Analysis of a Combined Filtered/Phase-Field Approach to Topology Optimization in Elasticity

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-02-19 DOI:10.1007/s00245-024-10104-x

Ferdinando Auricchio, Michele Marino, Idriss Mazari, Ulisse Stefanelli

引用次数: 0

Abstract

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.

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分析弹性拓扑优化的滤波/相场组合方法

我们提出了线性化弹性环境下拓扑优化的滤波/相场组合方法。通过变分收敛技术，证明了最小值的存在性并讨论了严格的参数渐近性。此外，我们还以保角有限元的精神研究了抽象空间离散化。最终，我们用拉格朗日等价地重新表述了静止性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.