Concurrent topology optimization of structures and orientation of anisotropic materials

Abstract

Both the distribution and orientation of anisotropic materials have great effects on the performance of civil and mechanical structures. Taking the maximum structural stiffness as the design objective, a concurrent method for determining the optimal distribution and orientation of orthotropic materials is proposed in this article. The method for determining material orientation theoretically overcomes the ‘repeated global minimum’ phenomenon, which often occurs in strain-based and stress-based methods, when the material is shear ‘strong’. Then, the concurrent optimization methodology for material distribution and orientation is developed by introducing an independent discrete topology variable and continuous material orientation angle. The optimized designs of material distribution and orientation are obtained concurrently by the gradient-based bi-directional evolutionary structural optimization method and the proposed material orientation optimization method. Numerical two- and three-dimensional examples are presented to demonstrate the effectiveness of the proposed concurrent optimization algorithm.