Some considerations on multi-material topology optimization using ordered SIMP

• Published in: Structural and multidisciplinary optimization 2022-09, Vol.65 (9), Article 261
• Main Authors: da Silveira, Otavio Augusto Alves, Palma, Lucas Farias
• Format: Article
• Language: English
• Subjects: Algorithms; Computational Mathematics and Numerical Analysis; Computing costs; Engineering; Engineering Design; Filtration; Finite element method; Interpolation; Isotropic material; Optimization; Research Paper; Theoretical and Applied Mechanics; Topology optimization; Variables
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-022-03379-7

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.