An accurate and robust quadrilateral shell element based on the Naghdi/Reissner/Mindlin shell theory

IF 3.5 3区工程技术 Q1 MATHEMATICS, APPLIED

Finite Elements in Analysis and Design Pub Date : 2026-04-01 Epub Date: 2026-02-04 DOI:10.1016/j.finel.2026.104526

Qi Ran , Huan Zhang , She Li , Xiangyang Cui

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引用次数: 0

Abstract

The DKMQ24 element, based on the Naghdi–Mindlin–Reissner shell theory, performs well in bending- and shear-dominated problems but remains sensitive to mesh distortion and suffers from in-plane shear locking. In this study, the membrane strain field is reconstructed using the Mixed Interpolation of Tensorial Components (MITC) method to reduce mesh sensitivity, and the Enhanced Assumed Strain (EAS) method is applied to alleviate in-plane shear locking. An improper bending approximation and the artificial stiffness for drilling rotation in DKMQ24 hindered the element from fully passing rigid-body tests; this issue is successfully resolved by adopting the standard bending strain formulation and redefining the drilling stiffness. Benchmark examples demonstrate that the enhanced DKMQ24 element eliminates in-plane shear locking, exhibits improved robustness against mesh distortion, and successfully passes rigid-body tests, providing a reliable and high-precision quadrilateral shell element for engineering applications.

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基于Naghdi/Reissner/Mindlin壳理论的精确且坚固的四边形壳单元

基于Naghdi-Mindlin-Reissner壳理论的DKMQ24单元在弯曲和剪切为主的问题中表现良好，但对网格畸变敏感，并且受到面内剪切锁定的影响。在本研究中，采用混合张量插值（MITC）方法重构膜应变场以降低网格敏感性，并采用增强假设应变（EAS）方法缓解面内剪切锁定。在DKMQ24中，由于弯曲近似和钻井旋转时的人为刚度不合理，导致该元件无法完全通过刚体试验；通过采用标准弯曲应变公式和重新定义钻孔刚度，成功地解决了这一问题。基准算例表明，改进后的DKMQ24单元消除了面内剪切锁紧，增强了网格畸变的鲁棒性，并成功通过了刚体测试，为工程应用提供了可靠、高精度的四边形壳单元。

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

Finite Elements in Analysis and Design 工程技术-力学

CiteScore

4.80

自引率

3.20%

发文量

审稿时长

27 days

期刊介绍： The aim of this journal is to provide ideas and information involving the use of the finite element method and its variants, both in scientific inquiry and in professional practice. The scope is intentionally broad, encompassing use of the finite element method in engineering as well as the pure and applied sciences. The emphasis of the journal will be the development and use of numerical procedures to solve practical problems, although contributions relating to the mathematical and theoretical foundations and computer implementation of numerical methods are likewise welcomed. Review articles presenting unbiased and comprehensive reviews of state-of-the-art topics will also be accommodated.