A Novel Topology Optimization Methodology Based on Energy Minimization Via α-β Swap Move

Abstract

To facilitate the creation of new holes and to prevent simultaneously a checkerboard pattern in a topology optimization (TO) procedure, a novel TO methodology based on energy minimization via α-β swap is proposed. An energy function, measuring simultaneously the accuracy and piecewise smoothness of a new topology, is proposed and employed to determine the optimal way to update the current topology. Also, the proposed alpha-beta swap operations enable different materials to be exchanged with one another, and thus can create new holes naturally without including any additional mechanism. Moreover, the embedded smooth term in the energy function is capable of constraining the irregularity of the topology and thus hindering the checkboard pattern. Two case studies, an inductive power transfer system and a printed circuit board (PCB) to demonstrate the feasibility and advantage of the proposed methodology. The tools used for the two case studies include Matlab and Ansys. As demonstrated by the numerical results, the proposed methodology outperforms conventional methods in terms of both enhancing the performance parameter and constraining the checkerboard pattern.

Topology Optimization for Electromagnetics: A Survey

“…In [152] the Allen-Cahn equation is used to update the design variables using the phase-field method of section III-C4. In [153] a method based on the α − β Swap Move theorem to improve the hole generation capability of boundary-based TO methods (e.g., the level-set described in III-C3) is proposed. In [154] the min-cut theorem is used to define a new methodology for 3D problems.…”