A modified model for concurrent topology optimization of structures and materials

This paper presents a study on the concurrent topology optimization of a structure and its material microstructure. A modified optimization model is proposed by introducing microstructure orientation angles as a new type of design variable. The new model is based on the assumptions that a structure is made of a material with the same microstructure, and the material may have a different orientation within the design domain of the structure. The homogenization theory is applied to link the material and structure scales. An additional post-processing technique is developed for modifying the obtained design to avoid local optima caused by the use of orientation angle variables.Numerical examples are presented to illustrate the viability and effectiveness of the proposed model. It is found that significant improvement in structural performance can be achieved by optimizing the orientation of microstructures in concurrent topology optimization of structures and materials.