拓扑优化
插值(计算机图形学)
拓扑(电路)
数学优化
数学
均质化(气候)
多项式插值
有限元法
应用数学
规范(哲学)
线性插值
多项式的
计算机科学
数学分析
结构工程
工程类
动画
生物多样性
生态学
计算机图形学(图像)
组合数学
法学
政治学
生物
作者
Bing Yi,Gil Ho Yoon,Rong Zheng,Long Liu,Daping Li,Xiang Peng
标识
DOI:10.1016/j.compstruc.2023.107041
摘要
Topology optimization is one of the engineering tools for finding efficient design. For the material interpolation scheme, it is usual to employ the SIMP (Solid Isotropic Material with Penalization) or the homogenization based interpolation function for the parameterization of the material properties with respect to the design variables assigned to each finite element. For topology optimization with single material design, i.e., solid or void, the parameterization with 1 for solid and 0 for void becomes relatively straight forward using a polynomial function. For the case of multiple materials, some issues of the equality modeling of each material and the clear 0, 1 result of each element for the topology optimization issues become serious because of the curse of the dimension. To relieve these issues, this research proposes a new mapping based interpolation function for multi-material topology optimization. Unlike the polynomial based interpolation, this new interpolation is formulated by the ratio of the p-norm of the design variables to the 1-norm of the design variable multiplied by the design variable for a specific material. With this alternative mapping based interpolation function, each material are equally modeled and the clear 0, 1 result of each material for the multi-material topology optimization model can be improved. This paper solves several topology optimization problems to prove the validity of the present interpolation function.
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