A rigorous and unified mass lumping scheme for higher-order elements

doi:10.1016/j.cma.2017.03.011

CORC > 武汉岩土力学研究所 > 中科院武汉岩土力学所 > 岩土力学所知识全产出 > 期刊论文

	A rigorous and unified mass lumping scheme for higher-order elements
	Sivaselvan, M. V.1; Yang, Yongtao 2; Zheng, Hong 3
刊名	COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
	2017
卷号	319 页码:491-514
关键词	Lumped mass matrices High-order elements Dynamic analysis Finite element method Manifolds
ISSN号	0045-7825
DOI	10.1016/j.cma.2017.03.011
英文摘要	In dynamic analysis with explicit time integration schemes, a lumped mass matrix (LMM) is preferable, because LMM can avoid solving the large scale simultaneous algebraic equations. Mathematically rigorous mass lumping schemes, such as the mass lumping by nodal quadrature and the row-sum technique, are applicable to only linear or bilinear elements. For higher-order elements, such as 8-node serendipity elements, the diagonal scaling procedure is the only lumping method that can be recommended to generate positive definite diagonal element mass matrices. Unfortunately, there is no mathematical theory in support of this approach. This study proposes a general mass lumping scheme applicable to higher order elements, where the virtual work of initial force is integrated over the problem domain that is viewed as the manifold covered by the finite element patches. By a series of numerical experiments, both free and forced vibration problems, it is suggested that even in the implicit time integration scheme the consistent mass matrix (CMM) can be superseded by the proposed LMM. Furthermore, the proposed LMM has much stronger adaptability to distorted meshes. (C) 2017 Elsevier B.V. All rights reserved.
WOS研究方向	Engineering ; Mathematics ; Mechanics
语种	英语
出版者	ELSEVIER SCIENCE SA
WOS记录号	WOS:000401398800021
内容类型	期刊论文
源URL	[http://119.78.100.198/handle/2S6PX9GI/4069]
专题	岩土力学所知识全产出_期刊论文国家重点实验室知识产出_期刊论文
作者单位	1.Univ Buffalo, Dept Civil Struct & Environm Engn 2.Chinese Acad Sci, Inst Rock & Soil Mech, State Key Lab Geomech & Geotech Engn ; 3.Beijing Univ Technol, Minist Educ, Key Lab Urban Secur & Disaster Engn ;
推荐引用方式 GB/T 7714	Sivaselvan, M. V.,Yang, Yongtao,Zheng, Hong. A rigorous and unified mass lumping scheme for higher-order elements[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2017,319:491-514.
APA	Sivaselvan, M. V.,Yang, Yongtao,&Zheng, Hong.(2017).A rigorous and unified mass lumping scheme for higher-order elements.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,319,491-514.
MLA	Sivaselvan, M. V.,et al."A rigorous and unified mass lumping scheme for higher-order elements".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 319(2017):491-514.