拓扑优化中去除数值不稳定性的算法研究

Research on Algorithms to Eliminate Numerical Instabilities in Topology Optimization

分析了拓扑优化计算中常出现的多孔材料、棋盘格、网格依赖性、局部极值等数值不稳定现象;分析了克服数值不稳定性现象的各种数值方法,及其各自的特点;提出了一种基于卷积因子前处理和小波分析后处理的综合过滤算法,能够有效消除拓扑优化中的数值不稳定现象。

The numerical instabilities in topology optimization, such as porous materials, checkerboard, mesh dependency, local minimal, etc. are analyzed. Meanwhile, some conventional methods to overcome numerical instabilities are listed and compared. A new mixed filter algorithm based on convolution pre process and wavelet post process is proposed. It can effectively eliminate the numerical instabilities in topology optimization.