Multiscale topology optimization for coated structures with multifarious-microstructural infill

In engineering, cellular structures are often manufactured with coating for protection or to improve certain functionalities. This paper concentrates on the design of coated structures consisting of an exterior solid shell and an inner base part filled by multifarious microstructures, and a novel multiscale topology optimization method is proposed. Firstly, a representation method and a material interpolation model are developed to describe a coated structure with multifarious-microstructural infill and define its properties, respectively. At macroscale, coating-base distribution is determined by the parametric level set method (PLSM) with re-initialization. To optimize structural performance at a computationally affordable cost, controllable kinds of microstructures are considered, and their spatial distribution over the whole base region is optimized by the ordered SIMP method with a threshold scheme. At microscale, the configurations of microstructures are generated by PLSM with the numerical homogenization method, in which the volume fraction limit values correspond to the design variables of the ordered SIMP method in macroscale. The compliance minimization problem subject to a material mass constraint is investigated, and sensitivity analysis is derived. Numerical examples are provided to demonstrate the effectiveness of the proposed method.