Topology optimization for the design of periodic microstructures composed of electromagnetic materials

Authors:
Tsuyoshi Nomura;Shinji Nishiwaki;Kazuo Sato;Koichi Hirayama
Affiliations:
Toyota Central R&D Laboratories, Inc., Nagakute, Aichi, Japan;Kyoto University, Kyoto, Japan;Toyota Central R&D Laboratories, Inc., Nagakute, Aichi, Japan;Kitami Institute of Technology, Kitami, Japan
Venue:
Finite Elements in Analysis and Design
Year:
2009

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Abstract

Electromagnetic structures that incorporate certain structural periodicities are known to display special behavior when subjected to electromagnetic waves, and can be designed to have specific functions such as inhibiting the intrusion of electromagnetic waves of certain frequencies into the periodic structure. This paper proposes a novel topology optimization method for periodic microstructures of electromagnetic materials using the concept of propagation behavior to implement designs that inhibit electromagnetic wave propagation. First, a way to apply topology optimization to the design of electromagnetic structures is briefly discussed. Next, the design specifications are clarified, and a new objective function is proposed to satisfy these specification. The optimization algorithm is developed using sequential linear programming (SLP) and the adjoint variable method (AVM). Several numerical examples are provided to confirm that the proposed method is capable of automatically generating physically reasonable periodic structures that have desired specified functions without relying on a predefined basic lattice.