Topology optimization is a computational design methodology that is used to find topologies of optimal design, that match design goals. Application of topology optimization in the area of electromagnetics is extremely interesting, since for many electromagnetic design problems the topology of inclusion structures in materials or components in devices can have a dramatic effect on the interaction of the designed structure with the electromagnetic waves. The success of the use of topology optimization for design of metamaterials, antennas, waveguides, etc. reported in literature suggests the importance of research into effective uses of topology optimization in electromagnetic design problems.The purpose of this dissertation is to investigate efficient electromagnetic analysis methods that can be combined with the method of topology optimization, as well as to develop a new way of using topology optimization to design electromagnetic devices with transformable complex surface geometry, using the concept of origami.The first part of the dissertation focuses on the investigation of a topology optimization framework for design of periodic structures for electromagnetic applications, using a rigorous and efficient finite element analysis method. The second part introduces a topology optimization based design method for origami folding patterns. To illustrate its use, the origami design method is employed to design frequency selective surfaces for electromagnetic applications, that can transform in their surface geometry to alter their working frequency through folding and unfolding.
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