Stress-based topology optimization based on global measure of distort energy density

A modified bi-directional evolutionary structural optimization (BESO) method for stress minimization topology optimization of continuum structures was proposed. A global measure was formulated by Kreisselmeier-Steihauser aggregation function to reduce the computational cost. The sensitivity numbers were derived by the computationally efficient adjoint variable method. The optimization process was stabilized by a sensitivity filtering and correction scheme. Design variables were updated by BESO with its material addition and removal scheme that drove the initial structure gradually evolved to the optimal design. The effectiveness of the proposed method was verified by three representative numerical examples. The efficiency of the topology optimization process was significantly improved by the proposed method. Compared with the compliance minimization design, the proposed method with appropriate stress norm parameter can effectively alleviate stress concentration. The maximum stress values of the optimal designs showed various degrees of decrease, thus enhancing the strength of structures. BESO method using discrete variables avoids the stress singularity and obtains the black-and-white design. © 2020, Zhejiang University Press. All right reserved.