过滤函数对拓扑优化效率和灰度单元的影响  

Influence of Filter Functions on Efficiency of Topology Optimization and Gray-scale Element

作　　者：杜家政[1] 陈炬 李功明 DU Jiazheng;CHEN JU;LI Gongmin(Faculty of Materials and Manufacturing,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]北京工业大学材料与制造学部,北京100124

出　　处：《北京工业大学学报》2025年第5期523-538,572,共17页Journal of Beijing University of Technology

基　　金：国家自然科学基金资助项目(11872080)。

摘　　要：为了提高拓扑优化效率和减少灰度单元的数量,基于独立连续映射(independent continuous mapping,ICM)方法引入幂函数、复合指数型函数以及有理分式函数作为过滤函数,建立以质量最小为目标、位移为约束的拓扑优化模型。通过数值算例,研究了3种过滤函数以及单元质量和单元刚度过滤函数的参数比对拓扑优化效率和灰度单元的影响。数值算例表明有理分式函数能有效减少中间灰度单元数量,提高收敛速度,降低结构质量。对于幂函数,当单元质量和单元刚度过滤函数的参数比为1∶7时效果最佳;对于复合指数型函数,当单元质量和单元刚度过滤函数的参数比为1.3∶0.1时效果最佳;对于有理分式过滤函数,当单元质量和单元刚度过滤函数的参数比为3∶63时效果最佳。To enhance the efficiency of topology optimization and reduce the number of gray units,power function,composite exponential function and rational fraction function are introduced as filtering functions based on independent continuous mapping(ICM)method,and a topology optimization model with minimum weight as the objective and displacement as the constraint is fomulated.Numerical examples were employed to investigate the effects of three kinds of filter functions and the parameter ratio of element weight and element stiffness filter functions on the efficiency of topology optimization and gray units were studied.Numerical examples show that the rational fraction function can effectively reduce the number of intermediate gray units,improve the convergence speed and reduce the weight of the structure.For the power function,when the parameter ratio of element weight and element stiffness filter function is 1∶7,the effect is optimal.For the composite exponential function,when the parameter ratio of element weight and element stiffness filter function is 1.3∶0.1,the effect is optimal.For the rational fraction filter function,when the parameter ratio of element quality and element stiffness filter function is 3∶63,the effect is optimal.

关 键 词：ICM方法 过滤函数 拓扑优化 位移约束 优化效率 灰度单元 

分 类 号：O34[理学—固体力学]