基于反应扩散方程的水平集结构拓扑优化方法与实现  

Topology optimization method and its implement of level set structure using reaction diffusion equation

作　　者：赖松 王坤[1] LAI Song;WANG Kun(School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430064, China)

机构地区：[1]华中科技大学能源与动力工程学院,武汉430064

出　　处：《计算机辅助工程》2021年第2期9-15,共7页Computer Aided Engineering

摘　　要：为实现更加先进的拓扑优化算法,研究采用反应扩散方程的水平集结构拓扑优化方法,通过理论推导给出算法中的参数选择建议。该方法允许在拓扑优化过程中生成新的孔洞,初始结构无须包含孔洞,不需要重新初始化步骤,从而可提高算法的收敛性。针对传统拓扑优化中主要采用体积约束、以柔度最小为目标和体积保留率设定存在一定主观性的问题,探究不同体积保留率下的结构应力水平的变化规律,结果显示可以依据结构最大应力水平与体积保留率的变化规律确定最优体积保留率。To realize a more advanced topology optimization algorithm,the level set structure topology optimization method using reaction diffusion equation is studied.The parameter selections in the algorithm are suggested by theoretical deduction.In this method,the generation of new holes in the process of topology optimization is allowed,and the initial structure does not need to set holes,and the initialization step need not restart,and then the convergence of the algorithm can be improved.In traditional topology optimization,the constraint is volume,and the objective is minimum flexibility,and the setting of volume retention rate is subjective.As to this issue,the variation law of structural stress level under different volume retention rate is explored.The results show that the optimal volume retention rate can be determined according to the variation law of the maximum stress level and volume retention rate of the structure.

关 键 词：反应扩散方程 水平集 拓扑优化 体积保留率 收敛 

分 类 号：TB115.2[理学—数学]