Multiple materials layout optimization in a layered structure

To obtain the optimal layout of multiple materials in a layered continuum with clear interfaces between materials, the series solid isotropic material with penalization (S-SIMP) method is proposed in this work. In practical engineering, many types of materials could be used simultaneously in a structure for reducing either cost or weight of structure. For the convenience of manufacturing, the inter-material boundaries should be simple and clear. Supposing m types of material in a structure to be layout, in the present method, in each sub-optimization, there are only k(<m) types of materials selected in layout optimization. Therefore, there are (m - k +1) sub-optimizations in finding the final layout of materials. In the first sub-optimization, these k types of materials have higher modulus than the rest materials. Simultaneously, the rest materials are replaced with void or the softest material. After each sub-optimization, the first material (with the highest modulus among the current materials) will be fixed in the next sub-optimization. The design domain of structure decreases step by step. Numerical examples are given to demonstrate the validity and efficiency of the presented approach.