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.

拓扑优化已成为设计组件时的一种流行选择，因为它可以减轻组件的重量，同时又可以保持其性能。在来自离散拓扑优化的设计中，边界通常是锯齿状的，需要后期处理以平滑此类边界。本文提出了一种后处理方法来平滑锯齿状的边界。后处理方法包括边界标识算法，该算法标识外部边界和内部边界（空隙）。外部边界可以进一步分为优化的锯齿状边界以进行平滑和保留原始存在的边界。然后应用样条拟合方法来平滑锯齿状边界。对于内部空隙，开发了一种空洞替换方法来替换多边形空洞，以消除空洞周围的尖角和应力奇异性。为了最小化空隙周围的应力集中，开发了一种新颖的位置优化方法来优化空隙位置。计算了所有空隙周围最大应力的敏感性。的近似最大值函数的p-范数函数和计算域导数的材料导数方法用于获得灵敏度。应用了基于梯度的求解器来解决优化问题，并且在行搜索期间同时移动了所有空隙。案例研究表明，开发的方法可以有效地平滑锯齿状的边界并使内部空隙周围的应力集中最小化。