We advance a combined filtered/phase-field approach to topology optimization in the setting of linearized elasticity. Existence of minimizers is proved and rigorous parameter asymptotics are discussed by means of variational convergence techniques. Moreover, we investigate an abstract space discretization in the spirit of conformal finite elements. Eventually, stationarity is equivalently reformulated in terms of a Lagrangian.

中文翻译：

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弹性拓扑优化的滤波/相场组合方法分析

我们提出了一种组合滤波/相场方法，用于线性弹性设置下的拓扑优化。利用变分收敛技术证明了极小值的存在性并讨论了严格参数渐进性。此外，我们本着共形有限元的精神研究了抽象空间离散化。最终，平稳性等效地用拉格朗日函数重新表述。