Multiscale concurrent topology optimization for cellular structures with multiple microstructures based on ordered SIMP interpolation

This paper presents a novel multiscale concurrent topology optimization method for cellular structures with various types of microstructures to obtain a superior structural performance at an affordable computation cost. At macroscale, different microstructures are regarded as different materials in a multi-material topology optimization. An ordered solid isotropic material with penalization (SIMP) interpolation model, which is efficient for solving multi-material topology optimization problems without introducing any new variables, is employed to generate an overall structure layout with predetermined multiple materials. At microscale, each macroscale element is viewed as an individual microstructure. All macroscale elements with the same material are represented by a unique microstructure. A parametric level set method (PLSM) is applied to evolve the shape and topology of the representative microstructures, whose effective properties are evaluated by a numerical homogenization method. The connectivity of adjacent microstructures is guaranteed by a kinematical connective constraint. Using the proposed method, the macrostructural topology as well as the locations and configurations of microstructures can be simultaneously optimized. Numerical examples are provided to test the effectiveness of the proposed method.