Multi-scale modal analysis for axisymmetric and spherical symmetric structures with periodic configurations

doi:10.1016/j.cma.2017.01.013

	Multi-scale modal analysis for axisymmetric and spherical symmetric structures with periodic configurations
	Li, Z. H.1,2; Ma, Q.1,2; Cui, J. Z.3
	2017-04-15
发表期刊	COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
ISSN	0045-7825
卷号	317 页码:1068-1101
摘要	A new modal analysis method with second-order two-scale (SOTS) asymptotic expansion is presented for axisymmetric and spherical symmetric structures. The symmetric structures considered are periodically distributed with homogeneous and isotropic constituent materials. By the asymptotic expansion of the eigenfunctions, the homogenized modal equations, the effective materials coefficients, the first-and second-order correctors are obtained. The derived homogenized constitutive relationships are the same as the ones which serve to homogenize the corresponding static problems. The eigenvalues are also expanded to the second-order terms and using the so called "corrector equation", the correctors of the eigenvalues are expressed in terms of the first-and second-order correctors of the eigenfunctions. The anisotropic materials are obtained by homogenization with different properties in the circumferential direction. Especially for the two-dimensional axisymmetric layered structure, the one-dimensional plane axisymmetric and spherical symmetric structures, the homogenized eigenfunctions and eigenvalues, as well as their corresponding correctors are all solved analytically. The finite element algorithm is established, three typical numerical experiments are carried out and the necessity of the second-order correctors is discussed. Based on the numerical results, it is validated that the SOTS asymptotic expansion homogenization method is effective to identify the eigenvalues of the axisymmetric and spherical symmetric structures with periodic configurations and the original eigenfunctions with periodic oscillation can be reproduced by adding the correctors to the homogenized eigenfunctions. (C) 2017 The Authors. Published by Elsevier B.V.
关键词	Asymptotic expansion homogenization method SOTS finite element algorithm Modal analysis Eigenvalue problem Axisymmetric and spherical symmetric structure Periodic configuration
DOI	10.1016/j.cma.2017.01.013
语种	英语
资助项目	National Key Basic Research and Development Program[2014CB744100] ; National Nature Science Foundation of China[11325212] ; National Nature Science Foundation of China[91530319] ; China Postdoctoral Science Foundation[2014M562616] ; China Postdoctoral Science Foundation[2016T91019]
WOS研究方向	Engineering ; Mathematics ; Mechanics
WOS类目	Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics
WOS记录号	WOS:000398373500043
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/25106
专题	计算数学与科学工程计算研究所
通讯作者	Li, Z. H.
作者单位	1.China Aerodynam Res & Dev Ctr, Hyperveloc Aerodynam Inst, Mianyang 621000, Peoples R China 2.BUAA, Natl Lab Computat Fluid Dynam, Beijing 100191, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li, Z. H.,Ma, Q.,Cui, J. Z.. Multi-scale modal analysis for axisymmetric and spherical symmetric structures with periodic configurations[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,2017,317:1068-1101.
APA	Li, Z. H.,Ma, Q.,&Cui, J. Z..(2017).Multi-scale modal analysis for axisymmetric and spherical symmetric structures with periodic configurations.COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING,317,1068-1101.
MLA	Li, Z. H.,et al."Multi-scale modal analysis for axisymmetric and spherical symmetric structures with periodic configurations".COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 317(2017):1068-1101.