Lightweight Optimization Design of Structures with Multiple Cellular Materials

Cellular materials have been widely applied to a lightweight design of structures. The mechanical properties of those materials depend on their microstructures at the microlevel/mesolevel, and the optimizaiton design of lightweight structures using multiple cellular materials is still challenging. This paper develops a topology optimization algorithm for a lightweight design of structures constructed by multiple cellular materials with specified microstructures. The mechanical properties of cellular materials are homogenized according to their microstructures and then integrated into topology optimization. The topology optimization problem is defined by minimizing structural compliance subject to a specified mass constraint. In order to identify the distribution of multiple cellular materials within the design domain, the multiple design variables are introduced based on the volume fractions of multiple cellular materials within each element. Meanwhile, the homogenized mechanical properties are linearly interpolated, and multiple floating projection constraints are imposed on the relaxed design variables to push them toward 0 or 1. Numerical examples demonstrate the successful implementation of the proposed algorithm by the optimal distribution and selection of multiple cellular materials.