Stress relaxation and sensitivity weight for Bi-directional evolutionary structural optimization to improve the computational efficiency and stabilization on stress-based topology optimization

Abstract

Stress-based topology optimization is one of the most concerns of structural optimization and receives much attention in a wide range of engineering designs. To solve the inherent issues of stress-based topology optimization, many schemes are added to the conventional bi-directional evolutionary structural optimization (BESO) method in the previous studies. However, these schemes degrade the generality of BESO and increase the computational cost. This study proposes an improved topology optimization method for the continuum structures considering stress minimization in the framework of the conventional BESO method. A global stress measure constructed by p-norm function is treated as the objective function. To stabilize the optimization process, both qp-relaxation and sensitivity weight scheme are introduced. Design variables are updated by the conventional BESO method. Several 2D and 3D examples are used to demonstrate the validity of the proposed method. The results show that the optimization process can be stabilized by qp-relaxation. The value of q and p are crucial to reasonable solutions. The proposed sensitivity weight scheme further stabilizes the optimization process and evenly distributes the stress field. The computational efficiency of the proposed method is higher than the previous methods because it keeps the generality of BESO and does not need additional schemes.