线性和非线性壳的 Hellan-Herrmann-Johnson 和 TDNNS 方法

IF 4.4 2区 工程技术 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS Computers & Structures Pub Date : 2024-10-03 DOI:10.1016/j.compstruc.2024.107543
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引用次数: 0

摘要

在本文中,我们通过分层方法将最近推出的用于非线性 Koiter 壳的混合 Hellan-Herrmann-Johnson (HHJ) 方法扩展到非线性 Naghdi 壳。额外的剪切自由度由 H(curl)-conforming Nédélec 有限元离散化,这意味着一种无剪切锁定方法。通过对模型进行线性化处理,我们得到了小应变机制下的线性基尔霍夫-洛夫和赖斯纳-明德林壳公式,对于板材,这两种公式分别简化为最初提出的基尔霍夫-洛夫和赖斯纳-明德林板材的 HHJ 和 TDNNS 方法。通过将膜应变插值到所谓的 Regge 有限元空间,我们得到了无锁定任意阶壳方法。此外,这些方法还可直接应用于具有扭结和分支壳体的结构。几个数值示例和实验验证了所提出的壳元素的卓越性能。
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The Hellan–Herrmann–Johnson and TDNNS methods for linear and nonlinear shells
In this paper we extend the recently introduced mixed Hellan–Herrmann–Johnson (HHJ) method for nonlinear Koiter shells to nonlinear Naghdi shells by means of a hierarchical approach. The additional shearing degrees of freedom are discretized by H(curl)-conforming Nédélec finite elements entailing a shear locking free method. By linearizing the models we obtain in the small strain regime linear Kirchhoff–Love and Reissner–Mindlin shell formulations, which reduce for plates to the originally proposed HHJ and TDNNS methods for Kirchhoff–Love and Reissner–Mindlin plates, respectively. By interpolating the membrane strains into the so-called Regge finite element space we obtain locking-free arbitrary order shell methods. Additionally, the methods can be directly applied to structures with kinks and branched shells. Several numerical examples and experiments are performed validating the excellent performance of the proposed shell elements.
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来源期刊
Computers & Structures
Computers & Structures 工程技术-工程:土木
CiteScore
8.80
自引率
6.40%
发文量
122
审稿时长
33 days
期刊介绍: Computers & Structures publishes advances in the development and use of computational methods for the solution of problems in engineering and the sciences. The range of appropriate contributions is wide, and includes papers on establishing appropriate mathematical models and their numerical solution in all areas of mechanics. The journal also includes articles that present a substantial review of a field in the topics of the journal.
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