Analytical sensitivity analysis for decoupling multi-scale topology optimization of composites

The present study proposes an analytical sensitivity analysis for a so-called multi-scale topology optimization introduced to minimization of compliance of three dimensional structural problems. The multi-scale topology optimization is a strategy to optimize topology of microstructures applying a decoupling multi-scale analysis based on a homogenization method. The stiffness of the macrostructure is maximized with a prescribed material volume of constituents under linear elastic regime. A gradient-based optimization strategy is applied and an analytical sensitivity approach based on the adjoint method is proposed to reduce the computational costs. It was verified from a series of numerical examples that the proposed method has great possibility for microscopic advanced material designs.