Evolutionary structural optimization for stress minimization problems by discrete thickness design

Stress minimization is a major aspect of structural optimization in a wide range of engineering designs. This paper presents a new evolutionary criterion for the problems of variable thickness design whilst minimizing the maximum stress in a structure. On the basis of finite element analysis, a stress sensitivity number is derived to estimate the stress change in an element due to varying the thickness of other elements. Following the evolutionary optimization procedure, an optimal design with a minimum maximum stress is achieved by gradually removing material from those elements, which have the lowest stress sensitivity number or adding material onto those elements, which have the highest stress sensitivity number. The numerical examples presented in this paper demonstrate the capacity of the proposed method for solving stress minimization problems. The results based on the stress criterion are compared with traditional ones based on a stiffness criterion, and an optimization scheme based on the combination of both the stress minimization and the stiffness maximization criteria is presented.