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This is to certify that the

thesis entitled

FINITE ELEMENT METHODS USED IN THE
ANALYSIS OF RUNNING SHOE SOLES

presented by

Maureen Ann Clements

has been accepted towards fulfillment
of the requirements for

M. S. Mech. Eng.

degree in

 

 

QLDEQflm-gfiga

Major professor

Date 10-29-85

 

0-7639 MSU is an Affirmative Action/Equal Opportunity Institution

 

MSU RETURNING MATERIALS:
Place in book drop to
LlBRARlES remove this checkout from
your record. FINES will

be charged if book is
returned after the date
stamped below.

 

 

 

 

 

mists-"4 {1‘21 4 U 4

N.

L “W

 

 

FINITE ELEMENT METHODS USED IN THE
ANALYSIS OF RUNNING SHOE SOLES

By

Maureen Ann Cle‘ments

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Mechanical Engineering

1985

ABSTRACT

FINITE ELEIVIENT METHODS USED IN THE
ANALYSIS OF RUNNING SHOE SOLES

By

Maureen Ann Clements

This thesis presents a design tool for the analysis of running shoe sole prototypes.

A computer program was written to serve as a very specific preprocessor for
ANSYS, a finite element program. The simplification of the finite element
modeling process will be demonstrated. This preprocessor uses a general physical
geometry to model a variety of shoe sole designs. Slightly different physical
geometries can be artificially modeled by material property manipulation, as long
as the basic configuration of the shoe is the same. Running shoe soles are made
up of multiple layers, usually containing outsole, midsole, and wedge sections.

The preprocessor allows for substitution of a layer while keeping the others
constant. The material properties in any layer can be specified or changed easily

leading to a versatile design tool. Displacement and stress plots show variations in

material configurations and provide trends to guide design changes.

 

 

ACKNOWLEDGEMENTS

I would like to express my thanks and gratitude to my major professor Dr.

Robert Soutas-Little for his acceptance, knowledge, and guidance.

1 would like to thank; Wolverine World Wide Inc., for funding my research,
Swanson Analysis Systems Inc., for the use of ANSYS, Chrysler Corporation for

their patience and support, and the entire Case Center staff for their helpfulness.

I would also like to thank Drs. Eric Goodman, Larry Seegerlind, Clark
Radcliffe, and M. V. Gandhi whose comments and advice on my research were

greatly appreciated.

A special thanks to my family, especially my mom and dad, whose love and

support always encouraged me to do my best.

And finally, I would like to thank all my friends, especially Brian Agar, Paul
Zang, and Mary Ellen Zang whose love and moral support helped me through the

rough spots.

ii

L

 

TABLE OF CONTENTS

LIST OF FIGURES .

Chapter 1 - lNTRODUCTION

Chapter 2 - FINITE ELEMENT METHODS

Chapter 3 — PROGRAM DESCRIPTION .

Chapter 4 — RESULTS

Chapter 5 - CONCLUSIONS

REFERENCES

APPENDD< A - WAVE FRONT SOLUTION EXAMPLE

APPENDIX B - MATERIAL PROPERTIES FOR THE CHARIOT AND
TRILOGY MODELS

APPENDIX C — STRESS AND DISPLACEMENT PLOTS

APPENDIX D — ANSYS PREPROCESSOR ROUTINES FOR SHOE
SOLE MODELING

iii

Page

iv

10
16
26
28
A1

B1
C1

D1

 

LIST OF FIGURES

Page
Figure 1.1 Pronation . . . . . . . . 2
Figure 3.1 Element Model of a Shoe Sole . . . . . 11
Figure 3.2 Element Ordering for Layer Specification . . . . 13
Figure 4.1 Brooks Chariot Wedge . . . . . . 16
Figure 4.2 Brooks Trilogy Outsole . . . . . . 18
Figure 4.3 Brooks Trilogy Outsole Model . . . . . 18
Figure 4.4 Load Configurations . . . . . . . 21
Figure 4.5 Chariot Stress Plot with Full Heel Load . . . . 22
Figure 4.6 Trilogy Stress Plot with Full Heel Load . . . . 22
Figure 4.7 Nodal Row 1 . . . . . . . . 23
Figure 4.8 Nodal Row 2 . . . . . . . . 23
Figure 4.9 Nodal Row 3 . . . . . . . . 24
Figure 4.10 Nodal Row 4 . . . . . . . . 24
Figure 4.11 Nodal Row 5 . . . . . . . . 25
Figure 4.12 Nodal Row 6 . . . . . . . . 25
Figure C.1 Chariot Stress Plot with Heel Strike Load. . . . C2
Figure C.2 Trilogy Stress Plot with Heel Strike Load . . . . C2
Figure C.3 Chariot Stress Plot with Full Foot Load . . . . C3

iv

 

Page

Figure C.4 Trilogy Stress Plot with Full Foot Load . . . . C3
Figure C.5 Chariot Stress Plot with Toe Off Load . . . . C4
Figure C.6 Trilogy Stress Plot with Toe Off Load . . . . C4
Figure C.7 Nodal Row 1 . . . . . . . . C5
Figure C.8 Nodal Row 2 . . . . . . . . C5
Figure C.9 Nodal Row 3 . . . . . . . . C6
Figure C.10 Nodal Row 4 . . . . . . . . C6
Figure C.11 Nodal Row 5 . . . . . . . . C7
Figure C.12 Nodal Row 8 . . . . . . . . C7
Figure 013 Nodal Row 9 . . . . . . . . C8
Figure C.14 Nodal Row 10. . . . . . . . C8
Figure C.15 Nodal Row 11. . . . . . . . C9
Figure C.16 Nodal Row 12. . . . . . . . C9
Figure C.17 Nodal Row 13. . . . . . . . C10
Figure C.18 Nodal Row 10. . . . . . . . C10
Figure C.19 Nodal Row 11. . . . . . . . C11
Figure C.20 Nodal Row 12. . . . . . . . C11
Figure C.21 Nodal Row 13. . . . . . . . C12
Figure C.22 Nodal Row 14. . . . . . . . C12
Figure C.23 Nodal Row 15. . . . . . . . C13

Chapter 1
INTRODUCTION

Running shoe design involves the study of the structure and dynamics of the
human while running using the fields of biomechanics and exercise physiology.
The goal of today’s running shoe design is twofold; to reduce injury, and to
improve performance by cutting down on muscular and cardio—vascular fatigue.
An average runner takes approximately 500 steps per mile and eighty percent of
the runners are regarded as heel strikers. They land on the outer part of their heel,
roll to the midfoot, and push off with the ball of their foot (metatarsal) and toes.
The most severe shock of the stride occurs when the foot first hits the ground.
This vertical impact force constitutes approximately 90—95% of the total shock
incurred by the runner and is in magnitude between two and three times the weight
of the runner [1,3]. Controlling motion and shock during impact is necessary to
reduce injury and provide comfort. The body has a natural motion during running
which has been termed pronation (See Figure 1.1). As the weight shifts from heel
to midfoot, the leg and hip flex to distribute the impact forces causing the foot to
roll inward, or pronate. Ten degrees of pronation may be acceptable although it is

felt that excessive pronation may lead to knee problems.

A more detailed look at the functional anatomy of the foot during strike is
described subsequently. Most runners use the entire foot during a stride, starting
with heel strike, then rolling onto the midfoot, and finally propelling off the
forefoot. Before the heel strike, the foot supinates (or is in the state of inversion).

That is, the foot is rotated at the ankle so that the inner edge of the foot is higher

Foot

 

Figure 1.1 Pronation.

relative to the outer edge. At heel strike, the ankle, knee and hip all flex to
cushion the shock. This flexing causes the foot to roll inward, or pronate. The
foot pronates for 55—85% of the period of foot strike [1]. In the final phase of the
step, the foot becomes more rigid to provide better lift. The hip and knee begin
extending, the heel and midfoot leave the ground, and the toes propel the foot off
the ground. The description of one step cycle explains the dynamics of the body to

which the shoe is subjected.

The objective of footwear designers is to produce a shoe that is more
responsive to the dynamics of the body. The goals of a running shoe design is to
provide stability and cushioning. These goals, however, are often contradictory as
soft shoe soles may provide good cushioning but bad stability and stiff shoe soles
may provide good stability but poor cushioning. Soles absorbing too much shock
return little energy to the body to enhance running. Shoe soles need the ability of
the material to return or reflect impact energy, called resilience. This property
helps the runner lift his foot at the end of a step. All of these factors are necessary

considerations in the design of running shoe soles.

A running shoe consists of several components to accomodate cushioning and
stability. The shoe consists of an ”upper” of leather and synthetic fabric which
constitutes the top and sides of the shoe. At the rear of the upper is the heel
counter, a firm cup which cradles the back of the heel and centers the foot to keep
it stable. The sole consists of a heel wedge of about 1/2” elevation to relieve strain
on the Achilles tendon. Below the heel wedge is the midsole, a layer of material
that provides both cushioning and stability. The bottom of the sole is an outsole
consisting of a durable layer of rubber with treads or studs that provide traction

and wear resistance.

The majority of the cushioning and stability is provided by the shoe sole
consisting of the wedge, midsole and outsole. These layers are now described in

detail.

The wedge and the midsole are usually made of EVA, a mixture of ethylene,
vinyl, and acetate, each providing a particular function. Ethylene provides
moldability, vinyl provides resilience and acetate provides structure and stiffness.
The wedge design usually consists of a single material or possibly two materials.
A common multiple material wedge consists of a heel section that contains two
overlapping triangular sections. The Brooks Chariot utilizes this wedge design

(See Figure 4.1).

The midsole is the most important part of the sole because it provides both
cushioning and stability. There are a variety of designs used in the midsole. One
example of a multidensity midsole is the Reebok Phase I Trainer which employs a
soft EVA under the heel and ball of the foot for cushioning, firmer EVA at the
inner or medial edge of the rear foot area to control pronation and hard EVA in

the heel wedge [2]. Some midsole designs are even more complex such as Muzik

Challenger II which contains two polyurethane bags filled with mineral oil inserted
into the sole under the ball and heel of the foot to emulate hydraulic shock

absorbers and cushion the body by distributing and equalizing body weight [4].

The outsole is an important part of the shoe sole because it reduces wear,
provides traction, and absorbs some impact. The outsole may be made of EVA,
styrene butadiene rubber or more abrasion resistant rubber such as Vibram’s
Infinity compound or Goodyear’s Indy 500 [2]. Recently shoe makers have started
to manufacture outsoles with blown rubber of styrene butadiene or carborylated
nitryl [2]. Blown rubber is lighter and provides better cushioning but is not as
durable. Early outsole design consisted of rectangular studs similar to a waffle to
absorb shock independently and to provide good traction. This design was
modified because each stud acted as a miniature stilt and reduced stability. New
waffle designs have lower stud profiles to retain shock absorbtion and traction but
reduce instability. In some cases, center studs were eliminated creating a gap
along the shoe’s central axis. This gap was intended to make the foot fall toward

the central axis in an effort to cut the tendency to fall off the axis and pronate.

As more information on how the body deals with shock and instability
becomes available, the designer will be able to develop shoes that are more

compatible with human motion.

Computers are being used in shoe design because of the increased
competition between manufacturers, the improved quality due to computerized
automation, and the increased sophistication of the design process. Puma and
Adidas have designed shoes that couple with a personal computer to track speed,
distance and compute calories burned [5]. Computers are also being used in the

manufacturing process but only on a limited basis. Computerized cutters now can

do some of the grading and cutting of upper materials using laser beams or high
velocity water. Moss Brown and Company are starting to use computerized
stitchers but stitching complex curves over 3D surfaces is beyond current
capabilities in manufacturing processes [2]. Computer aided design is also slowly
appearing in the industry. Computers are used to simplify the design of lasts (the
foot shape mold onto which the shoe is built) but the software has been difficult to
obtain. Converse is currently developing this type of software independently [1].

Nike is using CAD/CAM in shoe design development. Fully detailed drawings are
developed in 2D or 3D and these drawings can be scaled up or down automatically
on the computer. The studs on the outsole are added interactively. This design
information is then passed to the milling machines for cutting [6]. CAD can be
taken one step further in that the performance of shoe soles can be modeled using
finite element analysis. The shoe sole geometry, material properties, and load
configurations are input into a finite element program and the performance is

calculated. Different designs can be studied before actual prototypes are built.

This thesis discusses a design tool developed to aid in the finite element
analysis of the running shoe sole and presents two specific applications. Chapter
Two defines the finite element equations and the solution procedure employed by
ANSYS, a finite element analysis code available from Swanson Analysis Systems
Incorporated. Chapter Three describes a program written to speed the modeling
procedure and to set up the ANSYS input file. Chapter Four discusses the
modeling of two different shoe configurations; deflection and stress plots are
presented. Chapter Five includes the conclusions and possible future work. This

research was sponsored, in part, by a gift from the Brooks Shoe Company.

 

Chapter 2
FINITE ELEMENT METHODS

A purely analytical solution technique is not possible for a structure with an
irregular shape or multiple material properties. With the development of high
speed digital computers, complex structures could be analyzed using numerical
techniques such as the finite element method. Finite element methods involve the
discretization of a large continuous structure into a number of smaller elements.
The equations for each element with its individual boundary and loading conditions
can be assembled to describe the entire system. These equations were developed
for this application using the finite element code ANSYS on a PRIME 750 linked to
Tektronix graphics terminals. This chapter presents the equations used to study

the running shoe sole and the solution techniques used by ANSYS.

A static analysis was used to solve for displacements, stresses, and forces in
structures under the action of applied loads. The equilibrium equation for the

static analysis can be written in the matrix form

[Kl{u}={F} (2-1)
N
where [ K ] = total stiffness matrix 2 [ ke ]
m=1

{ u } = nodal displacement vector
N = number of elements

[ ke ] = element stiffness matrix

The resulting set of simultaneous linear equations was solved by the wave front

solution technique which will be described below.

The ANSYS program uses a wave front solution technique for the system of
simultaneous linear equations obtained from the finite elements. The number of
equations active at any point of the solution phase is the wave front size and the
ordering of the elements is crucial for minimizing the wave front size. This
minimization is important for reasons of efficiency because the computer time is
proportional to the square of the mean wave front size. The wave front size is also
dependent upon the sequence in which the elements are arranged. The node
numbers of all the elements are scanned to determine which element is the last to
use the node number. As the entire system of equations is assembled, the
equations for a node occurring last are solved in terms of the remaining unknowns
and eliminated from the matrix in core. The eliminated equations form the
stiffness matrix. Equations which contain a new node are added to the assembled
matrix. As nodes come and go during the solution process, the wave front size
expands and contracts. The following describes the wave front solution procedure

in equation form.
The active equations are:

L
2 Kkj uj = Fk (2.2)
j=1

where Kkj = stiffness term kj

uj nodal displacement j
Fk = nodal force k

k = row number

 

j = column number

L = number of equations

To eliminate an equation i = k, begin by normalizing

L
E Kij / Kii Uj = Fi / Kii (2.3)
i=1

This can be rewritten as

EKW uj = F*i (2.4)
j=1

where
K*ij = Kij / Kii (2.5)
F*i = Fi / Kii (2.6)

This equation is written to a file for later back substitution. Note, Kii is never zero
if the model is properly developed. The remaining equations are modified as

follows
K*kj = Kkj — Kki K*ij (2.7)

F*k = Fk - Kki F*i (2.8)

where k are i, so that

 

L-l
Z K*kj uj = F (2.9)
i=1

where k varies from 1 to n — 1. Having eliminated row i, the other rows are
eliminated by repeating the process. An example of this solution technique is

demonstrated in Appendix A.

 

Chapter 3
PROGRAM DESCRIPTION

The purpose of this chapter is to describe in detail an interactive program
developed as a design tool for the finite element analysis of running shoe soles.
The program structure is discussed and the advantage of using this program as a
specific preprocessor for ANSYS is delineated. The program was used to develop
the models of two different shoe sole configurations and to study their

characteristics.

A preprocessing program was written to overcome some of the labor
intensive characteristics inherent in the use of the finite element analysis. The
program uses a basic physical geometry and readily allows modeling of other
geometries by manipulation of the material properties, thus eliminating the time
consuming task of nodal coordinate definition. The program allows for the easy
definition and change of material properties, thus reducing the labor intensive task
of element property definition. The program discussed here interactively sets up

an ANSYS command file ready for processing.

The basic model consists of six layers of elements. There are two layers of
elements in the outsole, one layer of elements in the midsole, and three layers of
elements in the wedge. There are six elements from medial to lateral, and 14
elements from posterior to anterior in each column of the bottom three layers. The
wedge also has six elements per row but only extends eight elements per column

(See Figure 3.1). Due to the size limitations inherent in the educational version of

10

11

 

 

 

 

Figure 3.1 Element Model of a Shoe Sole.

ANSYS, the model is limited to six layers. The two layers of elements in the
outsole section allow for carving out portions in this area which is common in
outsole design. The three layers of elements in the wedge allow staircasing a
change in materials. The coordinate geometry was measured from a size nine
men’s Brooks Chariot running shoe. The basic outside dimensions of the Brooks
line of running shoes is very similar. This similarity allows modeling of a wide

range of Brooks running shoes using the preprocessor.

The type of element used is a 3D is0parametric solid. The element is defined
by eight nodes each having three degrees of freedom: translation in the x, y, and 2

directions.

The program sets up an ANSYS command file ready for analysis and is both
prompt and menu driven. The program has four major sections; the initialization,

the layer specifications, the element definition and the load specifications.

12

The first portion of the program consists of the initialization. The program
will prompt for the name of the command file in which to store the ANSYS input

file.

ENTER THE NAME OF THE ANSYS COMMAND FILE TO STORE THIS
INFORMATION. THE NAME SHOULD START WITH A ”C_” TO
INDICATE IT IS A COMMAND FILE.

The program then prompts for a title which is seen on all ANSYS outputs, such as

plots or tables.

ENTER THE TITLE OF THIS RUN.
The program then writes some necessary ANSYS commands. Finally, the nodal

coordinate information is written into the command file.

The next portion of the program consists of the prompts and menus for the
specifications of each layer. The input prompts are virtually the same for each
layer so only the specifications for the bottom of the outsole are shown as an
example. Also, the menus for specifying the Poisson’s ratio and elastic modulus
are virtually the same, thus, only the menus for the elastic modulus are shown
here. The program indicates to the user which layer is currently being specified.

For example,

YOU ARE SPECIFYING THE PROPERTIES FOR THE BOTTOM OF THE
OUTSOLE.

Then, the first menu appears.

DO YOU WANT THE ELASTIC MODULUS
1. THE SAME ACROSS THE ENTIRE LAYER?
2. SPECIFIED AT EVERY ELEMENT?
3. VALUES READ FROM AN EXTERNAL FILE?

If the user picks menu choice one, the program will prompt with

ENTER THE ELASTIC MODULUS

13

This elastic modulus will be written for every element in that layer. If the user

enters menu choice two, the program will prompt with

ENTER THE ELASTIC MODULUS FOR ELEMENT 1
This process is repeated until the property is specified for the entire layer. The
element specification begins at the lower left hand corner, proceeds to the right
and then continues to the toe (See Figure 3.2). Menu choice three responds with a

prompt to enter the name of the file in which the material properties are stored.

ENTER THE NAME OF THE FILE WITH THE ELASTIC MODULUS
PROPERTIES

After the input method has been decided, the program inquires of the user whether

the property information is to be permanently stored.

DO YOU WANT THIS ELASTIC MODULUS SPECIFICATION STORED
FOR FUTURE USE?

If the user responds ’yes’ the program will prompt for the name of the file.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

78 11
19 6

 

 

Figure 3.2 Element Ordering for Layer Specification.

14

ENTER THE NAME OF THE FILE TO STORE THIS LAYER’S ELASTIC
MODULUS INFORMATION.

The material properties can be stored regardless of the input method. The
program then writes the element definition and respective material property
specifications into the command file. The elements are automatically reordered to

reduce the wave front, however, the material specifications remain intact.

The program also allows for easy input of the load configuration. The load

related menu is

DO YOU WANT TO
1. DEFINE LOADS.
2. READ THE LOADS FROM AN EXTERNAL FILE.
3. EXIT.
Menu choice one will respond with the question of whether the user wants the

loads stored.

DO YOU WANT THIS LOAD DEFINITION STORED FOR FUTURE USE?

If the user responds ’yes’ the program prompts for the name of the file.

ENTER THE NAME OF THE FILE TO STORE THIS LOAD
INFORMATION

The program will then prompt for the total number of loads.

ENTER THE TOTAL NUMBER OF LOADS TO BE DEFINED

The next prompt is for the type of load, either deflection or force.

ENTER THE TYPE OF LOAD, D=DEFLECTION, F=FORCE.

Then, the label for the load is requested.

ENTER THE LABEL FOR THE LOAD. IF THE LOAD IS
A) DEFLECTION, THE OPTIONS ARE UX, UY, UZ, OR
ALL.
B) FORCE, THE OPTIONS ARE FX, FY, FZ, OR ALL.

15

Once the type of load and its label are known, it is necessary to define which nodes

these loads are applied to and the numeric value of the load.

ENTER THE STARTING NODE, ENDING NODE, NODE INCREMENT,
AND THE VALUE OF THE LOAD.

This prompting sequence continues until an EXIT is entered. Menu choice two will

ask for the file that holds the load configuration information.

ENTER THE NAME OF THE FILE WITH THE LOAD INFORMATION
The program then reads the information from the external file and writes it into
the ANSYS input file. Menu choice three exits the user from the program

completing the writing of the ANSYS input file.

This ANSYS preprocessor allows for a quick and easy initial study of model
configurations. This analysis provides some quantitative information, but the main
advantage of the analysis is the qualitative information it provides. It allows the
designer to create a library of layer configurations to mix and match to create a
wide range of shoe designs. The load definition is easy to define or change.
Basically, this program gives the designer an analysis tool to lead to a more exact
model definition for a complete quantitative analysis. The preprocessor program

and its subroutines are listed in Appendix D.

Chapter 4
RESULTS

This chapter discusses two shoes that were modeled using the ANSYS
preprocessor and solved using the ANSYS finite element program. The models
were subjected to four different load conditions to simulate the cycle of a step.

Stress and displacement plots are presented.

The first shoe modeled was the Brooks Chariot. The main area of design

interest in the Chariot is the two material wedge shown below (See Figure 4.1).

.‘ C, a}; "'3‘:

‘rpv-‘J

 

Figure 4.1 Brooks Chariot Wedge.

The wedge was modeled with a linear change in the elastic modulus in all the

elements defining the wedge. The midsole was modeled with the elastic modulus

17

the same across the entire layer of elements. Both layers in the outsole have the
same elastic modulus. Although there is a tread pattern on the outsole, it is
modeled as a solid because the majority of the outsole is in contact with the
ground. The Poisson’s ratio was assumed to be the same in all the materials in the

shoe sole.

The second shoe modeled was the Brooks Trilogy. The wedge in the Trilogy
is the same design used in the Chariot, but utilizes different materials. The model
uses elastic modulus values obtained through testing rather than using a linear
change in the property. These values were used in all three layers of elements
representing the wedge. The midsole also has an area of design interest. The area
under the metatarsal employs a material which is less stiff. The elements in this
area have a different elastic modulus. The outsole has a number of areas of
design interest. There are two wear plugs of a very stiff material. These plugs
were modeled by defining a high elastic modulus value for the elements in that
area. The Trilogy outsole also has a section that is carved out along the central
axis of the shoe. This area was modeled by defining a very small elastic modulus
in this area. The outsole also employs a number of different materials. Again, the
Poisson’s ratio was assumed to be the same for all materials. Figure 4.2 shows the
actual outsole, and Figure 4.3 shows how this outsole was modeled. The material

properties for each shoe are contained in Appendix B.

These two shoe models were subjected to four load configurations to simulate
a cycle of one step; heel strike, full heel, full foot, and toe off. The target loading
was 450 lbs. total force. Typical studies on shoes use a man with size nine feet
weighing approximately 150 lbs. As stated previously, the impact force is about
three times the weight of the runner resulting in a total force of 450 lbs. The loads

were deflection loads applied to the top layer of nodes. The forces were then

18

 

Mid Foot Section = 400 psi

 

Heel Section = 500 psi

I Wear Plugs = 600 psi

 

Figure 4.3 Brooks Trilogy Outsole Model.

 

19

summed to obtain the target force. The relationship between total deflection and
total force is almost linear, so only one iteration was required to adjust the
deflections so that a 450 lbs. total force loading was obtained. The nodes on the

bottom were constrained in all directions to give realistic ground reactions.

The heel strike load is a linearly decreasing deflection loading from medial to
lateral imposed on the top layer of nodes. The full heel load is a constant
deflection load. The fore foot load employs a linearly decreasing deflection load
from lateral to medial similar to the heel strike except imposed on different nodes.
And finally, the toe off load is a linearly increasing deflection load from medial to
lateral. Figure 4.4 shows the nodes which were subjected to the loading. The area
lightly shaded represents the nodes on the top layer subjected to deflection. The
area heavily shaded represents the nodes on the bottom layer which were

constrained in all directions.

The results for the full heel load configuration are presented in this chapter.

The results for the other loads are presented in Appendix C.

Stress plots are the first set of results to be presented. Figure 4.5 and Figure
4.6 show the stresses on the bottom of the shoe resulting from the full heel
loading. As the figures show, the effect of the carved out region in the Trilogy
outsole provides a more favorable stress distribution. The legend at the side of the
plot indicates the maximum and minimum stresses and the increment between
constant stress lines. The next set of results are the deflection plots. The

deflections for each nodal row in the area of interest are presented. A nodal row is

 

20

defined to be the nodal coordinate rows as the model goes from the heel to the toe.
The resultant forces are depicted on the top layer of nodes. The effect of the
carved out elements is apparent in both the deflection and resultant forces in nodal

rows four and five (See Figures 4.7 through Figure 4.12).

21

 

 

Full Heel

Heel Strike

 

 

Toe Off

Full Foot

Figure 4.4 Load Configurations

22

[I
e ‘4'

III.
II

:ll:::
'1

I
l::.
ll"

v I7.-
"'3‘“-
an
. l
l.-

liar

Ni“
11
Ill

I
v

.172
r :iiI-n
"Eur-'5'
Rae/4
\\\‘-—¢

I
“ll
\

cannot um FULLH

I"

 

Figure 4.5 Chariot Stress Plot with Full Heel Load.

=sun-2;:
new/.2:
fighting
I c 1

§

,0’
I

I {‘3
\“;EJ

 

- TRXLOGY UITH FULL

Figure 4.6 Trilogy Stress Plot with Full Heel Load.

23

Full Heel

       

T
m
C

 

TRILOGY

 

- "
I 0
I -4; '

165

 

 

 

 

Full Heel
25.0 21.2 88
l l l r l

Figure 4.7 Nodal Row 1.
311,,

25.1

 

 

 

 

CHARIOT

 

 

snoriilfi‘iI;
1’ -
M . . u
w . v
.A . —
. . w
, . u .
.
.r.pu1...h.ullrll
TELJI. . . .
... . c w
.A .- .
... a . w
t .. u .
-
p up“! > .4
c c . .
g . _
o . u o n
. . o . .
. . o o .
.. . . u .
. [offi-
. . . . u
. . . . .
. . . .
. . . u
. . L . .
o o . . .
(VII-"arr" -
. .
. .. . . (If
. . . . n
.. . . . .
g . g .
.\ s o u
.. . .
c - u .
_ “flint-(J.
\ C O- z
. . .. L
s \s o v
c c c .
MI . . _
L. \
I‘IIHNIHIr_
OIL

 

 

28.7 26.6 25.6

l l V l

"~.:A7-_»-----+u----- -----«-0-------vf

[“'--~~.I

315

29.7

 

 

 

 

 

ip---—---1o--.-On----

'------

 

 

I
’W
L

 

 

'f
I1

TRILOGY

74“;
.
anti .
. . o .
a . .
I . .
a a .
A .A a. .
. LIIrL
T1 .
u M u
4 n
o
.
.
fll
.
.

 

 

 

Figure 4.8 Nodal Row 2.

 

24

Full Heel

26.1

.4 . '~\

’1 \‘x‘

 

’f
l

"\U
0

ml

.
4

---
v-
n

 

 

22.8 20.8 2H}

19
‘1

.--.--L-------.------ ---.--.

\
‘1
“1|;‘

V

 

 

 

.1

t::::-3

‘1‘”

‘1

 

‘ “”' ""'":‘L‘"“"‘fi

.2

 

_--_--- ------ p-------
__---.- 00----

--’----_p------

 

a
_.
.
ol‘s
4

all
u.\ s
.. .
o.- n
s c. s
o o .
..... u
I‘d. .
it
. so. all
n . u
« ~
\ c
. .
\
(Ail-I

"'

--------.----.ir.-----Jc

 

- "in

 

[

 

.0 29.4

2 .5

.-’--f

.
.
u
.
.
u
o
c
.
o
a.
g
o
.

---
.‘-\-

Q
-‘--‘-

 

TRILOGY

J
I ."‘

 

AI!

.-.0..
o’-

-J--.

"\0

--a--v-fi

l'.
'l
l

-o---d-"{----Ooo

 

 

.0-‘h’-

"l":"'l"°"’\ Iv

 

Full Heel
28.3 25.4 23.4 2l5 2L3

l l l l

Figure 4.9 Nodal Row 3.

 

 

 

 

.--.--4

 

.- ---i
. -------d------dd

-O:§£o-o--a

-----\ -----

 

CHARIOT

‘4'

 

\. I

lift

2

l
I

U

 

 

T .

14.6 26.8

l l i l. l

0
°.

14.9

28.7

 

'J
-0 I,
I
J!

-
o l‘.’..

 

 

I

 

 

 

 

 

 

p-------p-.--.V-

[f

--\-
-\-
-‘ V
-‘
3.----“
‘ s
‘
‘L

 

TRILO GY

Figure 4.10 Nodal Row 4.

‘\---

v'v‘-ts-

 

 

25

Full Heel

26.5 23.7 220 198 20.0

11111

CHARIOT °

--\--

   
        

   
 

.
J--
ooooooo

    

 

.......................

27.6 15.5 9.4 14.6 25.6

l l l 1

 

 

 

 

 

‘ ' I {L I A ‘21
‘ ‘ L “I 1 S ‘4‘ Al’fl
I "‘ -fi‘ '1 A
6 '~ ~ "
2a .

- ----- . ------- -----a;-----;g:e:
1211:2131: °::;:-A.:.«-'
r4 ....... . ...... 1. ------ 1
TRILOGY L“'

 

 

 

 

Figure 4.11 Nodal Row 5.

Full Heel

CHARIOT

 

TRILOGY

 

Figure 4.12 Nodal Row 6.

L‘s a... a ...... _ g‘. .

Chapter 5
CONCLUSIONS

This thesis has shown the advantages of using this preprocessor as a tool for
the finite element analysis of running shoe soles. The program uses a basic
physical geometry and readily allows modeling of other geometries by
manipulation of the material properties. The program is very flexible and easily
accepts changes in loads or material properties. A library of layer designs can be
created to mix and match to produce a number of design prototypes. Although
some quantitative information is obtained through this analysis procedure, the
main benefit is the qualitative information it can provide. Design trends can be
identified by creating and analyzing a number of models with slight changes in
material properties, configurations, or layer definition. Once the design trends
have been identified, a precise model of the shoe can be created manually to

obtain quantitative information.

Future work could include using this same approach with the industrial
version of ANSYS which permits a greater number of element layers to be defined,
allowing for the development of more precise models. Also work could be done to
make the program more user friendly. These improvements could include
improved error checking, ”oops” features (to allow the designer to back up and
redefine a material property), or graphical displays. Graphics could be
implemented to indicate to the designer which element is under present

consideration.

26

27

There are a number of areas not addressed by this thesis. The program does
not account for any nonlinearity in the material properties. Also, the effect of the

interaction between the shoe upper and shoe sole has not been examined.

This thesis has presented a tool to aid the designer in the creation of a shoe
sole to reduce injury and improve performance. The preprocessor minimizes time
constraints placed on the designer allowing him to be more creative in the

development of shoe sole prototypes

REFERENCES

REFERENCES

. Baer, Tony. ”Designing for the Long Run.” Mechanical Engineering”
September 1984, pp. 66—75.

. Tucker, Jonathan B. ”Running Shoe Technology Picks Up the Pace.” High
Technology, March 1985, pp. 28-34.

. Cavanagh, Peter C. ”The Shoe-Ground Interface in Running.” American
Academy of Orthopeadic Surgeons Symposium on the Foot and Leg in Running
Sports. The C. V. Mosby Company, 1982, pp. 30—44.

”Athletic, Leisure Shoes Aid Fancy Footwork.” Design News April 4, 1984,
pp. 42—43.

. Ward, Sam. ”New Computerized Shoe Gives You a Run for Your Money.”
USA Today, July 8, 1985, p. 8.

. ”CAD/CAM Helps Nike Put Best Foot Forward”, IEEE Computer Graphics and
Applications February 1985, pp. 76—77.

Kohnke, Peter C. ”ANSYS Engineering Analysis System Theoretical Manual”,
Swanson Analysis Systems Incorporated, 1983.

Hull, Andrew J. ”Modelling Cylindrical Discontinuities in Running Shoe Soles
Using a Condensed Finite Element Formulation.” M. S. Thesis, Michigan State

University, 1985 .

28

APPENDICES

APPENDIX A

WAVE FRONT SOLUTION EXAMPLE

ANSYS uses a wave front solution procedure. This appendix shows the

solution of a three by three system of equations utilizing this solution technique.

The equations are

In - r y r w

 

 

 

 

 

 

k k k u f
11 12 13 1 1
k21 k22 k23 11‘12 l = 1 f2 ’ (A1
k k k u f
_31 32 33_ [31 131
The first equation is normalized so that (A2
u1 + (k12 / k11) u2 + (k13/ k11) u3 = f1/ k11 (A3
The normalized components are then
k*12 = k12 / k11 (A.A
k*13 = k13/ k11 (A:
f* = f1 / k11 (AG
The second iteration produces the following components
k*22 = [k22 - k21(k12 / k11)] (A.'

k*23 = [k23 —— k21(k13 / k11)] (A.:

k*32 = [k32 — k31(k12/ k11)]
k*33 = [k33 — k31(k13/ k11)]
f*2 = [f2 — k21(f1/ k11)]

f"‘3 = [f3 - k31(f1/ k11)]

which are assembled as

 

 

 

 

 

p l r 1 V

k* k* f"‘1
22 23 2

k* k* f*

_ 32 33] 3

 

The first equation becomes
u2 +[[k23 — k21(k13 / k11)] / [k22 — k21(k12 / k11)]] u3

= [f2 - k21(f1/ k11)] / [k22 — k21(k12 / k11)]

while the second equation becomes

k**33 u3 = f**3

u3 is solved for as

u3 = f**3 / k**3

where

k* *3 = [[k22 — k21(k12/ k11)] [k33 — k31(k13/ k11)]]
-— [[k32 - k31(k12/ k11)] [k23 — k21(k13/ k11)]]

f**3 = [[k22 — k21(k12/ k11)] [13 — k13(f1/ k11)]]
— [[k32 — k31(k12 / k11)] [f2 — k21(f1/ k11)]]

(A9
(A10
(A11

(A.12

(A.13

(A.14

(A.15

(Alt

(A1

(A1:

A—3

Solving this system of equations using Cramer’s Rule would yield the same result.
The advantage of using a wave front solution technique is the optimization of

computer time during the equation solution phase [8].

APPENDIX B

MATERIAL PROPERTIES FOR THE CHARIOT AND TRILOGY MODELS

This appendix contains the elastic modulus values in psi specified for each
element of the Chariot model and the Trilogy model. Poisson’s ratio was 0.25 for
all of the elements in both models. Note, the element numbers have been
reordered to reduce the size of the wave front. The elements start at the lower left
corner, proceed vertically, to the right, and finally toward the toe. The element

properties as specified remains intact, just the element numbers are changed.

B-2

ELASTIC MODULUS VALUES

ELEMENT CHARIOT TRILOGY
1. 260.0 500.0
2. 260.0 300.0
3. 130.0 350.0
4. 260.0 450.0
5. 260.0 450.0
6. 260.0 450.0
7. 260.0 500.0
8. 260.0 300.0
9. 130.0 350.0
10. 234.0 450.0
11. 234.0 450.0
12. 234.0 450.0
13. 260.0 500.0
14. 260.0 300.0
15. 130.0 350.0
16. 208.0 500.0

17. 208.0 500.0
18. 208.0 500.0
19. 260.0 600.0
20. 260.0 600.0
21. 130.0 350.0
22. 182.0 500.0
23. 182.0 500.0
24. 182.0 500.0
25. 260.0 500.0
26. 260.0 300.0
27. 130.0 350.0
28. 156.0 400.0
29. 156.0 400.0
30. 156.0 400.0
31. 260.0 500.0
32. 260.0 300.0
33. 130.0 350.0
34. 130.0 400.0
35. 130.0 400.0
36. 130.0 400.0
37. 260.0 500.0
38. 260.0 300.0
39. 130.0 350.0

ELEMENT

40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71 .
72.
73.
74.
75.
76.
77.
78.
79.

CHARIOT

260.0
260.0
260.0
260.0
260.0
130.0
234.0
234.0
234.0
260.0
260.0
130.0
208.0
208.0
208.0
260.0
260.0
130.0
182.0
182.0
182.0
260.0
260.0
130.0
156.0
156.0
156.0
260.0
260.0
130.0
130.0
130.0
130.0
260.0
260.0
130.0
260.0
260.0
260.0
260.0

TRILOGY

450.0
450.0
450.0
500.0
300.0
350.0
450.0
450.0
450.0
500.0
300.0
350.0
500.0
500.0
500.0
500.0
300.0
350.0
500.0
500.0
500.0
500.0
300.0
350.0
400.0
400.0
400.0
600.0
600.0
350.0
400.0
400.0
400.0
300.0
300.0
350.0
450.0
450.0
450.0
300.0

ELEMENT

80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
97.
98.
99.
100.
101.
102.
103.
104.
105.
106.
107.
108.
109.
110.
111.
112.
113.
114.
115.
116.
117.
118.
119.

CHARIOT

260.0
130.0
234.0
234.0
234.0
260.0
260.0
130.0
208.0
208.0
208.0
260.0
260.0
130.0
182.0
182.0
182.0
260.0
260.0
130.0
156.0
156.0
156.0
260.0
260.0
130.0
130.0
130.0
130.0
260.0
260.0
130.0
260.0
260.0
260.0
260.0
260.0
130.0
234.0
234.0

TRILOGY

300.0
350.0
450.0
450.0
450.0

10.0

10.0
350.0
500.0
500.0
500.0

10.0

10.0
350.0
500.0
500.0
500.0
500.0
300.0
350.0
400.0
400.0
400.0
500.0
300.0
350.0
400.0
400.0
400.0
300.0
300.0
350.0
450.0
450.0
450.0
300.0
300.0
350.0
450.0
450.0

ELEMENT

120.
121.
122.
123.
124.
125.
126.
127.
128.
129.
130.
131.
132.
133.
134.
135.
136.
137.
138.
139.
140.
141.
142.
143.
144.
145.
146.
147.
148.
149.
150.
151.
152.
153.
154.
155.
156.
157.
158.
159.

CHARIOT

234.0
260.0
260.0
130.0
208.0
208.0
208.0
260.0
260.0
130.0
182.0
182.0
182.0
260.0
260.0
130.0
156.0
156.0
156.0
260.0
260.0
130.0
130.0
130.0
130.0
260.0
260.0
130.0
260.0
260.0
260.0
260.0
260.0
130.0
234.0
234.0
234.0
260.0
260.0
130.0

TRILOGY

450.0
10.0
10.0

350.0

500.0

500.0

500.0
10.0
10.0

350.0

500.0

500.0

500.0

300.0

300.0

350.0

400.0

400.0

400.0

300.0

300.0

350.0

400.0

400.0

400.0

300.0

300.0

350.0

450.0

450.0

450.0

300.0

300.0

350.0

450.0

450.0

450.0
10.0
10.0

350.0

ELEMENT

160.
161.
162.
163.
164.
165.
166.
167.
168.
169.
170.
171.
172.
173.
174.
175.
176.
177.
178.
179.
180.
181.
182.
183.
184.
185.
186.
187.
188.
189.
190.
191.
192.
193.
194.
195.
196.
197.
198.
199.

CHARIOT

208.0
208.0
208.0
260.0
260.0
130.0
182.0
182.0
182.0
260.0
260.0
130.0
156.0
156.0
156.0
260.0
260.0
130.0
130.0
130.0
130.0
260.0
260.0
130.0
260.0
260.0
260.0
260.0
260.0
130.0
234.0
234.0
234.0
260.0
260.0
130.0
208.0
208.0
208.0
260.0

TRILOGY

500.0
500.0
500.0

10.0

10.0
350.0
500.0
500.0
500.0
300.0
300.0
350.0
400.0
400.0
400.0
300.0
300.0
350.0
400.0
400.0
400.0
300.0
300.0
350.0
400.0
400.0
400.0
300.0
300.0
350.0
400.0
400.0
400.0

10.0

10.0
350.0
400.0
400.0
400.0

10.0

 

 

 

ELEMENT

200.
201.
202.
203.
204.
205.
206.
207.
208.
209.
210.
211.
212.
213.
214.
215.
216.
217.
218.
219.
220.
221.
222.
223.
224.
225.
226.
227.
228.
229.
230.
231.
232.
233.
234.
235.
236.
237.
238.
239.

CHARIOT

260.0
130.0
182.0
182.0
182.0
260.0
260.0
130.0
156.0
156.0
156.0
260.0
260.0
130.0
130.0
130.0
130.0
260.0
260.0
130.0
260.0
260.0
260.0
260.0
260.0
130.0
234.0
234.0
234.0
260.0
260.0
130.0
208.0
208.0
208.0
260.0
260.0
130.0
182.0
182.0

TRILOGY

10.0
350.0
400.0
400.0
400.0
300.0
300.0
350.0
350.0
350.0
350.0
300.0
300.0
350.0
350.0
350.0
350.0
300.0
300.0
350.0
400.0
400.0
400.0
300.0
300.0
350.0
400.0
400.0
400.0

10.0

10.0
350.0
400.0
400.0
400.0

10.0

10.0
350.0
400.0
400.0

ELENIENT

240.
241.
242.
243.
244.
245.
246.
247.
248.
249.
250.
251.
252.
253.
254.
255.
256.
257.
258.
259.
260.
261 .
262.
263.
264.
265.
266.
267.
268.
269.
270.
271.
272.
273.
274.
275.
276.
277.
278.
279.

CHARIOT

182.0
260.0
260.0
130.0
156.0
156.0
156.0
260.0
260.0
130.0
130.0
130.0
130.0
260.0
260.0
130.0
260.0
260.0
260.0
260.0
260.0
130.0
234.0
234.0
234.0
260.0
260.0
130.0
208.0
208.0
208.0
260.0
260.0
130.0
182.0
182.0
182.0
260.0
260.0
130.0

TRILOGY

400.0
300.0
300.0
350.0
350.0
350.0
350.0
300.0
300.0
350.0
350.0
350.0
350.0
300.0
300.0
350.0
400.0
400.0
400.0
300.0
300.0
350.0
400.0
400.0
400.0
10.0
10.0
350.0
400.0
400.0
400.0
10.0
10.0
350.0
400.0
400.0
400.0
300.0
300.0
350.0

ELEMENT

280.
281.
282.
283.
284.
285.
286.
287.
288.
289.
290.
291.
292.
293.
294.
295.
296.
297.
298.
299.
300.
301.
302.
303.
304.
305.
306.
307.
308.
309.
310.
311.
312.
313.
314.
315.
316.
317.
318.
319.

CHARIOT

156.0
156.0
156.0
260.0
260.0
130.0
130.0
130.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0

TRILOGY

350.0
350.0
350.0
300.0
300.0
350.0
350.0
350.0
350.0
300.0
300.0
350.0
300.0
300.0
350.0

10.0

10.0
350.0

10.0

10.0
350.0
400.0
400.0
350.0
400.0
400.0
350.0
400.0
400.0
300.0
400.0
400.0
300.0
400.0
400.0
300.0
400.0
400.0
300.0
400.0

ELEMENT

320.
321.
322.
323.
324.
325.
326.
327.
328.
329.
330.
331.
332.
333.
334.
335.
336.
337.
338.
339.
340.
341.
342.
343.
344.
345.
346.
347.
348.
349.
350.
351.
352.
353.
354.
355.
356.
357.
358.
359.

CHARIOT

260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0

B-.1O

TRILO GY

400.0
300.0
400.0
400.0
300.0
400.0
400.0
250.0
400.0
400.0
250.0
400.0
400.0
250.0
400.0
400.0
250.0
400.0
400.0
250.0
400.0
400.0
250.0
300.0
300.0
200.0
300.0
300.0
200.0
300.0
300.0
200.0
300.0
300.0
200.0
300.0
300.0
200.0
400.0
400.0

 

ELEMENT

360.
361.
362.
363.
364.
365.
366.
367.
368.
369.
370.
371.
372.
373.
374.
375.
376.
377.
378.
379.
380.
381.
382.
383.
384.
385.
386.
387.
388.
389.
390.
391.
392.
393.
394.
395.
396.

CHARIOT

130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0
260.0
260.0
130.0

B—11

TRILOGY

200.0
300.0
300.0
150.0
300.0
300.0
150.0
300.0
300.0
150.0
300.0
300.0
150.0
300.0
300.0
150.0
400.0
400.0
150.0
300.0
300.0
150.0
300.0
300.0
150.0
300.0
300.0
150.0
300.0
300.0
150.0
300.0
300.0
150.0
300.0
300.0
150.0

APPENDIX C

STRESS AND DISPLACEIVIENT PLOTS

This appendix contains the stress and displacement plots for three load
configurations; heel strike, full foot, and toe off. The stress plots shown are the
stresses occurring on the bottom of the shoe sole. The effect of the carved out
elements in the outsole of the Trilogy is apparent in all of the Trilogy stress plots.
This effect is also apparent in the nodal deflection plots and resulting forces. The
legend at the side of the stress plots indicates the maximum and minimum stresses

and the increment between constant stress lines.

ITER-l
SIEESS PLOT

RUTO1SCRLING

CHARIOT UITH HEELSTRXK

 

Figure C.1 Chariot Stress Plot with Heel Strike Load.

r58;
SIGE

GUTO SCRLING
DIST-6.33
XF-l.88
YF-4.7
2F-.1O
HIDDEN

HX-134
”NO 0813?
INC

 

Figure C.2 Trilogy Stress Plot with Heel Strike Load.

RN 5

Y
1
00

S
I:
.7
T1
.p.
R
E

40“!”
Mill
\
0“
VI

.1
SS PLOT

ND Until-“ll".-
OD;

CC H-O

T0 SCRLING

c:
H
In
-4

. .d
u a
L»
no

H ~<x
2 H‘I'I
0 .0 II
. _.

on

W

tnqucv'uttu rung rap

 

Figure C.4 Trilogy Stress Plot with Full Foot Load.

«mm
.d.‘*
.. N\In

can
0"

'0

RH
55 PLOT

CC Haw-«DDT;
0 MM m

. ups-o onnnm

A—q
.. .

'1

1
p
S
I
S
S
a
2
D.
X
Y
2
H

H 3
zaxu‘l‘lflD-o
nu .0.

I- ago.

D

CHGRIOT UIT" TOEOFF

 

Figure C.5 Chariot Stress Plot with Toe Off Load.

3 mun-«nun-
D
2
D

3XN-(XON

I
F- .
F- .
F .
X
x.
m0.
INC-

 

Figure C.6 Trilogy Stress Plot with Toe Off Load.

11.6

 

V‘.‘
f
I

s

l

      

.1

 

 

 

 

 

 

 

 

 

16.0 20.0

 

110

Heel Strike
6.5

.1 1.1 1

 

 

4AA
I
I
.

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

all 7 1.. . 1.1. 0 Llamas“?! W
. adhfluurshrflwil ZIIWIL I)"; r.“ n “ DIVAII I) n u . .4 u
. o B .l I'Jlfllu . c . 2 .. . . 3 \ .. . _ . o
v s. SIIIHWKI ..u .s n . . LP" " u . _ n u u .
D 1 . O O O ‘- O - . O u
...E T ......r. ...: ..
x s . ll 5‘ I
. .1; . . . . . 3 i... . 7~ . rialELUTI.
II 8 wlrrslb '- a I \llI‘i-Ll \ . XI- IL‘I \
.5 " «74.11111... 1.34.]... ”TI 1 Vallw .....u.: L 6.11101. L. L." n u
. \ s s. . . . .
......m ... ....... u m nwU .......... n 1;." u n
s . . s . v . . x . . .
. . . . 1. 4 . . . .
. . . . . 9 s .V. rm . . . ~ .1 l .
..1.. 2 .1 1.1.1 R 0 V .1. ..1 2 u. 1....1."
q . B J _ . .4 1 3 a. . . .. . . 3 . . w. \ .
s. . .. w . . . w a 6 ~ \ .. . s. s. .. . n n
.u u ... .. d k ........... 6 .....
. . 2 It .31. .. u u . ”M .m m z! . Twp... “ 11.11....1VIW. - 111. u u
1.» WU . . . 41. TL S 2 N A .. 4 .1 . . 2 \ M L . . .
n o o s o c s c u \ a o .
.u 2...... 7 1 ...unw
" s. s. . u u _ C a D s. fix v u s u n . .\ .
. 2 I P b. s u . . W I Us: .. u . 1LH r u . H
I . .L . s s . .1 . x _
. n s. . u n u .~ .\ .. . u n .s . . . h
. . w. m v w. m .wc . .. .. . . . . x. . H
. ..lrl ' II I n . . v 7:. .
.IIIV”. in! X47339. A IlrII-O
. H L m I! A u
.u . . . .r L
WIV_ . f A A . _
1 (MIL; Li; _ “ {FALL .
all If?! I OIL

 

 

 

 

 

 

CHARIOT

TRILOGY

CHARIOT
TRILOGY

Figure C.8 Nodal Row 2.

 

C-6

Heel Strike

13.1 21.4 50.9 40.1 25.5

..LL V
L. v"‘; I

 

I '\
I l
l R
...... ~ ‘ ~ ~ .1 Li‘i. _ l
L J "’1‘ ------ .C:::::‘:‘sl+=:2e::«3?
"“---- ----""I-------1;.

8.0 142 263 42.8 33.6

 

 

 

 

 

 

'l

 

 

 

 

“““
O

 

 

 

 

 

 

 

Figure C.9 Nodal Row 3.

Heel Strike

127 204 287 360 27.8

CHARIOT

 

 

 

 

 

TRILO GY

 

 

 

 

 

 

 

Figure C.10 Nodal Row 4.

 

Heel Strike

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

E 1""u1fi-"n -"" ------ it"VT-ZJ:
L 'w!‘ """ j ....... ----- ...... 1.-...71 1
I A, ""T-----q---goo ..... —1—--’-'vv\'
-.. . ...... w---“ ______ 1 ...... s
TRILOGY / I f 3
....... ' --’----
1

 

 

 

 

 

Figure C.11 Nodal Row 5.

Full Foot

CHARIOT

 

TRILOGY

 

Figure C.12 Nodal Row 8.

 

Full Foot

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

CHARIOT
TRILOGY
Figure C.13 Nodal Row 9.
Full Foot
103 195 28.4 40.5 25.4
1"" 1 V it it 11
CHARIOT 1 1::_::::1i::::::‘:::: ---- 1:13--'-11‘-¢‘-=‘-==53~
[ I l ‘ “‘1 """"" i """"" ‘1'
85 15.7 28.7 46.1 308
m l l l l
TRILOGY t I"; I": ““““ ’1 "if? ------ i-
[ l l “"“T” W121

 

 

Figure C.14 Nodal Row 10.

 

 

 

 

 

 

 

 

Full Foot
10.3 28.2 29.8 42.2 27.2
41-1' 41 v g
cm. 1 [L--_.-,.:-.:::::i::::::-41,
[ r'"' --------- 1- ---------- 1
115 314 45.4 30.0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

V‘

1’ 1 7 "i """"" V l -------- l -
TRILOGY .6 / """‘L;'L:_‘:i:i:i:::’:::::':"l::::::::::l"-.
[ I "‘1 1

Figure C.15 Nodal Row 11.
Full Foot

91 173 252 36.4 22.3

-,,_ W V i J/
CHARIOT / 1'::;‘;:j'l::::::: """""" “i”
7 I l """ l """" l

3,3 188 242 354 22.1

1 " i i i i i

i _‘ --- ‘‘‘‘‘‘‘ I 1I

T 1 -- ------- l ---------- 1.
RILOGY (7 1 1 ......... :::::l:::::“'l"‘ :1
z I l E j

 

 

 

Figure C.16 Nodal Row 12.

C—lO

 

 

 

 

 

 

 

 

 

 

 

 

 

Full Foot
CHARIOT [ f l “““ l ‘ l
{ f l l l _____
I l l l l
f l I l """""" fl
TRILOGY If f I l AAAAAA 1
I l l l
Figure C.17 Nodal Row 13.
Toe Off
15.5 260 19.8 129 5.9

 

 

 

 

 

 

 

CHARIOT / A ...... Z -------- l """"""""""""""""""""" l
f. """"" - f ......... i ...... 1
z I L T. l
215 322 2L8 l2 4 6 4

TRILOGY ["-

 

- 7"v'w

Figure C.18 Nodal Row 10.

 

 

C—11

Toe Off

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure C.19 Nodal Row 11.

Toe Off
31.2 23.9 15.8

 

 

 

 

 

 

 

 

7 ''''''''''''''''''' Z _________________ I """"" l
L l l
313 21.8 16
.1, 1, M
..... fl
1 ,1
Y .......... f. _________ f V vvvvvv

 

 

 

 

L’Lfllfl

 

L Figure c.2o Nodal Row 12.

 

C—12

Toe Off

19.9 30.4 23.8 18.0 74

 

.1 1,1,1

 

f f ----.---L -- '
CHARIOT "4 --- 1‘“ i l .--.1 ........ 1
:L -------- J -------- r-"Mi'rjgj 1

 

 

 

 

 

‘‘‘‘‘

 

 

 

 

 

Figure C21 Nodal Row

Toe Off

 

13.

 

 

 

 

 

 

 

. 1 1 1.
1r _____ -«----+ _____ w
TRILOGY .... .1 u__ 1
-.--.---I)---- ".1”. II I

 

 

f """ T """ 1 lm'

 

...L ‘I’J
LP

 

L Figure C.22 Nodal Row 14.

 

C-13

Toe Off

........................

 

 

 

 

 

 

 

 

 

 

1 ll -1 1 1

CHARIOT f: l l 1 ""41
f I f 1 i 1

Z in”! ...... l 1

TRILOGY C l ..... J. ..... J 1
f I I F L l

 

 

Figure C.23 Nodal Row 15.

 

 

 

APPENDIX D

ANSYS PREPROCESSOR ROUTINES FOR SHOE SOLE MODELING

This appendix contains the program and its subroutines developed as a
preprocessor for ANSYS. These routines were written on a Prime 750 computer
and compiled under Fortran77. Also included is the command file used to compile

and load the program and its associated subroutines.

 

000 0

000 0000 0

000 000 0000

PROGRAH DRIVER

THIS PROGRAH IS THE DRIVER FOR THE CREATION OF AN ANSYS INPUT
FILE OF A RUNNING SHOE SOLE HODEL.

SEHHON/ LOG / ASKEVERYPR. ASKEVERYEH. GETPRL. GETEHL. PUTPRL. PUTE
+

COHHON/ PREHSPEC / ELASHOD(AOO). POISRATIOIAOO)

LOGICAL ASKEVERYPR. ASKEVERYEH. GETPRLo GETEHLp PUTPRL. PUTPRL

SET UP THE INITIALIZATION FOR THE ANSYS COHHAND FILE. THIS INCLUDES
URITING THE NODAL COORDINATE INFORHATION.

CALL INIT
DEFINE THE HATERIAL SPECIFICATIONS FOR ALL LAYERS IN THE OUTSOLE

CALL BOTOSOLE
CALL TOPOSOLE
CALL HIDSOLE

CALL BOTVEDGE
CALL HIDUEDGE
CALL TOPUEDGE

REORDER THE HATERIAL PROPERTY INFORHATION FOR EACH ELEHENT IN ORDER
TO REDUCE THE HAVE FRONT. URITE THE ELEHENT ORDER INTO THE ANSYS FILE.

CALL VRITELEH

DEFINE THE LOAD SPECIFICATIONS
CALL LOADS

"RITE THE FINAL INFORHATION NEEDED TO COHHENCE THE SOLVING PROCESS
CALL SOLVER

CLOSEIB)
END

 

SUIROUTINE INIT

THIS SUBROUTINE URITES THE INI
COHHAND FILE. THIS INFORHATION
THE NAHE OF THE COHHAND FILE.
COORDINATES.

CHARACTER'32 CFILENAHE. TITLE
PROHPT THE COHHAND FILE NAHE

PRINT'o’ ENTER THE NAHE OF THE ANSYS COHHAND FILE TO STORE THIS
+HODEL INFORHATION.’

PRINT'.’ THE NAHE SHOULD START WITH A 'C_” TO INDICATE IT IS A
+COHHAND FILE.’

READ(1.’(A)’) CFILENAHE

OPENISoFILE=CFILENAHE)

C WRITE THE INITIAL SECTION OF THE COHHAND FILE

URITE(6.IOOO)

1000 FORHAT(’ANSYS’)
URITE(6.2000)

2000 FORHAT('/INTER.NO’)
URITEI6o2SOO)

€500 FORHAT(’/PREP7’)

C PROHPT FOR THE TITLE. URITE IT TO THE FILE» AND CONTINUE UITH PREP?
g COHHANDS

AL INFORHATION NEEDED FOR THE ANSYS
NCLUDES. A NUHBER OF PREP7 COHHANDS.
E TITLE OF THE RUN. AND THE NODAL

TI
I
TH

000 000000

PRINTI.’ ENTER THE TITLE OF THIS RUN'
READ(1.'(A)’) TITLE
URITEI6o3000) TIT E
3000 FORHAT(’/TITLE. ’.A32)
VRITE(6.4000)
(’ET.I.45’)

3000 FORHAT
g’ VRITE THE NODAL COORDINATE INFORHATION

OPEN(10.FILE=’XYZNODES’)

8500(109.) XOYDZ

VRITE(6.SOOO) I.X.Y.Z
5000 FORHAT(’N.'.13.‘.’. I
10 CONTINUE

CLOSE(10)

RETURN

END

O.5.’.’-FlO.5v’.’.FIO.5)

SUBROUTINE CLSALL

THE PURPOSE OF THIS SUBROUTINE IS TO CLOSE ALL UNITS THAT UERE
OPENED FOR THE LAYER SPECIFICATIONS BEFORE THEY ARE USED AGAIN

0000

CLOSEI
RETURN
END
SUBROUTINE ASK
TEE PURPOSE OF THIS SUBROUTINE IS TO DETERHINE THE HETHOD OF
[FPUT FOR THE HATERIAL PROPERTY SPECIFICATIONS AND TO DETERHINE
THESE PROPERTIES NEED TO BE STORED FOR FUTURE USE.
CHARACTER'I ANS

+glO-HI'ION/ LOG / ASKEVERYPR. ASKEVERYEH. GETPRL. GETEHL. PUTPRL. PUTE

0 00000

 

 

 

non non MOOO 000 000 unnn nnn non unnn

00

LOGICAL ASKEVERYPR.ASKEVERYEH.GETPRLoGETEHLoPUTPRLvPUTEHL

ASKEVERYPR = .FALSE.
ASKEVERYEH I .FALSE.

PROHPT FOR THE INPUT HETHOD FOR THE POISSON’S RATIO INFORHATION

PRINTfio’ DO YOU UANT THE POISSON‘S RATIO’

PRINT“.’ 1. THE SAHE ACROSS THE ENTIRE LAYER?’
PRINT”:’ 2. SPECIFIED AT EVERY ELEHENT?’
PRINT!.’ 3. VALUES READ FROH AN EXTERNAL FILE?’
READI19') IANSUER

CHECK FOR VALID INPUT

IFIIANSUER.NE.1 .AND. IANSUER.NE.2 .AND. IANSUER.NE.3) THEN
PRINTI.’ ANSUER OUT OF RANGE. ’

GO TO 1

ENDIF

SET THE APPROPRIATE LOGICAL VARIABLES

IF(IANSUER.EQ.2) ASKEVERYPR = .TRUE.
IFIIANSUER.EO.3) THEN

CALL GETPR

GETPRL 8 .TRUE.

ENDIF

ASK IF THE POISSON’S RATIO VALUES SHOULD BE STORED FOR FUTURE USE

PRINT'.’ DO YOU UANT THIS POISON‘S RATIO SPECIFICATION STORED FOR

* FUTURE USE?’
READIlo’IA1’) ANS

CHECK FOR VALID INPUT

IFIANS.NE.’Y’ .AND. ANS.NE.’N’) THEN
PRINT'.’ ENTER EITHER Y OR N. ’

GO TO 3

ENDIF

SET THE APPROPRIATE LOGICAL VARIABLES

IFIANS.EQ.’Y') THEN
PUTPRL = .TRUE.
CALL PUTPR

ENDIF

PROHPT FOR THE INPUT HETHOD FOR THE ELASTIC HODULAS INFORHATION

PRINT'o’ DO YOU UANT THE ELASTIC HODULAS’

PRINT'o’ I. THE SAHE ACROSS THE ENTIRE LAYER?’
PRINT'o’ 2. SPECIFIED AT EVERY ELEHENT?’
PRINT“:’ 3. VALUES READ FROH AN EXTERNAL FILE?’

READIIol) IANSUER
CHECK FOR VALID INPUT

IF(IANSUER.NE.I .AND. IANSUER.NE.2 .AND. IANSUER.NE.3) THEN
PRINTfié’ ANSUER OUT OF RANGE. ’

GO TO
ENDIF

SET THE APPROPRIATE LOGICAL VARIABLES
IF(IANSUER.EQ.2) ASKEVSPYEU = .TRUE.
IF(IANSVER.EQ.3) THEN
CALL OETEn
GETEHL = .TRUE.
ENDIF

“SK IP'TUE ELASTIC HODULAS VALUES SHOULD as STORED FOR FUTURE USE

 

PRINTN.’ DO YOU UANT THIS ELASTIC HODULAS SPECIFICATION STORED FOR

+ FUTURE USE?’
READII.’(A)’) ANS

CHECK FOR VALID INPUT

IFIANS.NE.’Y’ .AND. ANS.NE.’N’) THEN
PRINTlo’ ENTER EITHER Y OR N. ’

GO TO 4

ENDIF

SET THE APPROPRIATE LOGICAL VARIABLES

IFIANS.EQ.’Y’) THEN
PUTEHL 3 .TRUE.
CALLFPUTEH

D0

000

000

SUBROUTINE HATSPECSIISTART.IEND.INC)

THE PURPOSE OF THIS SUBROUTINE IS TO PROHPT THE USER TO INPUT
THE HATERIAL PROPERTIES BASED ON THE HETHOD OF INPUT CHOSEN AND
STORED IN LOGICAL VARIABLES

COHHON/ PREHSPEC / ELASHOD(400). POISRATIO(AOO)
COHHON/ LOG / ASKEVERYPR. ASKEVERYEHo GETPRL. GETEHL. PUTPRL. PUTE

+HL
COHHON / STUFF / FIRST.PRALLoEHALL.ICNTER

LOGICAL FIRSToASKEVERYPRoASKEVERYEH-GETPRL9GETEHLoPUTPRLoPUTEHL

THE HETHOD OF INPUT IS TO SPECIFY A MATERIAL PROPERTY UHICH IS
THE SAHE ACROSS THE ENTIRE LAYER. PROHPT FOR THAT VALUE.

IF((.NOT.ASKEVERYPR).AND.(.NOT.GETPRL).AND.(FIRSTI) THEN
PRINTI.’ ENTER POISSON‘S RATIO ’

READ(1.!) PRALL

ENDIF

IFII.NOT.ASKEVERYEH).AND.(.NOT.GETEHL).AND.(FIRST)) THEN
PRINTGo’ ENTER THE ELASTIC HODULAS ’

READI1.!) EHALL

ENDIF

SPECIFYING THE POSSON’S RATIO FOR THE LAYER

DO 10 I=ISTARToIENDoINC
ICNTER I ICNTER + l

C
E PROHPT FOR A VALUE AT EVERY ELEHENT

IF(ASKEVERYPR) THEN
100 VRITEII.IOOO) ICNTER
0 FORHATI' ENTER POISSON‘S RATIO FOR ELEHENT v.13)

REAOII.») POISRATIO(I)
READ THE VALUE FROH AN EXTERNAL FILE

ELSEIFIGETPRL) THEN
READI7ofl) POISRATIO(I)

IggA¥ALUE IS THE SAHE ACROSS THE LAYER. VRITE THAT VALUE INTO THE

ELSE
POISRATIOII) = PRALL
ENDIF

00000

000 0000 0

000

0000

IF THE VALUES ARE TO BE SAVEO. URITE TO AN EXTERNAL FILE

000

IFIPUTPRL) URITE(11.!) POISRATIO(I)
SPECIFYING THE POSSON’S RATIO FOR THE LAYER

PROHPT FOR A VALUE AT EVERY ELEHENT

IFIASKEVERYEH) THEN
URITEI1.2000) ICNTER

2000 FORHATI’ ENTER ELASTIC HODULAS FOR ELEHENT ’.13)
READI1.!) ELASHODII)

C
5 READ THE VALUE FROH AN EXTERNAL FILE
'ELSEIFIOETEHLI THEN

READ(8.!) ELASHODII)
ELSE

000000

C
E AHRAYALUE IS THE SAHE ACROSS THE LAYER. URITE THAT VALUE INTO THE
C
ELASHODII) = EHALL
C ENDIF
5 IF THE VALUES ARE TO BE SAVED. URITE TO AN EXTERNAL FILE

IFIPUTEHL) URITE(12.!) ELASHOD(I)
1° CONTINUE

RETURN

END

 

0 00000 0 0000 0 00000

0 0000

SUBROUTINE PUTPR
THE PURPOSE OF THIS SUBROUTINE IS TO PROHPT FOR THE FILE NAHE IN
HI ICH THE POISON’S RATIO PROPERTIES ARE TO BE VRITTEN AND OPEN
THAT FILE 0N UNI 11

CHARACTER'32 PRPUTNAHE

PRINT.INFENTER THE NAHE OF THE FILE TO STORE THIS LAYER S POISON‘ S
+RA

READ(1.’(A)’ ) PRPUTNAH E

OPEN(11.FILE E-PRPUTNAHE)

ESTUR

SUBROUTINE GETPR

THE PUPOSE OF THIS SUBROUTINE IS TO PROHPT FOR THE FILE UITH
THE POISON’S RATIO PROPERTIES AND TO OPEN THAT FILE ON UNIT 7

CHARACTER'32 PRFILE
PRINT'.’ ENTER THE NAHE OF THE FILE VITH THE POISSON‘S RATIO PROPE

+RTIES
RE '(A)') PRFIL
DPEN(7 FILE= PRFILE)E

SUBROUTINE PUTEH

THE PURPOSE OF THIS SUBROUTINE IS TO PROHPT FOR THE FILE NAHE IN
VHICH THE ELASTIC HODULAS PROPERTIES ARE TO BE VRITTEN AND OPEN
THAT FILE ON UNIT I2

CHARACTER'32 EHPUTNAHE

PRINTlv' ENTER THEN NAME OF THE FILE TO STORE THIS LAYER S ELASTIC
+HODULAS INFORHATIO
R ’(A)’) EHP TNAHE
OP$N(12. .FILE= EHPUTNAHE)

SUBROUTINE GETEH

THE PURPOSE OF THIS SUBROUTINE IS TO PROMPT FOR THE FILE VITH
THE ELASTIC HODULAS PROPERTIES AND TO OPEN THAT FILE ON UNIT 8

CHARACTER132 EHFILE

PRINT- ENTER THE NAHE OF THE FILE WITH THE ELASTIC HODULAS PROPE
RTIES.

REAOII . A) ) EHFILE

OPEN(8 FI LE-EHFILE)

RETURN

END

 

000 000 00000

00000

00000

000

00000 000

SUBROUTINE BOTDSOLE
THIS SUBROUTINE PROHPT FOR THE HATERIAL PROPERTIES OF THE BOTTOH OF
THE OUTSOLE ANO STORES THIS INFORHATION UNTIL THE ELEHENTS ARE VRITTEN
INTO THE COHHAND FILE.

COHHON / STUFF / FIRST.PRALL.EHALL.ICNTER
LOGICAL FIRST

INDICATE TO THE USER UHICH LAYER HE IS DEFINING
{EINT'.’ YOU ARE SPECIFYING PROPERTIES FOR THE BOTTOM OF THE OUTSO
+

FIND OUT HOU THE MATERIAL PROPERTIES UILL BE SPECIFIED

ICNTER = 0
CALL ASK

DEFINE THE HATERIAL PROPERTIES
THIS SUBROUTINE CALL OCCURS TUICE BECAUSE OF THE UAY THE ELEHENTS
ARE ORDERED.
ISTART I 1
IEND I 283
INC I 6
FIRST I .TRUE.
CALL MATSPECS(ISTART.IEND.INC)
START I 289
IEED. 394
FI IRST FA SE
CALL HATSPECS(ISTART.IEND.INC)
CALL CLS
RETURN
END
SUBROUTINE TOPOSOLE
THIS SUBROUTINE PROMPT FOR THE MATERIAL PROPERTIES OF THE
THE OUTSO LE AND ST TORES THIS INFORHATION UNTIL THE ELEHENTST ARE 0URITTEN
NTO THE COHHAND FILE-

COHRON / STUFF / FIRST.PRALL.EMALL.ICNTER
LOGICAL FIRST

INDICATE TO THE USER UHICH LAYER HE IS DEFINING
ICNTER I O
PRINTi.’ YOU ARE SPECIFYING PROPERTIES FOR THE TOP OF THE OUTSOLE-
+
FIND OUT HOU THE MATERIAL PROPERTIES VILL BE SPECIFIED
CALL ASK
DEFI INE THE MATERIAL PROPERTIES
THIS SUBROUTINE CALL OCCURS TUICE BECAUSE OF THE VAY THE ELEHENTS
ARE ORDERE
ISTART I 2
IEND I 284
INC I 6
FIRST I .TRUE.
CALL MATSFECS(ISTART.IEND.INC)
ISTART = 290
IEND. 395
RST FALS
CALL MATSPECS(ISTART.|END.INC)

CALL CLSALL
EETU RN

 

00000

000

00000 000

00000

000

000 000

SUBROUTINE MIDSOLE

THIS SUBROUTINE PROMPT FOR THE MATERIAL PROPERTIES OF THE MIDSOLE
AN STO THIS INFORMATION UNTIL THE ELEMENTS ARE URITTEN INTO

D RE
THE COMMAND F LE.

COMMON / STUFF / FIRSToPRALLoEMALL-ICNTER
LOGICAL FIRST

INDICATE TO THE USER UHICH LAYER HE IS DEFINING

ICNTER I O
PRINTI.' YOU ARE SPECIFYING PROPERTIES FOR THE MlDSOLE.’

FIND OUT HOV THE MATERIAL PROPERTIES WILL BE SPECIFIED
CALL ASK
DEFINE THE MATERIAL PROPERTIES
THIS SUBROUTINE CALL OCCURS TUICE BECAUSE OF THE WAY THE ELEMENTS
ARE ORDER
ISTART I 3
IEND I 285
IN I
FIRST I .TRUE.
CALL MATSPECS(ISTART.IEND.INC)
ISTART = 291
IEND. I 396
NC 3
IRST I

CALL MATSPECS(ISTART.IENDleC)
CALL CLSA ALL

RETURN

E D

SUBROUTINE BOTUEDGE
THIS SUBROUTINE PROMPT FOR THE MATERIAL PROPERTIES OF THE BOTTOM OF
THE HEDGE AND STORES THIS INFORMATION UNTIL THE ELEMENTS ARE URITTEN
INTO THE COMMAND FILE.

COMMON / STUFF / FIRST.PRALL.EMALL:ICNTER
LOGICAL FIRST

INDICATE TO THE USER UHICH LAYER HE IS DEFINING
ICNTER = O
PRINTI.’ YOU ARE SPECIFYING PROPERTIES FOR THE BOTTOM OF THE UEDGE
*I
FIND OUT HOV THE MATERIAL PROPERTIES HILL BE SPECIFIED
CALL ASK
DEFINE THE MATERIAL PROPERTIES
ISTART I A
IEND I 285
INC I 6
FIRST I .TRUE.
EALL MATSPECS<ISTART.IENDoINC)

RST I .FALSE.
CATLM CLSALL

 

00000

000

000 000

000 00000

000 000

D—10

SUBROUTINE MIDHEDGE

THIS SUBROUTINE PROMPT FOR THE MATERIAL PROPERTIES OF THE MIDDLE OF
THE HE GE AND STORESETHIS INFORMATION UNTIL THE ELEMENTS ARE URITTEN

INTO THE COMMAND

COMMON / STUFF / FIRST PRALL EMALLuICNTER
LOGICAL FIRST

INDICATE TO THE USER UHICH LAYER HE IS DEFINING
ICNTER I O
PRINTI.' YOU ARE SPECIFYING PROPERTIES FOR THE MIDDLE OF THE WEDGE
+.'
FIND OUT HOV THE MATERIAL PROPERTIES HILL BE SPECIFIED
CALL ASK
DEFINE THE MATERIAL PROPERTIES
ISTART I 5
IEND I 287
INC I
FIRST I .TRUE.
CALL MATSPECS(ISTART.IENDleC)
FI I .FA SE.

CALL CLSALL
RETURN
END

SUBROUTINE TOPVEDGE
THIS SUBROUTINE PROMPT FOR THE MATERIAL PROPERTIES OF THE TOP
THE HEDGE AND STORES THIS INFORMATION UNTIL THE ELEMENTS ARE WRITTEN
INTO THE COMMAND FILE.

COMMON / STUFF / FIRST.PRALL.EMALL-ICNTER
LOGICAL FIRST

INDICATE TO THE USER UHICH LAYER HE IS DEFINING

ICNTER = 0 .
PRINTiv' YOU ARE SPECIFYING PROPERTIES FOR THE TOP OF THE UEDGE.‘

FIND OUT HOV THE MATERIAL PROPERTIES HILL BE SPECIFIED
CALL ASK
DEFINE THE MATERIAL PROPERTIES
ISTART = 6
IEND I 288
INC I 8
FIRST I .TRUE.
CALL MATSPECS(ISTART.IEND.INC)
F ST I .FALSE.
CALL CLSALL
RETURN
END

 

000 000 0 0000

500
1000
2000

FORMAT(’MAT.’ I3)
URITE(6¢IOOO) I.POISRATIO(I)
FORMAT<’NUXY.’.I3.‘.’.F10.4)
HRITE(6o2000) IcELASMOD(I)
FORMAT(’EX.'.I3.‘o’oF10.4)

D-11

SUBROUTINE NRITELEM

THE PURPOSE OF THIS SUBROUTINE IS TO NRITE THE PROPER MATERIAL
PROPERTIES FOR EACH ELEMENT. AND THEN DEFINE THAT ELEMENT

COMMON/ PREMSPEC / ELASMOD(400). POISRATIO(400)

INTEGER ONE.TUO.THREE¢FOUR.FIVE.SIX.SEVEN.EIGHT

OPEN THE FILE WITH THE ELEMENT DEFINITION
OPEN(9.FILEI’ELEMENTS’)
VRITE THE MATERIAL PROPERTIES FOR EACH ELEMENT

DO 10 II1o396
URITEISvSOO) I

C
S HRITE THE ELEMENT DEFINITION

3000
10

0000

00

200

000 H000

U 0000

READ(9o!) ONEoTUOoTHREEoFOUR.FIVE.SIX.S
HRITEI6o3000) ONE.THO.THREE.FOUR.FIVEoS
FORHAT(’EO’O14....DIAO’I’D[49,..IEAO’U’
CONTINUE

CLOSE(9)

RETURN

END

EN.EIGHT
SEVENuEIGHT

I
. 5.'.'.IA.'.'.I4.'.'.M>

V
X
I

SUBROUTINE LOADS

THE PURPOSE OF THIS SUBROUTINE IS TO DEFINE THE LOADS TO APPLY
TO THE MODEL

CHARACTER'I LOADTYPE
CHARACTERII NS
CHARACTERIA
CHARACTERi32 LOADFILE
CHARACTER'32 STRLOAD

LOGICAL NRIT
VRIT I .FALSE.

l"

ABEL

ICNT I 0

CONTINUE

ICNT I ICNT + l

PROMPT FOR THE METHOD OF INPUT FOR THE LOAD DEFINTION

PRINTlo’ DO YOU RANT TO ’

PRINTlo’ 1. DEFINE LOADS.’

PRINTlo’ 2. READ THE LOADS FROM AN EXTERNAL FILE.’
PRINTIo’ 3. EXIT.’

READ(I.I) IANS
CHECK FOR VALID INPUT

IF(IANS.NE.1 .AND. IANS.NE.2 .AND. IANS.NE.3) THEN

PRINTIi’ ANSNER OUT OF RANGE. '

THE FIRST TIME THROUGH. ASK IF THE LOAD DEFINITION NEEDS TO BE
STORED FOR FUTURE USE

IF((IANS.EO.I).AND.(ICNT.EO.I)) THEN
PRINTI.’ DO YOU RANT THIS LOAD DEFINITION STORED FOR FUTURE USE7'
READ(lo'(A)’) ANS

 

000

000

000 0000

‘000

0000 000

0000 000"

D—12

CHECK FOR VALID INPUT

IF(ANS.NE.’Y’ .AND. ANS.NE.’N’) THEN
PRINT'.’ ENTER EITHER Y OR N. ’

GO TO 3

ENDIF

SET APPROPRIATE LOGICAL VARIABLES

IF¢ANS.EO.’Y’) THEN
URIT I .TRUE.

PROMPT FOR THE NAME OF THE FILE TO STORE THIS INFORMATION
AND OPEN UNIT 14

PRINTI.’ ENTER THE NAME OF THE FILE TO STORE THIS LOAD INFORMATION
+

REAO<1.'IA>I> STRLOAD
OPEN(14.FILE=STRLOAD>

PROMPT FOR THE NUMBER OF LOADS TO BE DEFINED AND VRITE INTO THE FILE

PRINTI.’ ENTER THE TOTAL NUMBER OF LOADS TO BE DEFINED.’
READ(I.!) NUMLOADS

URITE(14.!) NUMLOADS

ENDIF

ENDIF

THE LOAD IS TO BE USER DEFINED. PROMPT FOR THE LOAD DEFINITION

IF(IANS.EO.1) THEN ‘

PRINT'.’ ENTER THE TYPE OF LOAD. D I DEFLECTION. F = FORCE.’
READCI.’(A)’) LOADTYPE

PRINTfl.’ ENTER THE LABEL FOR THE LOAD. IF THE LOAD IS’
PRINTI.’ A) DEFLECTION THE OPTIONS ARE UX. UY. 02 OR ALL’
PRINT'.’ B) FORCE. THE OPTIONS ARE FX. FY. F2. OR ALL’
READ(1.’(A)’) LABEL

CHECK FOR VALID INPUT

IF(LOADTYPE.EO.’D’ .AND. LABEL.NE.’UX’ .AND. LABEL.NE.’UY’ .AND. L
+ABEL.NE.’UZ’ .AND. LABEL.NE.’ALL’) THEN

PRINT'.’ INCORRECT LABEL. ’

GO TO 4

ENDIF

IF(LOADTYPE.EO.’F’ .AND. LABEL.NE.’FX’ .AND. LABEL.NE.’FY’ .AND. L
+ABEL.NE.’FZ’ .AND. LABEL.NE.’ALL’) THEN

PRINTU.’ INCORRECT LABEL. ’

GO TO 4

ENDIF

PROMPT FOR WHICH NODES THIS LOAD IS TO BE APPLIED
AND URITE THIS INTO THE COMMAND FILE

PRINTI.’ ENTER THE STARTING NODE. ENDING NODE. NODE INCREMENT. AND
+THE VALUE OF THE LOAD.’

READ(I.I) ISTART. IEND. INC. VALUE

VRITE(6.1000) LOADTYPE.ISTART.LABEL.VALUE.IEND.INC

ooo FORMAT<AI.’.’.13.’.’.A4.’.’.F10.4.’..'.I3.’.’.I3)
‘ORITE THE LOAD INFORMATION TO A FILE IF REOOESTEO

IF(URIT) VRITE(14.1000) LOADTYPE.ISTART.LABEL.VALUE. IEND.INC

THE LOADS ARE TO BE READ FROM AN EXTERNAL FILE. PROMPT FOR THE FILE
NHICH CONTAINS THE VALUES AND VRITE IT TO THE COMMAND FILE

ELSEIF ANS.EO.2) THEN

ENTER THE NAME OF THE FILE UITH THE LOAD INFORMATION.’
A)’) LOADFILE

ILEILOADFILE)

) NUMLOADS

I
O
9
o
o

(
Z (
3 F
3 N

2000

10

100

D—13

DO 10 III.NUMLOADS

READI13o2000) LOADTYPE.ISTART.LABEL.VALUE.IEND.INC
FORMAT(AI.1X.I3.1X.A4.1X.F10.4v2Xo13.1X.13)
URITE(6.1000) LOADTYPE.ISTART.LABEL.VALUE.IEND.INC
IF(URIT) URITE(14.1000) LOADTYPE.ISTART.LABEL.VALUE. IEND.INC
CONTINUE

CLOSE(13)

GO TO 100

ELSE

GO TO 100

ENDIF

GO TO 200

CONTINUE

CLOSE(14)

RETURN

END

SUBROUTINE SOLVER

C
C THE PURPOSE OF THIS SUBROUTINE IS TO URITE THE ANSYS
g INFORMATION THAT IS NEEDED FOR SOLUTION TO THE COMMAND FILE

6000

NRITE(6.500)
FORMAT(’KRF.I’)
URITEI6.1000)

FORMAT(’ITER.1.I.I’)
NRITE(6.2000)
FORMAT(’AFVRIT’)
NRITE(6.3000)
FORMAT(’FINISH’)
NRITE(6.4000)
FORMAT(’/EXEC’)
NRITE(6.5000)
FORMAT(’/INPUT.27’)
URITE(6.6000)
FORMAT(’FINISH’)
RETURN

D—14

FTN77 DRIVER -DEBUG ~FULLCHECK
FTN77 INIT -DEBUG -FULLCHECK
FTN77 CLSALL -DEBUG -FULLCHECK
FTN77 ASK -OEBUG -FULLCHECK
PTN77 MATSPECS -DEBUG -FULLCHECK
FTN77 PUTPR ~DEBUG -FULLCHECK
FTN77 PUTEM -DEBUG -FULLCHECK
FTN77 GETPR -DEBUG -FULLCHECK
PTN77 GETEM -DEBUG ~FULLCHECK
FTN77 BOTOSDLE -DEBUG -FULLCHECK
FTN77 TOPOSOLE -DEBUG -FULLCHECK
FTN77 MIDSOLE -DEBUG -FULLCHECK
FTN77 TOPUEDGE -DEBUG -FULLCHECK
FTN77 MIDNEDGE -DEBUG -FULLCHECK
FTN77 BOTNEDGE -DEBUG -FULLCHECK
FTN77 URITELEM -DEBUG -FULLCHECK
FTN77 LOADS -DEBUG -FULLCHECK
FTN77 SOLVER -DEBUG -FULLCHECK

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