Different from the independent optimization of macrostructures or materials, a two-scale topology optimization algorithm is developed in this paper based on the bi-directional evolutionary structural optimization (BESO) method for concurrently designing a macrostructure and its composite microstructure. The objective is to minimize the mean compliance of the structure which is composed of a two-phase composite. The effective properties of the composite are calculated through the homogenization method and integrated into the finite element analysis of the structure. Sensitivity analysis for the structure and microstructure is conducted by the adjoint method. Based on the derived sensitivity numbers, the BESO approach is applied for iteratively updating the topologies for both the structure at the macro level and the microstructure of composite at the micro level. Numerical examples are presented to validate the effectiveness of the proposed optimization algorithm.
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