论文标题
拓扑优化问题的SIMP模型的数值分析，以最大程度地减少线性弹性中的合规性
Numerical analysis of the SIMP model for the topology optimization problem of minimizing compliance in linear elasticity
论文作者
论文摘要
我们研究了具有惩罚方法（SIMP）的固体各向同性材料的有限元近似，以最大程度地降低线性弹性结构的符合性的拓扑优化问题。为了确保存在无限维度问题的局部最小化器，我们考虑了两种流行的正则化方法：$ w^{1，p} $ - 键入惩罚方法和密度过滤。先前的结果证明，材料分布空间中的弱（ - *）收敛到无限维度问题的局部最小化器。值得注意的是，不能保证收敛到\ emph {ash}孤立的局部最小化器。在这项工作中，我们表明，对于每个孤立的本地或全局最小化器，都存在一系列有限元的局部最小化器，它们在适当的空间中强烈收敛到最小化器。作为副产品，这确保存在一系列未过滤的离散材料分布的序列，这些分布没有表现出棋盘。
We study the finite element approximation of the solid isotropic material with penalization method (SIMP) for the topology optimization problem of minimizing the compliance of a linearly elastic structure. To ensure the existence of a local minimizer to the infinite-dimensional problem, we consider two popular regularization methods: $W^{1,p}$-type penalty methods and density filtering. Previous results prove weak(-*) convergence in the space of the material distribution to a local minimizer of the infinite-dimensional problem. Notably, convergence was not guaranteed to \emph{all} the isolated local minimizers. In this work, we show that, for every isolated local or global minimizer, there exists a sequence of finite element local minimizers that strongly converges to the minimizer in the appropriate space. As a by-product, this ensures that there exists a sequence of unfiltered discretized material distributions that does not exhibit checkerboarding.
