Differential evolutionary topology optimization using shape representation based on KL expansion

Abstract

Topology optimization is a structural optimization method in which design variables are updated based on the design sensitivity of the objective function and constraints to approach the optimal structure. However, the solution obtained by optimization based on design sensitivity is a local optimum, which is not suitable for nonlinear and multimodal problems. In this study, we propose a topology optimization method based on differential evolution, which is an excellent computational method for global search. While differential evolution has high global search capability, it is computationally expensive, so it is effective to reduce the number of design variables. Therefore, the Karhunen-Loève (KL) expansion is applied to the density function and the terms with small eigenvalues are truncated to express the structural density with a limited number of design variables. We have also proposed a method of binarization by gradually increasing the penalty parameter. In order to construct the optimization algorithm, the optimization is performed for the stiffness maximization problem of a cantilever beam, and the validity of the proposed method is verified by comparing it with the optimization results based on the design sensitivity.