Multi-material topology optimization considering material cost and displacement constraints

Abstract

This study proposes a multi-material topology optimization approach considering the effect of material cost. The proposed method can derive the optimized configuration, the choice of materials to use, and their arrangement, which can minimize material cost while satisfying a maximum displacement constraint. An approach based on Discrete Material Optimization with material definition independence and symmetry is employed to represent the arrangement and geometry of multiple materials for an isotropic linear elastic model. This structural representation method solves the problems of local minima solutions regarding the order of material definitions and the introduction of physically difficult-to-interpret parameters, which have been issued in the past. As a result, the proposed method is highly compatible with actual product design systems. As a strength constraint, a maximum displacement constraint based on the p-norm idea is introduced. The objective function is defined as the material cost function assuming the introduced structural representation approach. Finally, a study of several numerical examples is performed. The validity and effectiveness of the proposed approach is demonstrated.

Keywords

• topology optimization
• multi-material
• material cost
• displacement constraint
• finite element method