用于 Reissner-Mindlin 板的无锁定 Argyris-Lagrange 有限元

IF 1.4 2区数学 Q1 MATHEMATICS

Calcolo Pub Date : 2024-07-29 DOI:10.1007/s10092-024-00608-x

Yunqing Huang, Shangyou Zhang

引用次数: 0

摘要

(C^1\)-\(P_{k+1}\) (\(k\ge 4\))阿基里斯有限元与拉格朗日有限元相结合，在板厚度方面是无锁定的，在三角形网格上求解赖斯纳-明德林板方程时是准最优的。该方法是真正符合或一致的，因为在公式中没有引入还原算子。本文给出了理论证明和数值验证。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Locking-free Argyris–Lagrange finite elements for the Reissner–Mindlin plate

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Locking-free Argyris–Lagrange finite elements for the Reissner–Mindlin plate

The \(C^1\)-\(P_{k+1}\) (\(k\ge 4\)) Argyris finite elements combined with the \(C^0\)-\(P_k\) Lagrange finite elements are locking-free with respect to the plate thickness, and quasi-optimal when solving the Reissner–Mindlin plate equation on triangular meshes. The method is truly conforming or consistent in the sense that no reduction operator is introduced to the formulation. Theoretical proof and numerical verification are presented.

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来源期刊

Calcolo 数学-数学

CiteScore

2.40

自引率

11.80%

发文量

审稿时长

>12 weeks

期刊介绍： Calcolo is a quarterly of the Italian National Research Council, under the direction of the Institute for Informatics and Telematics in Pisa. Calcolo publishes original contributions in English on Numerical Analysis and its Applications, and on the Theory of Computation. The main focus of the journal is on Numerical Linear Algebra, Approximation Theory and its Applications, Numerical Solution of Differential and Integral Equations, Computational Complexity, Algorithmics, Mathematical Aspects of Computer Science, Optimization Theory. Expository papers will also appear from time to time as an introduction to emerging topics in one of the above mentioned fields. There will be a "Report" section, with abstracts of PhD Theses, news and reports from conferences and book reviews. All submissions will be carefully refereed.