Some considerations on multi-material topology optimization using ordered SIMP

Ordered solid isotropic material with penalization (SIMP) interpolation has emerged as an interesting technique in multi-material topology optimization. The computational cost of this approach is independent of the number of materials considered. However, an unusual behavior is observed when using the original material model equations (Zuo and Saitou in Struct Multidisc Optim 55:477-491, 2017). This paper proposes modified material and cost models for ordered interpolation. This new ordered SIMP presents the desired interpolation characteristics discussed in the original paper and is suitable for non-monotonic properties. Density filtering is used to remove checkerboard patterns and ensure mesh convergence. A threshold projection is tailored for multi-material ordered SIMP in order to reduce the presence of intermediate densities. A comparative analysis of the original interpolation with the modified one is made through various numerical examples. Some issues related to the filtering techniques and boundary effects on an ordered SIMP are identified.

Automated summary

This paper proposes modified material and cost models for ordered solid isotropic material with penalization (SIMP) interpolation, addressing the unusual behavior observed when using the original material model equations. The new ordered SIMP presents the desired interpolation characteristics and is suitable for non-monotonic properties, using density filtering and threshold projection to remove checkerboard patterns and reduce the presence of intermediate densities. A comparative analysis of the original interpolation with the modified one is conducted through various numerical examples, identifying some issues related to the filtering techniques and boundary effects on an ordered SIMP.