Concurrent topology optimization of structures and their composite microstructures

• A new tow-scale topology optimization algorithm is proposed based on BESO.
• Optimization is carried out for structures and their composites simultaneously.
• Homogenization is used for linking the analyses at the macro and micro levels.
• Various optimal macrostructures and microstructures are reported and discussed.

Different from the independent design of macrostructures or material microstructures, a two-scale topology optimization algorithm is proposed by using the bi-directional evolutionary structural optimization (BESO) method for the concurrent design of the macrostructure and its composite microstructure. It is assumed that the macrostructure is made of composite materials whose effective properties are calculated through the homogenization method. By conducting finite element analysis of both structures and materials, sensitivity numbers at the macro- and micro-scale levels are derived. Then, the BESO method is used to iteratively update the macrostructures and the composite microstructures according to the elemental sensitivity numbers at both scales. Some 2D and 3D numerical examples are presented to demonstrate the effectiveness of the proposed optimization algorithm. A variety of optimal macrostructures and optimal material microstructures have been obtained.