A time-saving FEM-based approach for structural topology optimization with exact boundary representation

Abstract

A time-saving finite element method (FEM) based approach for structural topology optimization with exact boundary representation is proposed in this work. The optimization process consists of two loops. The first loop adopts a fixed and fairly coarse mesh. Afterwards, the second loop reconstructs the material domain and hence the boundary representation becomes exact. A novelty of this work is that our two-loop approach is realized with the domain reconstruction (not just remeshing). The convergence of the second loop is only made possible by imposing the volume constraint in an exact fashion. The proposed approach can save a substantial amount of computational time while allowing the exact representation of boundary (no grayscale throughout the second loop). For the two-loop approach, its computational time can be reduced to merely 13.6% of that for the single loop approach. The optimized structure is also found independent of mesh size. In addition, the two-loop approach resolves the issue of a deteriorated connectivity of the reconstructed domain Ω once the constrained volume is set extremely small.

Keywords

• topology optimization
• exact boundary representation
• time-saving
• reaction-diffusion equation
• level set function