a topic for future investigations.

An important consideration for fiber-reinforced composites is their behavior in the
presence of moisture and temperature change. Natural fiber composites are often more
susceptible to moisture absorption than synthetic composites if they are not properly
treated against moisture. This behavior was not modeled mathematically and is a topic for

future investigations.

83

3.3 Optimization of Floor Panel Case Study: Optimization Problem Formulation
3.3.1 Optimization Objectives

The goal of this investigation is to achieve optimum mechanical performance
while meeting environmental performance objectives. The environmental performance
will be formulated into a constraint in the following sections, thus the single performance
objective is to find the minimum mass frame that meets all mechanical and

environmental constraints.

3.3.2 Design Variables

Optimum mechanical and environmental performance is sought while allowing
the shape and material make-up of the flame to change.

The shape of the frame will change by allowing the movement of specified nodes
from specified default locations. The default locations for all fiame nodes are shown in
Figure 3.16. Nodal coordinates are assigned to the default frame by placing the origin at
node 1 as shown in Figure 3.16. Dimensions are in inches, and nodal coordinates are
simply the x and y distances in inches from the origin. For example, the nodal

coordinates for node 4 are (6, 3).

84

A'A

L *
/|\
x |

£24681012141618202224262830323436384042
:0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l 41
35 7 9 ll13151719[21232527293133353739

—.T' 6"-—.— I

 

 

 

Figure 3.16. Frame Node Numbering

The highlighted nodes (3, 4, 7, 8 etc.) are allowed to move horizontally within a
specified range. All nodes are six inches apart in the default locations. To avoid
overlapping of members, highlighted nodes are allowed to move five inches to the right
(+) or to the left (~). The frame is constrained to remain symmetric, thus node movements
on the left are mirrored on the right. The line of symmetry is shown in Figure 3.16. A
movement value, or a delta value, is assigned during the optimization process. The
corresponding symmetric node will mirror this delta value. This process is illustrated in

Table 3.2.

 

Node 4 Node 40

 

 

 

Original Nodal

Coordinates 6,3 1 14,3
delta value 1 -1
Final nodal

 

 

 

 

coordinates 7,3 1 13,3

 

Table 3.2. Illustration of Nodal Symmetry

85

Each member is composed of six fiber layers and each fiber layer can be any of
the four available fiber types, which are short fiber, randomly oriented hemp, continuous
fiber e—glass, continuous fiber carbon and continuous fiber jute. The fiarne is constructed
by first assembling foam building blocks the size and shape of the windows (see Figure
3.8), wrapping these foam blocks with the appropriate fiber layers, and finally infiltrating
the system with resin. Fiber layer face sheets are also placed on the top, bottom, and sides
of the frame. Each member is thus composed of the fiber layers of the adjacent building
blocks or building block and face sheet. The fiber layers types are variable within each
building block or face sheet. The frame materials must remain symmetric about the
centerline shown in Figure 3.16, thus the fiber layers assigned to window block 1 are
identical to those assigned to window block 20 (see Figure 3.8).

The final variable is the thickness of each fiber layer. Three fiber layers are
wrapped around each building block or are placed in each face sheet. These layers have a
variable thickness that is assigned by block or face sheet. Thicknesses are symmetric

about the centerline shown in Figure 3.16.

3.3.3 Constraints

Constraints were applied to control mechanical and environmental performance.
Mechanical constraints include maximum allowed deflection and maximum allowed
strain. The environmental constraint is a limit on the environmental rating assigned based
on the life cycle rating of the materials used in the frame. The environmental rating will

be discussed in greater detail in the following sections.

86

The maximum allowed deflection is a limit on serviceability for a typical flooring
system. Deflections are limited to prevent cracking of plaster ceilings or other finishing
agents and to prevent user discomfort. A conservative maximum deflection value of
U400 was chosen, where L is the span length of 120 inches. It was found that the
deflection constraint is not active in this floor panel investigation because the limit on
strains was more restrictive. Thus a conservative limit was chosen to attempt to make this
constraint active, however the deflection constraint is still not active in this investigation
but merely operates as a serviceability check.

Maximum allowed strain for each fiber material is computed as follows:

The factored load equation is as follows:
YDPD + YLPL = HI (1)
The factors are as stated in traditional building codes (ASCE 2003) and the ratio

of live to dead load is assumed as follows:

71) =1-4 (2)
7L =1-6 (3)
:71; = 10 (4)

Therefore, the loading equation can be written as:
17.4 * PD = Pg (5)
Equation 5 is used to appropriately calculate maximum loading. Maximum

strain, 60' , due to this load is computed for the frame and compared to the maximum

allowable strain values. Allowable strain values are determined as shown in equation 6

87

with limit state multiplier values (6}) shown in Table 3.3. Values of 8“,, for each

material are shown in Table 3.4 (data from Mohanty 2005).

8U S flr‘ sperm

,3] = dead load limit state

,62 = service limit state

,63 = strength limit state

 

 

 

 

 

 

 

 

Hemp/UP short fiber contin fiber
E CFRP/ GFRP CFRP/ GFRP
[31 0.05 0.075 0.1
B2. 0.15 0.2 0.25
[33 0.33 0.4 0.5

 

 

Table 3.3. Multiplier Values by Load State

 

 

 

 

 

 

 

Composite 8.,“ (%)
jute/UPE 1 .5

E glass/UPE 2.5
carbon/UPE 1 .8
hemp/UPE 1 .6

 

 

Table 3.4. Ultimate Strains

(6)

Allowable strains are computed using equation 6 and the dead load limit state for

each fiber type. These values are reported in Table 3.5.

88

 

Composite 8..
jute/UPE 0.0015
E glass/UPE 0.0050
carbon/UPE 0.0036
hemp/UPE 0.0016

 

 

 

 

 

 

 

 

Table 3.5. Maximum Allowable Strains

The maximum allowed strain for each member in the frame depends on the fiber
layers present in that member. It is assumed that the maximum allowable strain for the
member corresponds to the maximum allowable strain of the least restrictive material
present in the member. This will allow each member to become firlly strained for the
member with the highest strain capacity. E-glass and carbon correspond to the least
restrictive strain limits and jute and hemp fibers correspond to the most restrictive
allowable strain limits. If e-glass and hemp are present in a member, than the maximum

allowed strain will be the maximum allowed strain for e-glass.

3.3.4 Optimization Problem Statement
The optimization problem is stated formally below.
Objective: Minimize total fiame volume
Constraints:
' Nodal coordinates can move +/- 5” from the their original position.
Original positions shown in Figure 3.16.
' Layer materials can be one of four pre-defined options

0 Material 1 = long fiber jute

89

0 Material 2 = long fiber E glass
0 Material 3 = long fiber carbon
0 Material 4 = short fiber hemp

I Layer thicknesses: Outside layers can be between 0.05 and 1.0 inches
thick, middle layer ranges fi'om 0.05 to 0.75 inches thick.

I Strain: Allowable strain for each material is defined in Table 3.5.
Maximum strain in each member cannot exceed the allowable strain for
the least restrictive material present in that member.

I Symmetry: Symmetry about the centerline shown in Figure 3.16 is

maintained for nodal displacement, material choices and layer thicknesses.

Variables:
I Nodal coordinates in the x direction of designated variable nodes (see Figure
3.16- variable nodes are bold):

o X coordinates of the following nodes change (delta) from a set original
position. Variable node movements are mirrored across the line of
symmetry.

deltaLeft = [4 3 8 7 12 11 16 15 20 21]
I Layer materials of each layer (2 face sheets and the core- see Figure 3.11) in
each building block or face sheet (see Figure 3.11 and 3.12).

I Layer thickness of each layer in each building block (see Figure 3.12)

90

3.3.5 Optimization Method

The commercial software package HEEDS (Red Cedar Technology 2005) was
used to perform the optimization of this flame problem. See Section 2.5 for further
discussion on HEEDS methods. I-IEEDS employs a proprietary algorithm that has a
genetic algorithm at its core. Mathematical modeling software was used to solve the
necessary composite math and was tied to HEEDS to perform the optimization. A

description of the optimization procedure is included in the next chapter.

3.4 Optimization of Floor Panel Case Study: Environmental Performance
3.4.1 Environmental Goals for Design

Composites are normally optimized for mechanical performance, but
environmental performance is often not considered. The goal for the environmental
aspect of this design is to quantify the environmental performance of the design and
specify some meaningful performance measure. The end user could then specify the
desired environmental performance of the finished product, or could compare and

contrast several finished products with varying environmental ratings.

3.4.2 Life Cycle Ratings for Composite Materials

One of the five environmental categories in LEED certification is Materials and
Resources (see Section 2.6.3). Within this category, rapidly renewable materials represent
one of the seven divisions within this category. The goal is to reduce the use of finite raw
materials and long-cycle renewable materials. Rapidly renewable materials are defined as

materials that are harvested within a ten-year cycle or shorter. A LEED point in this

91

category is earned by using rapidly renewable materials for 2.5% of the total value of all
building materials and products based on cost. An additional point may be earned if
rapidly renewable materials represent 5.0% or greater of all building materials.

The use of rapidly renewable materials (bio-based fiber reinforced composites)
has been recognized by industry as an important contributor to green building (U SGBC
2006). The use of rapidly renewable materials decreases energy usage because they
generally require smaller inputs of land, natural resources, capital and time when
compared to conventional building materials with longer growth cycles (U SGBC 2006).
The use of energy and inputs in the production of a material can be quantified using a
technique called life cycle assessment. Life cycle assessment is a method of measuring
environmental impacts of a product through its life cycle, often from cradle to grave
(BRE & NetComposites 2004). The Building Research Establishment, a nonprofit in the
United Kingdom, has published a guide titled “The Green Guide” that quantifies the
environmental impact of commonly used composites across 12 environmental and 2
social impact categories. These categories are shown in Table 3.6. The Green Guide
assigns a letter grade to each category, A for superior environmental performance, to E
for inferior environmental performance. Number grades have been substituted for the
materials shown in Table 3.6 so that these rankings can be used as environmental ratings
in the composite optimization of the floorboard. In Table 3.6, A is replaced with 1, B
with 2, and so on. A total environmental grade is computed as the simple average of all

the environmental categories.

92

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93

3.4.3 Environmental Ratings for Optimization Problem

The normalized ratings from Table 3.6 are used to rate the floor board designs
found during optimization to obtain a total environmental rating for each design based on
volume of each material present. A design composed entirely of hemp or jute would earn
an environmental rating of 1.0. A design composed entirely of carbon would earn an
environmental rating of 1.832. The environmental rating is used as a constraint by
specifying that the final environmental rating must not exceed a given value, i.e.1.50.

The panels considered in this thesis are composed of several composite materials,
thus the environmental ratings are an average of the ratings of the individual composites.
Multiple composites combined into a hybrid composite may have an effect on some of
the environmental categories. For instance, one of the environmental indicators is “waste
disposal.” Hemp and carbon composites both received a rating of 2 while glass received a
5. It is feasible to think that by combining glass fibers with hemp and carbon in a hybrid
composite, that it will be difficult to separate and dispose of the individual components. It
may thus be reasonable to assign a waste disposal rating of 5 to the hybrid due to this
interaction. For simplicity, simple averages were used in this study, however, one should
be aware that life cycle ratings may have unforeseen interactions as described above. One
should also be aware that the environmental ratings calculated are based only on the
categories shown in Table 3.6. There may be additional environmental concerns outside
the scope of these environmental ratings. For instance, a hybrid composite composed of
materials that receive lower (read better) enviromnental ratings may also have lower
strength capacity. Thus the size and weight of the member may have to increase to still

meet performance objectives. It may thus be more expensive to transport or may increase

94

the total size of the product that it is used to construct. This may have a negative
environmental impact. However, secondary effects such as this were outside the scope of
this thesis.

The ratings have an unavoidable degree of subjectivity to them. The original
grades assigned to each material by the BRE were assigned by a panel of experts and are
based on detailed environmental studies of each material. However, the selection of 12
environmental indicators and 2 societal indicators and their weights reflect the values of
the BRE committee. A different life cycle assessment committee may not have chosen
the same 14 categories or assigned the same weights. Also, the final grade used in this
study is a numerical average of the total environmental and total societal ratings. A
weight of 0.75 was chosen for the environmental rating and a value of 0.25 for the
societal rating. Despite this, the life cycle assessment ratings presented here are used with
confidence as they represent the best current technique for ranking environmental

performance of materials.

3.5 Mathematical Modeling

A program was written to evaluate the composite and overall properties of the
floor panel cross section and to perform necessary computations to optimize the floor
panel cross section with HEEDS. A brief overview of the functions performed by the
program is detailed below.

Optimization of the floor panel cross section is performed by assigning values to
all design variables, evaluating the objective firnction and constraints, and repeating. The

program performs all necessary computations for each iteration. Given that values have

95

been specified for all variables, the program performs the following functions. The

moment of inertia, cross sectional area, effective axial in-plane stiffness, Ex, and the

effective flexural stiffness, Exf are computed for each floor panel cross-section member.

The computation of the stiffness values was described in Chapter 2 (see Section 2.2.2.2).
Next, the global element stiffness matrix is constructed according to the stiffness method.
A fiame element stiffness matrix is generated for each member in the standard form
shown in Chapter 2 (see Section 2.2.2.2). These stiffness matrixes are appropriately

assembled to create the total global stiffness matrix.

The total global stiffness matrix, Kglobal: is reduced to account for pin supports at

nodes 1 and 41 as shown in Figure 3.16. Equivalent nodal loads are computed based on
the distance between adjacent nodes. The equivalent nodal loads, F, applied to the top

nodes will change if the nodes are able to move. This is illustrated below:

wa wa/2 wL

 

 

 

 

 

 

 

 

 

 

H H 11.: 1111111 1
\ /

 

 

 

 

 

 

—C V

 

 

 

 

“—43—"

=c/2+d/2

Figure 3.17. Equivalent Nodal Loads
Nodal displacements, vg, and strain in each frame member are computed

according to the methods shown in Section 2.2.2.3.

96

3.6 Conclusions

The optimization problem setup of a floor panel was presented in this chapter to
investigate the mechanical and environmental performance of a fiber reinforced
composite material. The optimization problem and methods were described and key

outputs were discussed. Optimization studies and results are presented in the next chapter.

97

4 DISCUSSION AND RESULTS

4.1 Overview

The optimization of a fiber reinforced polymer composite floor panel constrained
to both mechanical and environmental performance was investigated. The optimization
problem sought to minimize volume while meeting performance constraints in the form
of deflection and strain limits, while also meeting environmental constraints in the form
of a maximum allowed rating determined by life cycle analysis ratings of the constituent
materials. Optimization was performed with use of the program HEEDS. The
optimization process, the results of the optimization, and a discussion on environmental

performance applicability to current industry practice is provided in this chapter.

4.2 Design and Optimization Process

Optimization of the floor panel was performed with the optimization software
HEEDS. The optimization design process and outputs are described in the following
section. Optimization was carried out for a range of environmental constraint values. The

results of this optimization are presented.

4.2.1 Optimization Design Process Description

The structural and environmental properties of the floor panel were investigated
by optimizing the truss system presented in Section 3.2. The goal of the optimization is to
find the optimum combination of materials, layer thicknesses and overall flame layout
that meets the design objectives and constraints outlined in Section 3.2. A flowchart of

the general HEEDS optimization routine was presented in Chapter 2, Figure 2.14. This

98

flowchart is expanded with illustrations of the optimization process specific to the floor
panel case study presented in Chapter 3.

Steps 1 and 2 of the optimization process are shown in Figure 4.1 below.

 

Step 1: Establish Baseline Design

 

 

 

1
Step 2: Select Value for Variables

. r7 |

Previous Iteration

 

 

 

 

 

 

 

 

Step 3

 

 

 

 

 

 

Figure 4.1. Optimization Procedure, Steps 1 and 2

Step 1: Default values are established for node position, material types and
material thicknesses for the flame. This design became the baseline design against which
subsequent designs are judged.

Step 2: Values for all variables are selected during this step. An x displacement,
named delta x below, for each node that is variable within the flame is selected. An

example selection of nodal displacements is illustrated in Table 4.1 and Figure 4.2.

[W II I l l l l l I l
Node 34 7 8111215161920
Ideltax | -2| 2| 3.5| -3.5| -2.5| 2.5| -3.5| 3.5| 1.5| -1.5|

 

Table 4.1 Variable Node Delta 1: Selection

99

ANA.

)1

/|\

w=8.331b/1in
111111111111111.11111111111111111111111
/ ' . \

 

1.—
{F—
u..—
*—
‘—
‘—

 

‘—
Ip—r
n—1
p.—
‘0‘—
*1

 

 

 

 

 

 

 

 

0-—0II—

 

\

A A A A A
v v v 'v " vv v V

-———-—l—.— 6" (ty'p 1
1

— xmax = :1: 5" (typ)

120"

0

 

——r3"«-——

 

 

 

 

 

 

 

 

Figure 4.2 Delta x Illustration

A material type and layer thickness for each layer in each building block in the
flame is also chosen at this step. An example selection of material types and layer
thicknesses for blocks on the left half of the flame is illustrated in Table 4.2 and Figure
4.3. Each number corresponds to a material fiber type: 1 for jute, 2 for hemp, 3 for carbon
and 4 for glass. Materials and layer thicknesses are assigned by block. There are ten
blocks on each half of the flame as well as a three-layer composite on the top, bottom and
each side of the flame. Material selections and thicknesses are mirrored across the line of

symmetry shown in Figure 4.2.

100

 

Table 4.2 Example Material Types and Layer Thicknesses

 

 

BLOCK 1

 

 

 

 

IIIIIIIIIIIIIIIIIII

BUILDING
BLOCK 2

 

 

 

 

 

 

 

 

IJLIIIIIIIIIILIJLLIIY

 

BUILDING
BLOCK 3

 

 

 

 

 

 

Figure 4.3 Material Types and Layer Thicknesses, Blocks 1-3

101

 

 

 

 

Step 2

1

 

 

 

Step 3: Evaluate Design

 

 

 

 

Step 4: Judge Design, Establish Design Performance
4a: Evaluate Constraints

Assign penalties to violated constraints
4b: Evaluate Objective Function

1

Step 5

 

 

 

 

 

 

 

Figure 4.4. Optimization Procedure, Steps 3 and 4

Steps 3 and 4 of the optimization process are shown in Figure 4.4 above.

Step 3: The design is evaluated with a general-purpose mathematical program that
was written to evaluate problem constraints and objectives. The program computes the
resulting composite properties for each flame member.

Step 4: The objective of the optimization is to minimize total material volume.
Constraints include maximum allowed deflection, maximum allowed strains, and a
maximum enviromnental rating. The program computes the resulting displacements in
the flame, strains in each flame member, and environmental rating. Strain output flom
the program is shown in Figure 4.5. Material percentages and environmental rating are

shown in Table 4.3.

102

DISTANCE (IN.)

u—e

W
m
'o
3—5
8

1

 

—a
N

E

 

 

 

l l l l l l l l l l

36 48 60 72 84 96 108 120
DISTANCE (IN.)

 

 

 

 

 

 

O
p—n
N
N
A

Figure 4.5. Member Strain Illustration

1 .43

 

Table 4.3 Material Percentages and Environmental Rating

Step 5 of the optimization process is shown in Figure 4.6 below.

103

 

 

 

Step 4 To Step 2 To Step 1

 

 

 

 

 

 

 

 

 

 

 

Step 5: Compare to Baseline Design: Higher Performance?

1

Yes No

1

Replace Baseline Design

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.6. Optimization Procedure, Step 5

Step 5: The current design is compared to the baseline design and evaluated for
performance. If the current design meets constraints and objectives better than the
baseline design, the baseline design is replaced. Design iterations continue until the

optimization process has reached the maximum number of iterations specified by the user.

4.2.2 Optimization Outputs

Plots of the optimization progress for the objective function, the constraints and
the design variables are available flom I-IEEDS. A record of current best designs is also
created during optimization. Output for the floor panel optimization includes final best
design values for nodal displacements, layer materials and thicknesses, panel volume,
member strains and environmental rating. HEEDS plots for the objective function and
environmental constraint are shown below. Typical frnal design outputs include strain for

all members (Figure 4.5), variable node displacement (Table 4.1), materials chosen for

104

each building block (Table 4.2), and material percentages and environmental rating
(Table 4.3).
A I-IEEDS plot of volume values over the course of a typical optimization routine

is shown in Figure 4.7.

 

 

 

 

 

 

Figure 4.7. Volume Values over Course of Optimization

The points on the plot depict the design chosen at each iteration point. The solid
line plots the current best design found. Figure 4.7 illustrates two aspects of the HEEDS
optimization process; the design search method and the convergence of designs. HEEDS
employs a genetic algorithm at its core. Design traits are selected based on the previous
generation and the best traits are carried through to the next. The current best design line
shows fairly steady downward progression for the first 2000 iterations. The heavy
concenflation of design points around the current best design line illustrates the fact that
the majority of the design space exploration is done close to the current best design.
When the current best design volume has been steady for many iterations, the

105

Optimization process begins searching the farther reaches Of the design space to avoid
settling on a local minimum. This is illustrated by the location Of design points during the
period Of iterations flom 2500 to 4000. It is reasonable to conclude that the Optimization
routine has converged to an Optimized solution at around 2500 iterations due to the fact
that the design space was explored for another 1500 iterations with no improvement to
the best design. Optimizations results as presented above are typical Of all Optimizations
performed in this study.

The HEEDS plot for the environmental constraint is plotted in Figure 4.8. The
environmental constraint is a maximum allowed value that the panel can have. Higher
numbers correspond to a less environmentally fliendly panel. For this particular
Optimization, the maximum allowed environmental rating was set to 1.50. The majority
Of designs considered during this Optimization were well under the environmental
constraint Of 1.50. The final Optimum design is near the active constraint value of 1.50,
but not exactly 1.50. This constraint is not active, so either it is not possible for this
constraint to be active at the Optimum point due to other constraints, or the design found
is near optimum, but not exactly the Optimum design. The convergence Of the HEEDS
optimization process was discussed above and it is believed to that the achieved
convergence is satisfactory. However, the combination Of the genetic algorithm search
process and a large number Of design variables make the achievement of a true optimum
difficult. Instead, a design that is satisfactorily close to the Optimum point has been

achieved through this process.

106

 

 

Figure 4.8. HEEDS Progress to Environmental Rating

4.3 Optimization Results and Discussion

The resulting panel flom the Optimization process presented above is the least
volume panel that meets strain constraints for each member, a deflection constraint for
the panel, and an environmental constraint. The appropriate strain constraints were
assigned to the panel based on published allowable strain for the materials used in panel
construction. The deflection constraint was chosen to limit deflections for serviceability
concerns. The deflection constraint did not affect the optimization Of the panel, as the
resulting panel experienced deflections much smaller than the limiting value of U400.

Thus, the strain and environmental constraints controlled the design Of the panel. The

107

environmental constraint controlled the proportion Of materials with unfavorable
environmental ratings to materials with more favorable environmental ratings. This
constraint was varied across a range Of values, flom the lowest achievable rating Of 1.0 to
the highest rating achieved with Optimization Of 1.50, tO determine its effect on the panel
design. Figure 4.9 depicts the volume Of Optimized designs over the range Of
environmental ratings. A lower allowable environmental rating restricts the use Of
materials with high individual environmental ratings. Thus, more natural fibers will be
used, and less synthetic fibers. However, the natural fibers are more compliant and
weaker than synthetic fiber reinforcement, and thus more material is required in the panel
design to meet strain constraints. It is expected that a design with a low environmental
rating will have a greater volume than a design with a high environmental rating. This
trend can be clearly seen in Figure 4.9. The results shown in Figure 4.9 are characteristic
Of a Pareto Front in that the same figure could have been Obtained by treating minimum
volume and minimum environmental rating as dual Obj ective functions. The points shown
in Figure 4.9 are Optimized solutions found over a range Of environmental rating
constraint values. The resulting trend line represents the Pareto Front, or line Of points
where minimum volume cannot be improved without negatively effecting environmental

rating and vise versa.

108

 

 

3400

y = -2848.5x + 6339.2
3200 °
3000

\ O
2800
. \
2600 . \
2400 ’

2200

 

 

 

 

Volume (cu-In.)

 

 

 

 

 

2000

 

T

1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5
Envlronmental Rating

Figure 4.9. Environmental Rating v Volume

Figure 4.10 depicts the cost of optimized designs over the range of environmental
ratings. Costs for the four fibers considered in this design are listed in Table 4.4. The
least expensive fibers are also the fibers with the lowest environmental ratings. However,
the designs with the lowest environmental ratings also have greater total volumes than the
designs with higher environmental ratings (see Figure 4.9). However, the cost difference
between the natural fibers and the synthetic fibers, particularly when considering carbon,
is large enough to Offset the changes in volume. Thus, it was expected that designs with
higher, or worse, overall environmental ratings would also have the highest cost. This
trend can be clearly seen in Figure 4.10.

Cost versus material percentage is depicted in Figure 4.11. As expected, the least

expensive designs contain the greatest percentage of natural fibers (hemp and jute), while

109

 

the most expensive designs contain the greatest percentages Of synthetic fibers (glass and

 

carbon).
Cost Info Jute Glass Carbon
b/cu.-in. 0.051 0.053 0.092 0.065
.-in. .15 .16 .55 1.63
Table 4.4. Fiber Material Costs
$1,000

 

 

 

$900
y= 1311.7x- 1002.9
$800

$700

 

 

 

 

$4,, ,/

 

 

 

 

 

 

$300 0
$200
$100
$0 1 . . T . T . 4 e
1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5

Environmental Rating

Figure 4.10 Environmental Rating v Cost

110

 

 

 

 

 

(4
40 \ E; —o—%Herrp
+% Glass
3° xx ‘ ‘ A +7. Carbon
y +% Jute
20
10 //

0 . . . . r .
$300.00 $400.00 $500.00 $600.00 $700.00 $800.00 $900.00 $1,000.00

Cost

 

96 Material

 

 

 

 

 

 

 

 

Figure 4.11 Cost v. Material Percentage

Figure 4.12 depicts the percentages Of each material present in the Optimized
designs over the range Of environmental ratings. The environmental rating is simply a
weighted average Of the environmental ratings Of the individual fibers. Thus, designs with
low environmental ratings will contain a larger percentage Of natural fibers and lower
percentage Of synthetic fibers. This general trend can be seen in Figure 4.12 and is
presented as a average trend line in Figure 4.13. Only hemp shows a clear downward
progression and only carbon shows a clear upward progression. The percentage use of
jute and glass fibers varies over the range Of environmental ratings, but does not show a
clear downward or upward progression. Therefore, it can be deduced that the amount of
jute and glass as considered in the current panel design does not have a controlling effect

on the overall environmental rating.

111

% Material

 

 

 

 

 

 

 

 

 

 

 

 

60
50 K
40 V
w m
20
10 W
o T I l T
1 1.1 12 1.3 1.4 1.5
Enviroumntd Rating

Figure 4.12 Environmental Rating v Material Percentages

112

 

 

+%the
-I—%Herrp
+%Giaes
—)(—%Carbon

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

_ +%Jute
3 +%Hemp
i +%Glass
:2 +%Cabon
0 T . . .
1.0 1.1 1.2 1.3 1.4 1.5

Environmental Rating

Figure 4.13 Environmental Rating v Material Percentages: Trends

The percentages Of hemp and carbon present in all designs over the range Of
environmental ratings are presented without jute and glass information for clarity in
Figure 4.14. The downward trend for hemp and upward trend for carbon can be more

clearly seen.

113

 

  

 

 

 

  

 

 

 
 

 

 

 

 

 

 

 

 

 

y = -84.498x + 143.51
50
I
40 -— I %Hemp
E 3: %Carbon
i 30 — Linear (%Hemp) ’9 I
a: — . Linear (%Carbon) 5 / \-
20 ' 7‘ x
/ y=115.19x-119.02
10 , ’
V ’ "
O ' I I I I f
1 1.05 1.1 1.15 1.2 1.25 1.3

Environmental Rating

Figure 4.14. Environmental Rating v. Material Percentages: Hemp and Carbon

Figure 4.15 depicts the structural performance rating in the Optimized designs

over the range Of environmental ratings. Structural performance (S) was defined as

follows:

I.
s =10,000[Z " +—]l

5
L 6aIIow w

 

a
where r = —
8U

(1)

(2)

The first term considers the percentage Of ultimate strain, 8/ cu, Of each member

according to the length Of the member and sums these terms. L is sum Of the length Of all

members in the panel. The second term is a measure Of panel deflection divided by

allowed deflection. The weight Of the system is represented by w. The term is scaled by a

factor Of 10,000 for ease of data presentation. The structural performance term measures

the degree to which members are fully strained and the panel is fully deflected and then

114

divides this combined percentage by the volume Of the panel. A panel with a high number
of members flrlly strained is an efficient design and therefore more near tO an Optimum
solution than a panel with a lower number Of members fully strained. This metric is
normalized for the volume Of designs to eliminate the effect Of changing volumes over
the range Of environmental designs. The performance measure fluctuates around a value
of 3 over the range of environmental ratings (see Figure 4.15). This demonstrates that the
structural performance Of the Optimized panels is reasonably constant over the range Of
environmental ratings considered. Each design is an Optimized design and it is therefore
rational that structural performance remains fairly Constant if an Optimized design is
being achieved each time. This is demonstrated in Figure 4.15. The performance measure
is plotted against the material percentages in Figure 4.16. Data points are unifomrly
scattered about the plot. This figure confirms that the performance measure was relatively

stable over the range Of Optimized designs.

115

 

96 Material

Performance Measure

10

4.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4 e
e
3.5
: .
3 e .
2.5 ————‘——g
2
1.5
1
0.5
0 T T T T
1 1.1 1.2 1.3 1.4 1.5
Environmental Rating
Figure 4.15 Environmental Rating v Performance Measure
. A
: v
T e % Harm
; X X 1 I I I % Glass
. :3. % mm
. I 4' g x % Jute
X | g x I
x I
2 2.5 3 3.5 4
Performance

Figure 4.16 Performance Measure v Material Percentage

 

The floor panel Optimized in this thesis is compared to a commercially available
fiber reinforced composite panel with the product name Durashield shown in Figure 4.17
manufactured by Strongwell (Strongwell 2008) in Table 4.5. Three panel designs
presented above are included in Table 4.5. They are identified as Panel 1, which is the
panel with an achieved environmental rating of 1.39, and Panels 2 and 3 with
environmental ratings of 1.22 and 1.056 respectively. Size is a measure of panel thickness
versus span and is identical for all panels. Weight, panel strength capacity, and
environmental ratings are also reported. It can be seen that the hybrid natural/synthetic
panels developed in this thesis are comparable is weight and capacity measures. The
commercial panel is the lightest panel, but also has the highest environmental rating. The
trade Off between panel weight and environmental rating is clearly shown in Table 4.5

and the hybrid/synthetic panel data fits well with the commercial panel data.

 

Figure 4.17. Durashield Panel (Strongwell 2008)

Panel Size Weight (lbs) Capacity (ps1) Environmental Rating

 

Durashield 3"x10' 78.5 121 1.832
Panel 1 3"x10' 106 100 1.39
Panel 2 3"x10' 124 100 1.22
Panel 3 3"x10' 150 100 1.056

Table 4.5. Comparison to Commercial Panel

117

The floorboard panel is now compared to a previous generation hybrid
natural/synthetic panel named BioPanel (Quagliata 2003) in Figures 4.18 and 4.19.
BioPanel is constructed of a short fiber randomly orientated hemp core and woven jute
fabric face sheets. Both panels have a 3” thick cross-section. The cross section of
BiOPanel is shown in Figure 4.19. It can be seen in Figure 4.18 that the allowable
pressure Of the floorboard panel developed in this thesis is higher than that achieved by
BiOPanel. This is due in to the Optimized cross section and hybrid material makeup Of the
floorboard developed in this work, which outperforms the un-Optimized configuration

and all-bio content of the BiOPanel.

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0. 1

0

 

BiOPanel Floor Board Panel

Figure 4.18 Allowable Pressure (psi) of 3” Panels

 

Figure 4.19 Hemp BioPanel with Top and Bottom Woven Jute Fabric

118

4.4 Validation

The results presented for the floorboard panel were numerical in nature. It is
necessary to consider if the results found are feasible and correct. This was done in three
ways: multiple runs Of the same algorithm were performed to assess convergence and
reliability Of the design method, the floorboard panels were compared to commercial
panel systems whose design evolved by trial and error, and the performance was
compared against other floor panel systems.

The shape Of the floorboard cross section was partially determined by the
locations Of the variable nodes. Figure 4.20 shows a typical cross sectional shape for the
floorboard panel. This basic shape was Obtained by HEEDS with each Optimization run
with small variations. This shape was also validated by running HEEDS multiple times
for a single Optimization set up. It was found that the final shape and basic panel design
varied very little between Optimization runs.

It was expected that the flame would assume a truss-like shape to carry loads
more efficiently. It can be seen in Figure 4.20 that members connected to variable nodes
have assumed a more slanted position; however, the final cross section is not a uniform
truss cross section. This may be due to the large design space that was considered in this
thesis. There are a large number Of design variables and thus the most efficient design
may not be achieved through shape Optimization alone. Nonetheless, the solution is not
too far flom Optimal solutions found in industry by traditional trial-and-error design
approaches. It can be seen that the shape Of the Optimal solution flom this work (Figure
4.20) is very similar to the cross section of the DuraSpan (Martin Marietta 2008)

composite bridge deck shown in Figure 4.21. DuraSpan is a product that was developed

119

 

through trial and error by Martin Marietta Composites. It is a fiber-reinforced polymer 1

 

(E-glass/ vinylester) composite that is available in 5” and 7.66” depths and the shape used

was developed by Martin Marietta to efficiently carry larger loads (vehicle traffic) than

the floor panel studied in this thesis. The similarities of the cross sections are Obvious,

which validates that while the Optimal shape Obtained flom this work (Figure 4.20) may

seem non-intuitive upon first inspection, the design’s efficiency seems to be corroborated

by the existence Of similar solutions Obtained by other methods. This comparison lends

validation tO the Optimized shape found in the floor panel case study.

Finally, the performance Of the floor panel was compared tO other panels as was

discussed in the previous section.

r—s
m
1

% STRAINED
—0-19

— 20—39
— 40-59

— 60-79
— 80-100

 

 

 

 

 

O\
1*?

 

 

 

111: Ill! 11 I

 

 

 

 

 

DISTANCE (IN.)
"13

o
y—a
N
N
.hr
L»
Q

l l l l I

48 6'0 72 84 96 108 120
DISTANCE (IN.)

Figure 4.20. Member Strain Illustration

 

 

,- . ‘5». . .\_- ‘ . , _~.. a, ._ - . _ _' . -..- -‘ a .-. -;.. .~ .1. m r 7 _‘
. , V .3. ‘ .‘ . " .', , _ , .‘ II .1. ‘. * . ‘7 ‘
2.. , .: r. - . .; . . :‘ .- 1 1 « ,
‘ ,‘ 1 \ - ‘ « '1' k Ii I
- ‘~ \” «f ‘1‘. .3 ' " . ti' ' . .1“ ' t ‘ 1.315 . , » 111'. "‘
.. - _ w ..“1 . h- . . N _._- ..

 

Figure 4.21 DuraSpan Deck Panel Cross-Section Schematic (Martin Marietta 2008)

120

4.5 Industry Applicability
4.5.1 User Defined Environmental Performance

The use of materials that minimize environmental impact must be carefully
weighed against traditional design considerations such as strength, weight and cost. The
use of life cycle assessment has been demonstrated tO be a useful metric for
environmental design (Karnpe 2001, Wegst and Ashby 1998). In particular, the use Of life
cycle assessment can be a helpful metric when comparing a specific performance index,
such as bending stifflress against environmental impact. Efforts have been made to create
a database of material properties and to develop a method that would allow a designer tO
evaluate mechanical, environmental and cost metrics early in the design process (W egst
and Ashby, 1998, De Benedetti, B et al. 2002). The floor panel Optimization presented in
this thesis also seeks to allow the designer to tailor the finished product to achieve
mechanical and environmental performance. It has been demonstrated that an Optimized
mechanical performance can be Obtained while achieving designated environmental
ratings. The range Of results presented would allow a design to select the floor panel that
met their specific needs. It has also been demonstrated through a specific structural
example that a problem can be Optimized for both mechanical and environmental

performance.

4.5.2 Applicability to Current Industry Practice
The growth Of the green building industry has in turn created a greater demand for
environmentally fliendly building materials. The need for materials that meet green

building Objectives will continue to rise as developers look tO build green. One Of the

121

 

most tangible examples Of applied green building is the LEED rating system that was
introduced in Chapter 2. The fiber reinforced floor panel that was the topic Of this thesis
was Optimized using an environmental rating that was based on the life cycle assessment
rating of the constituent materials. Life cycle assessment is a useful tOOl for process and
material comparisons, but the results Of a life cycle assessment are not universally
recognized or agreed upon in nearly the same fashion as the LEED ratings. For this
reason, it is Of interest to discuss the impact an environmental floor panel such as the one
developed in this thesis would have on a LEED rating.

LEED ratings are achieved by earning a specified number of points (see Chapter 2,
Table 2.2). LEED points are divided into five categories (see Chapter 2, Table 2.3), for a
total of 69 possible points. Environmental materials fall into the “Materials and
Resources” category. This category contains 13 Of the total possible 69 points. Points in
the Materials and Resources category are further broken down into the categories shown

in Table 4.6.

122

 

117

 

Credit

Description

Points

 

Building Reuse: Maintain 75% of

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.1 Existing Walls, Floors and Roofs 1
Building Reuse: Maintain 95% of

1.2 Existing Walls, Floors and Roofs 1
Building Reuse: Maintain 50% Of

1.3 Interior Non-Structural Elements 1
Construction Waste Management:

2.1 Divert 50% From Disposal 1
Construction Waste Management:

2.2 Divert 75% From Disposal l tO 2

3.1 Materials Reuse: 5% 1

3.2 Materials Reuse: 10% 1 to 2
Recycled Content: 10% (post-

4.1 consumer + 1/2 pre-consumer 1
Recycled Content: 20% (post-

4.2 consumer + 1/2 pre-consumer 1 to 2
Regional Materials: 10% Extracted,

5.1 Processed & Manufactured Regionally 1
Regional Materials: 20% Extracted,

5.2 Processed & Manufactured Regionally 1 tO 2
Rapidly Renewable Materials (2.5% Of

6 total building material costs) 1 to 2
7 Certified Wood 1 to 2

 

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Table 4.6 LEED Materials and Resources Points by Section

The fiber reinforced floorboard panel is composed Of synthetic and rapidly
renewable materials. Credit 6 is for the use of rapidly renewable materials. One point is
awarded for the use Of rapidly renewable materials in the amount of 2.5% or greater Of
the total project material cost. An additional point may be earned for the use Of rapidly
renewable materials in the amount Of 5% or greater. An owner or architect who was

trying to achieve a LEED rating would thus benefit flom use of the floorboard panel

 

 

developed in this thesis as it could potentially help earn up to two points. Furthermore,
the owner or architect could tailor the composition Of the floorboard panels to meet the
required LEED percentage while also taking into account the change in volume and price

that accompany a change in material percentages.

4.6 Conclusions

The Optimization of a fiber reinforced composite floor panel was carried out to
investigate the mechanical and environmental performance Of the Optimized designs.
Floor panel designs were Optimized for minimum volume while meeting strain and
deflection constraints and also meeting an environmental rating limit. Optimized designs
were created for a range of environmental ratings. It was shown that the optimization
process results in a useful library of design alternatives that can be used by a designer

concerned with both mechanical and environmental performance.

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5 CONCLUSIONS AND RECOMMENDATIONS

5.1 Conclusions

The results flom the presented computational Optimization study have shown that

the design Of a load bearing natural and synthetic fiber reinforced floor panel can be

effectively Optimized for both mechanical and environmental Obj ectives. The findings Of

this thesis have led tO the following conclusions regarding the design of structural

members flom fiber-reinforced composites.

The hybrid design problem applied to a floorboard application
demonstrated that strategic arrangement Of hybrid material in an Optimized
design could satisfy prescribed environmental constraints.

Life cycle assessment ratings provide a reasonable and quantitative
measure Of the environmental impact Of a given material and are easily
applicable to an optimization problem.

Environmental considerations can be easily incorporated into the design
process by including environmental ratings in the design process. A range
of designs can be created for a specific structural use thus allowing the
user to select the best combination Of environmental rating and final
product geometry.

Hybrid designs Of fiber reinforced polymer composite floor panels using
blends Of synthetic and natural fibers were capable Of handling typical
residential loadings and were similar in size to typical floorboard panel
materials, thus making them competitive in terms Of performance and

geometry.

125

 

0 Due to the consideration Of building techniques at the onset of the design
process, the final floorboard panel has a practical fabrication method in
place and will not require complicated techniques to manufacture the final

product.

5.2 Recommendations for Future Work

Recommendations for future work based on the findings Of this study are
provided for the materials system, the structural system, and computational efficiency.
Future work is needed tO expand the number and type Of design variables, as well as the
library Of final designs. Computational efficiency will need to improve with increased
design problem complexity and increased output desired. It will also be beneficial tO
manufacture and test several final designs to determine ease of fabrication as well as

comparability to traditional floorboard panels and other structural systems.

5.2.1 Increased Complexity of the Optimization Problem

Fiber reinforced polymer composites can be arranged in a floorboard panel
configuration and Optimized tO perform in a load bearing application while
simultaneously considering the environmental impact Of the chosen constituent fibrous
reinforcement materials. Future work is needed to expand the complexity of the current
Optimization problem. Suggested design variables that should be considered include: the
matrix material, an expanded list Of possible fiber reinforcement materials, and additional

geometric variables.

126

. I. g'r'X.

 

The current study considered a single polyester matrix material. Much work has
been done by others to develop matrix materials that contain a portion of organically
derived materials, such as soybean Oil, or are completely derived flom organic and
natural sources. A similar life cycle assessment rating should be applied to the possible
matrix material Options. An increased number Of designs as well as an increased range Of
environmentally rated materials would be possible.

The current study considered four possible fiber materials. The list Of fiber
reinforcement materials should be expanded tO allow for increased design possibilities
and a greater study Of the effect Of possible construction materials.

The current study allowed for changes in geometry Of the floorboard cross section
by allowing intermediate nodes to move horizontally and also allowing a change Of
thickness to each material layer. Greater geometric fleedom could be incorporated into
the design by allowing additional design variables such as fiber orientation layer, vertical

node displacements, and overall span length.

5.2.2 Expansion of the Library of Final Designs

The current work produced a range Of final designs that were Optimized for
minimum mass while meeting mechanical and environmental constraints. The range Of
final designs was created by altering the environmental constraint so that designs with
roughly similar mechanical performance could be compared based on their differing
environmental performance and geometries. Future work is needed to expand the library

of final designs. The library should be expanded for both the current design setup, and

also for design setups that include increased variables as discussed in the previous section.

127

Il—F—___ '

It would also be beneficial to consider multiple load bearing applications and create a

design library for a range of design applications.

5.2.3 Computational Efficiency

An Optimization method that incorporated a genetic algorithm was used to solve
the Optimization problem in this study. The genetic algorithm worked well for this
application, but its efficiency must be improved if the number Of design variables is to
increase, or a greater number of designs is required. It is recommended that parallel
computing methods or high speed processing methods be incorporated with the genetic

algorithm software to increase productivity and allow for greater data output.

5.2.4 Laboratory Manufacturing and Testing

The final recommendation is tO expand the current study by incorporating a
laboratory or flrll scale manufacturing and testing component. The current designs have
been formulated so that manufacture will be straightforward. It would be beneficial tO
build and test several final library designs tO determine the actual ease of fabrication.
Future work is also needed to test the manufactured floorboard design and compare its

performance to conventional systems.

128

 

1r

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