A post-processing method to remove stress singularity and minimize local stress concentration for topology optimized designs

Abstract

Topology optimization is becoming a popular choice in designing components as it can reduce a component's weight while mostly maintaining its performance. In the designs from a discrete topology optimization, the boundaries are usually jagged and post-processing is required to smooth such boundaries. A post-processing method is presented in the paper to smooth the jagged boundaries. The post-processing method includes a boundary identification algorithm that identifies the external boundaries and internal boundaries (voids). The external boundaries can be further separated into the optimized jagged boundaries to be smoothed and the originally existing boundaries to be kept. A spline fitting method was then applied to smooth the jagged boundaries. For internal voids, a void replacement method was developed to replace the polygonal voids to eliminate the sharp corners and stress singularity around the voids. A novel location optimization method was developed to optimize the void locations with the objective of minimizing the stress concentration around voids. The sensitivity of the maximum stress around all voids was calculated. The p-norm function that approximates the maximum function and the material derivative method that calculates the domain derivative were used to obtain the sensitivity. A gradient-based solver was applied to solve the optimization problem and all voids were moved simultaneously during the line search. Case studies demonstrated that the developed approach can effectively smooth the jagged boundaries and minimize the stress concentration around the internal voids.