We study the finite element approximation of the solid isotropic material with penalization (SIMP) model for the topology optimization of the compliance of a linearly elastic structure. To ensure the existence of a minimizer to the infinite-dimensional problem, we consider two popular restriction methods: $W^{1,p}$-type regularization and density filtering. Previous results prove weak(-*) convergence in the solution space of the material distribution to an unspecified minimizer of the infinite-dimensional problem. In this work, we show that, for every isolated minimizer, there exists a sequence of finite element minimizers that strongly converges to the minimizer in the solution space. As a by-product, this ensures that there exists a sequence of unfiltered discretized material distributions that does not exhibit checkerboarding.

翻译：我们研究了固态异地材料的有限元素近似值,以惩罚性(SIMP)模型优化线性弹性结构的合规性。为了确保对无限维度问题存在一个最小化器,我们考虑两种流行的限制方法: $W+1,p}美元类型规范化和密度过滤。 以往的结果证明,在材料分配的解决方案空间中,向未指明的无限维度问题最小化器的未定最小化器的聚合(- * ) 差强人意。 在这项工作中,我们显示,对于每一个孤立的最小化器来说,都有一系列有限元素最小化器,它们与溶解空间的最小化器紧密结合。 作为副产品,这确保存在一系列未过滤的离散材料分布,但不会显示检查盘。