An Effective Topological Representation and Dimensionality Reduction Approach for MultiMaterial Structural Topology Optimization

Abstract

Topology optimization is among the most effective tools for innovative and lightweight structural designs. Multimaterial design is considered to achieve better structural performance than singlematerial design. To significantly reduce the design space dimensionality and facilitate the optimization of multimaterial structural design problems, this study proposes an effective topological representation and dimensionality reduction approach based on the materialfield series expansion (MFSE) model. In the proposed method, a specified number of material phases is described within a single material field with a piecewise Heaviside projection function. The topology optimization problem is solved by determining the optimal MFSE coefficients. Owing to the single materialfield topological description and series expansion, the number of design variables is independent of the finite element mesh and the number of material phases. In terms of dimensionality reduction, the proposed method outperformed all reported stateoftheart algorithms for multimaterial topology optimization. The validity and universality of the proposed method are illustrated in two and threedimensional numerical examples.