Concurrent design of composite macrostructure and multi-phase material microstructure for minimum dynamic compliance

A method for the concurrent topology optimization of composite macrostructure and periodic microstructure with multi-phase materials is proposed, where the objective is to minimize the dynamic compliance of the macro structure under harmonic excitation force. Based on a material interpolation scheme with multiple materials, the sensitivity of the dynamic compliance with respect to the design variables on the two scales is analyzed. The concurrent topology optimization model of composite macrostructure and multi-phase periodic microstructure is built, where constraints are imposed on the material volumes. Correspondingly, a numerical technique and an optimization procedure based on the bi-directional evolutionary structural optimization (BESO) method are presented. Results of numerical examples show that the proposed method is effective for the concurrent design of composite macrostructure and material microstructure for minimum dynamic compliance.