An incremental interpolation scheme with discrete cosine series expansion for multi-material topology optimization

Topology optimization is a powerful tool for structural design, while its computational cost is quite high due to the large number of design variables, especially for multi-material systems. Herein, an incremental interpolation approach with discrete cosine series expansion (DCSE) is established for multi-material topology optimization. A step function with shape coefficients (i.e., ensuring that no extra variables are required as the number of materials increases) and the use of the DCSE together reduces the number of variables (e.g., from 8400 to 120 for the optimization of the clamped-clamped beam with four materials). Remarkably, the proposed approach can effectively bypass the checkerboard problem without using any filter. The enhanced computational efficiency (e.g., a ∼89.2% reduction in computation time from 439.1 s to 47.4 s) of the proposed approach is validated via both 2D and 3D numerical cases.