一种改进的密度过滤拓扑优化方法

An Improved Topology Optimization for Density Filtering

目前拓扑优化的密度过滤是基于单元距离的卷积算法解决有限元的棋盘格问题,但其产生大量灰色模糊区域(非0-1解),不利于后续实际工程应用,往往需要后处理才能得到清晰的结果特征。为提高拓扑优化效率,同时减少灰色区域的影响,提出一种各向异性的密度过滤算法。基于图像存在不连续特征的概念,拓扑优化结果得到的边界也应该保留一定的不连续性,因此各向异性的密度过滤将有限元之间密度差值和距离作为权重系数,有效减少边界的单元生成灰色区域的可能性,减少拓扑优化的后处理工作。利用各种常见的拓扑优化模型进行验证。结果表明:所提方法可有效解决拓扑优化常见的棋盘格、网格依赖性以及灰色模糊区域的情况;与传统的密度过滤方法相比,所提方法仅用15%的时间即可得到目标柔度降低10%的拓扑优化结果。

At present,the density filtering of topology optimization is based on the convolution algorithm of element distance to solve the checkerboard problem of finite element,but it produces a large number of gray fuzzy areas(non-0-1 solution),which is not suitable for the subsequent practical engineering application,and it often needs post-processing to get clear result features.In order to improve the efficiency of topology optimization and reduce the influence of grey area,an anisotropic density filtering algorithm is proposed.Based on the concept that discrete image exists in the topology,the boundary from optimization results should also retain a certain discontinuity,so the anisotropic density filtering takes the density differences between finite elements and distance as the weight coefficient,effectively reduces the boundary unit generates the possibility of a grey area,and reduces post-processing work in topology optimization.Through various common topology optimization examples,the results show that the proposed method can effectively solve the checkerboard,mesh dependence and gray fuzzy area.Compared with the classical density filtering method,the proposed method only takes 15%time to get the topology optimization results with the target compliance reduced by 10%.