| Frame-invariance in finite element formulations of geometrically exact rods |
| Zhong PN; Huang GJ(黄国君) ; Yang GW(杨国伟); Yang, GW (reprint author), Chinese Acad Sci, Inst Mech, Key Lab Mech Fluid Solid Coupling Syst, Beijing 100190, Peoples R China.
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| 发表期刊 | APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION
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| 2016
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| 卷号 | 37期号:12页码:1669-1688 |
| ISSN | 0253-4827
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| 摘要 | This article is concerned with finite element implementations of the threedimensional geometrically exact rod. The special attention is paid to identifying the condition that ensures the frame invariance of the resulting discrete approximations. From the perspective of symmetry, this requirement is equivalent to the commutativity of the employed interpolation operator I with the action of the special Euclidean group SE(3), or I is SE(3)-equivariant. This geometric criterion helps to clarify several subtle issues about the interpolation of finite rotation. It leads us to reexamine the finite element formulation first proposed by Simo in his work on energy-momentum conserving algorithms. That formulation is often mistakenly regarded as non-objective. However, we show that the obtained approximation is invariant under the superposed rigid body motions, and as a corollary, the objectivity of the continuum model is preserved. The key of this proof comes from the observation that since the numerical quadrature is used to compute the integrals, by storing the rotation field and its derivative at the Gauss points, the equivariant conditions can be relaxed only at these points. Several numerical examples are presented to confirm the theoretical results and demonstrate the performance of this algorithm. |
| 关键词 | Geometrically Exact Rod
Finite Element Method
Interpolation
Equivariance
Frame Invariance
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| DOI | 10.1007/s10483-016-2147-8
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| URL | 查看原文
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| 收录类别 | SCI
; EI
; CSCD
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| 语种 | 英语
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| WOS记录号 | WOS:000389200900007
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| 关键词[WOS] | geometrically exact rod
; finite element method
; interpolation
; equivariance
; frame invariance
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| WOS研究方向 | Mathematics
; Mechanics
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| WOS类目 | Mathematics, Applied
; Mechanics
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| 课题组名称 | LMFS流固耦合与数值计算(LHO)
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| 引用统计 |
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| 文献类型 | 期刊论文
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| 条目标识符 | http://dspace.imech.ac.cn/handle/311007/59939
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| 专题 | 流固耦合系统力学重点实验室
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| 通讯作者 | Yang, GW (reprint author), Chinese Acad Sci, Inst Mech, Key Lab Mech Fluid Solid Coupling Syst, Beijing 100190, Peoples R China. |
推荐引用方式
GB/T 7714 |
Zhong PN,Huang GJ,Yang GW,et al. Frame-invariance in finite element formulations of geometrically exact rods[J]. APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION,2016,37,12,:1669-1688.
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| APA |
Zhong PN,黄国君,杨国伟,&Yang, GW .(2016).Frame-invariance in finite element formulations of geometrically exact rods.APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION,37(12),1669-1688.
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| MLA |
Zhong PN,et al."Frame-invariance in finite element formulations of geometrically exact rods".APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION 37.12(2016):1669-1688.
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