Consistent generalized finite element method: An accurate and robust mesh-based method even in distorted meshes

IF 4.2 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Engineering Analysis with Boundary Elements Pub Date : 2025-02-01 DOI:10.1016/j.enganabound.2024.106084

Jinwei Ma , Qinglin Duan , Rong Tian , Siqi Shu

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引用次数: 0

Abstract

A consistent generalized finite element method (C-GFEM) is proposed, showing excellent accuracy and convergence in distorted quadrilateral and hexahedral meshes. Both displacement approximation and domain integration are taken into consideration regarding the declining performance of the finite element method (FEM) in distorted meshes. In the displacement approximation, extra-degrees of freedom-free and linearly independent enrichments developed in GFEM are employed, which restores the reproducibility of the approximation in distorted meshes. In the domain integration, the idea of correcting nodal derivatives in the framework of the Hu–Washizu three-field variational principle is introduced into GFEM, based on which consistent integration schemes using quadrilateral and hexahedral elements are developed in this work. Furthermore, to consistently enforce the essential boundary condition, additional terms of boundary integral are introduced into the weak form. As a result, the proposed C-GFEM can pass patch tests and keep high accuracy even though the computational mesh is distorted. Its perfect performance in distorted meshes is sufficiently demonstrated by the numerical investigation of several benchmark examples.

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一致广义有限元法：一种基于网格的方法，即使是在扭曲的网格中，也具有精确和鲁棒性

提出了一种适用于畸变四边形和六面体网格的一致广义有限元法（C-GFEM），该方法具有良好的精度和收敛性。针对有限元法在变形网格中性能下降的问题，提出了位移逼近法和域积分法。在位移近似中，采用了GFEM中开发的额外自由度和线性无关的富集，从而恢复了变形网格中近似的再现性。在区域积分方面，将Hu-Washizu三场变分原理框架下的节点导数校正思想引入到GFEM中，在此基础上提出了四边形和六面体单元的一致积分方案。此外，为了保证基本边界条件的一致性，在弱形式中引入了边界积分的附加项。结果表明，C-GFEM在计算网格失真的情况下仍能通过斑块测试，保持较高的精度。通过几个基准算例的数值研究，充分证明了该方法在畸变网格中的良好性能。

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

Engineering Analysis with Boundary Elements 工程技术-工程：综合

CiteScore

5.50

自引率

18.20%

发文量

368

审稿时长

56 days

期刊介绍： This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods. Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness. The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields. In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research. The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods Fields Covered: • Boundary Element Methods (BEM) • Mesh Reduction Methods (MRM) • Meshless Methods • Integral Equations • Applications of BEM/MRM in Engineering • Numerical Methods related to BEM/MRM • Computational Techniques • Combination of Different Methods • Advanced Formulations.