Mixed and nonconforming finite element approximations of Reissner-Mindlin plates

doi:10.1016/j.cma.2003.07.009

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	Mixed and nonconforming finite element approximations of Reissner-Mindlin plates
	Duan, HY; Liang, GP
	2003
发表期刊	COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
ISSN	0045-7825
卷号	192 期号:49-50 页码:5265-5281
摘要	We consider a mixed finite element approximation of the Reissner-Mindlin plate model, which plays an important role in the simulation of plates and shells of small to moderate thickness. On triangles and quadrilaterals, low-order finite elements are proposed: the rotation is approximated by conforming isoparametric (bi)linear elements and the transverse displacement by constant elements and the shear stress by the lowest-order Raviart-Thomas elements. We prove that the new method satisfies the K-ellipticity and the Inf-Sup condition in the abstract framework of the Babugka-Brezzi theory for mixed problems. Consequently, the method is uniformly stable and uniformly optimally convergent (independent of the thickness of the plate). Moreover, a local postprocessing approach and the implementation by either the augmented Lagrangian algorithm or the hybridization method are discussed, including equivalence to some nonconforming methods. In particular, a new nonconforming method is deduced, which can accommodate arbitrary regular quadrilaterals. (C) 2003 Elsevier B.V. All rights reserved.
关键词	Reissner-Mindlin plates mixed finite element method local postprocessing hybridization nonconforming element
DOI	10.1016/j.cma.2003.07.009
语种	英语
WOS研究方向	Engineering ; Mathematics ; Mechanics
WOS类目	Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics
WOS记录号	WOS:000186854400004
出版者	ELSEVIER SCIENCE SA
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18443
专题	中国科学院数学与系统科学研究院
通讯作者	Duan, HY
作者单位	Chinese Acad Sci, Math Inst, Beijing 1000080, Peoples R China
推荐引用方式 GB/T 7714	Duan, HY,Liang, GP. Mixed and nonconforming finite element approximations of Reissner-Mindlin plates[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2003,192(49-50):5265-5281.
APA	Duan, HY,&Liang, GP.(2003).Mixed and nonconforming finite element approximations of Reissner-Mindlin plates.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,192(49-50),5265-5281.
MLA	Duan, HY,et al."Mixed and nonconforming finite element approximations of Reissner-Mindlin plates".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 192.49-50(2003):5265-5281.