Two-Scale Finite Element Approximation of a Homogenized Plate Model

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-09-11 DOI:10.1137/23m1596272

Martin Rumpf, Stefan Simon, Christoph Smoch

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 62, Issue 5, Page 2121-2142, October 2024.
Abstract. This paper studies the discretization of a homogenization and dimension reduction model for the elastic deformation of microstructured thin plates proposed by Hornung, Neukamm, and Velčić [Calc. Var. Partial Differential Equations, 51 (2014), pp. 677–699]. Thereby, a nonlinear bending energy is based on a homogenized quadratic form which acts on the second fundamental form associated with the elastic deformation. Convergence is proved for a multi-affine finite element discretization of the involved three-dimensional microscopic cell problems and a discrete Kirchhoff triangle discretization of the two-dimensional isometry-constrained macroscopic problem. Finally, the convergence properties are numerically verified in selected test cases and qualitatively compared with deformation experiments for microstructured sheets of paper.

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均质板模型的双尺度有限元逼近

SIAM 数值分析期刊》第 62 卷第 5 期第 2121-2142 页，2024 年 10 月。摘要本文研究了 Hornung、Neukamm 和 Velčić 提出的微结构薄板弹性变形的均质化和降维模型的离散化[Calc. Var. Partial Differential Equations, 51 (2014), pp.］因此，非线性弯曲能是基于同质化二次方程形式，该形式作用于与弹性变形相关的第二基本形式。对所涉及的三维微观单元问题的多参数有限元离散化和二维等距约束宏观问题的离散基尔霍夫三角形离散化进行了收敛性证明。最后，在选定的测试案例中对收敛特性进行了数值验证，并与微结构纸张的变形实验进行了定性比较。

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

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.