Concurrent optimization of macrostructures and material microstructures and orientations for maximizing natural frequency

In this paper, an efficient concurrent optimization method of macrostructures, and material microstructures and orientations is proposed for maximizing natural frequency. It is assumed that the macrostructure is composed of uniform material with the same microstructure but with various orientation. The bi-directional evolutionary structural optimization (BESO) method is applied to optimize the macrostructure and its material microstructure under a given weight constraint. Meanwhile, the optimality condition with respect to local material orientation is derived and embedded in the two-scale design of macrostructures and material microstructures. Numerical examples are presented to demonstrate the capability and effectiveness of the proposed optimization algorithm. The results show that the current design of macrostructures, material microstructures, and local material orientation greatly improves structural dynamic performance.