Modelling of Kirchhoff and Mindlin–Reissner Plate Bending With Hybrid-Trefftz Stress Elements

IF 2.7 3区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

International Journal for Numerical Methods in Engineering Pub Date : 2025-03-24 DOI:10.1002/nme.7668

J. A. Teixeira de Freitas, Carlos Tiago, E. M. B. R. Pereira

引用次数: 0

Abstract

The polynomial bases usually applied in the implementation of hybrid-Trefftz stress elements for plate bending are extended to include the formal solutions necessary to model high-gradient stress fields associated with boundary layer and singular wedge effects. To this end, the approximation of the stress-resultant field includes the (Trefftz) solutions of the harmonic, biharmonic, and Helmholtz governing systems of differential equations. Numerical testing problems are selected to show that the element can be used to solve the Kirchhoff model and to adequately simulate both boundary layer and singular wedge effects in thin and moderately thick Mindlin–Reissner plates.

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基于混合trefftz应力单元的Kirchhoff和Mindlin-Reissner板弯曲建模

将通常用于板弯曲混合trefftz应力单元实现的多项式基扩展到包括与边界层和奇异楔效应相关的高梯度应力场模型所需的形式解。为此，应力合成场的近似包括微分方程的调和、双调和和亥姆霍兹控制系统的（Trefftz）解。数值测试问题表明，该单元可以用来求解Kirchhoff模型，并充分模拟薄和中厚Mindlin-Reissner板的边界层和奇异楔效应。

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

International Journal for Numerical Methods in Engineering 工程技术-工程：综合

CiteScore

5.70

自引率

6.90%

发文量

276

审稿时长

5.3 months

期刊介绍： The International Journal for Numerical Methods in Engineering publishes original papers describing significant, novel developments in numerical methods that are applicable to engineering problems. The Journal is known for welcoming contributions in a wide range of areas in computational engineering, including computational issues in model reduction, uncertainty quantification, verification and validation, inverse analysis and stochastic methods, optimisation, element technology, solution techniques and parallel computing, damage and fracture, mechanics at micro and nano-scales, low-speed fluid dynamics, fluid-structure interaction, electromagnetics, coupled diffusion phenomena, and error estimation and mesh generation. It is emphasized that this is by no means an exhaustive list, and particularly papers on multi-scale, multi-physics or multi-disciplinary problems, and on new, emerging topics are welcome.