结合单元渐进删除的变密度拓扑优化方法  

Topology Optimization Method Using SIMP Combined with Evolutionary Deletion of Elements

作　　者：徐中明[1] 李丹彤 张志飞[1] 范维春 许恩永 Xu Zhongming;Li Dantong;Zhang Zhifei;Fan Weichun;Xu Enyong(College of Mechanical and Vehicle Engineering,Chongqing University,Chongqing 400000;Dongfeng Motor Corporation of Liuzhou,Liuzhou 545005)

机构地区：[1]重庆大学机械与运载工程学院,重庆400000 [2]东风柳州汽车有限公司,柳州545005

出　　处：《计算机辅助设计与图形学学报》2023年第3期482-490,共9页Journal of Computer-Aided Design & Computer Graphics

基　　金：广西创新驱动发展专项资金(2019046-12).

摘　　要：在面向连续体拓扑优化问题的固体各向同性惩罚微结构模型中,由于密度或灵敏度过滤的存在,优化结果中会出现灰度单元,影响结构的清晰度.针对此问题,运用渐进结构优化法的思想提出了一种结合单元渐进删除的变密度法.在SIMP法的基础上加入单元渐进删除的过程,单元删除阈值由平均单元相对密度及缩减系数确定,引入包括2个可调控参数的Sigmoid函数表达缩减系数,从而逐渐删除优化过程中产生的灰度单元.在讨论参数取值变化对缩减系数影响的基础上,以MBB梁为例确定参数取值的范围.将结合单元渐进删除的变密度法应用于MBB梁和悬臂梁柔度优化的算例,实验结果表明,该方法可与灵敏度过滤、密度过滤以及Heaviside投影相结合,具有较好的通用性,并能够有效地抑制SIMP法的灰度单元,显著地提升了优化效率.Solid isotropic microstructures with penalization(SIMP)can be used to solve the continuum topology optimization problem.Due to the existence of sensitivity or density filtering in SIMP,gray-scale elements will appear in the optimization results,which affects the clarity of the structure.In order to solve this problem,SIMP combined with evolutionary deletion of elements is proposed using the idea of evolutionary structural optimization.A process of evolutionary deletion of elements is added into SIMP method,elements deletion threshold is determined by the average element density and reduction factor.Sigmoid function is introduced to define a reduction factor which contains two parameters,so that the gray-scale elements can be gradually removed during the process.After discussing the influence of parameters on the reduction factor,the range of parameters is determined by taking the MBB beam as an example.SIMP combined with element evolutionary deletion is applied to numerical examples such as MBB beam and cantilever beam,it is proved that the method can be combined with sensitivity filtering,density filtering,and Heaviside projection,which shows good applicability.In addition,this method suppresses the gray-scale elements in the SIMP method effectively,and improves the efficiency.

关 键 词：拓扑优化 变密度法 单元过滤 灰度单元 渐进删除 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]