A two-stage approach for structural topology optimization

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This paper proposes a two-stage optimization algorithm for topology optimization based on the homogenization method. The multistage approach aims to increase the stability and overall efficiency of homogenization-based topology optimizations. The homogenization method employed in this study uses a material constraint, which seeks the optimal configuration with the least amount of compliance. In a two-stage approach, a finite element model with a large element size was employed in the first stage of the topology optimization. The purpose of using a smaller number of finite elements is to increase the chances of attaining a good topology while the associated computational cost is limited. At the end of the first optimization stage, the optimal topology obtained is subsequently used to construct an initial topology in a finite element model with a smaller element size. The second-stage topology optimization is thus performed with the goal of capturing a topology of good quality with detailed contour description. A number of smoothing strategies for converting the optimal topology into the initial topology in a finer FEM model space are entailed. The stability and effectiveness of the proposed two-stage topology optimization algorithm are illustrated by two structural design problems.