基于改进灵敏度过滤策略的SIMP方法

在传统变密度法SIMP(Solid Isotropic Microstructures with Penalization)中,Sigmund灵敏度过滤策略是解决拓扑优化结果数值不稳定问题的重要方法之一。但在SIMP方法中采用Sigmund灵敏度过滤策略时,有时优化结果会有较多的灰度单元。为了减少拓扑优化结果中灰度单元的数量,提出了一种基于改进灵敏度过滤策略的SIMP方法。在过滤后单元灵敏度的计算中,增加了一个与中心单元过滤前灵敏度有关的部分,该部分在过滤后灵敏度中所占的比重需要通过过滤权重来调节。通过对灵敏度过滤需要的分析,确定了过滤半径和中心单元密度值是影响过滤权重的因素。根据拓扑优化实例的优化结果给出了过滤半径影响过滤权重的情况,并基于过滤半径对过滤权重的影响情况构建了过滤权重的函数。在改进灵敏度过滤策略的基础上,结合双重SIMP算法给出了本文SIMP方法的流程。最后,以悬臂梁结构和简支梁结构为例,验证了本文方法的有效性。与Sigmund灵敏度过滤策略相比,改进的灵敏度过滤策略能有效地减少灰度单元。与双重SIMP方法相比,本文SIMP方法能有效地减少数值不稳定现象。

SIMP method based on modified sensitivity filtering strategy

The Sigmund sensitivity filter strategy is one of the most important methods of solving numerical instability problem in SIMP (Solid Isotropic Microstructures with Penalization) method.However,many gray-scale elements may arise in the SIMP method of Sigmund sensitivity filter.To decrease the numbers of gray-scale elements in the topology optimization,a SIMP method of modified sensitivity filter strategy is presented.The calculation of sensitivity after filtering should take into consideration a section associated with sensitivity of the center element before filtering,which need adjust the ratio by the filter weight in the sensitivity after filtering.The analysis of the requirements of sensitivity filter finds that the filter radius and density value of the center element can affect filter weight.The relationship of filter weight and the filter radius is obtained via the topological optimal case,and then the function of filter weight is built based on the relationship.Based on modified sensitivity filter strategy,the procedure of the proposed SIMP method is shown combined with the Double-SIMP method.Finally,validity of the proposed method is verified by taking cantilever beam structure and the simply supported beam structure as examples.Compared with the old Sigmund sensitivity filter strategy,the improved strategy effectively reduces gray elements.Compared with the Double-SIMP method,the proposed SIMP method can effectively decrease numerical instability.