A modified model for concurrent topology optimization of structures and materials

Abstract

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. This paper presents a modified concurrent optimization model with three kinds of design variables. At the micro scale, topological design variables are employed for describing the distribution of base material within a material cell so that the material microstructure can be defined. At the macro scale, in addition to topological design variables for describing the distribution of material with microstructure within the design domain, microstructure orientation angles are introduced for defining material axis directions at different locations. Numerical examples have shown that significant improvement in the performance of optimized designs can be achieved.