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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
Source PublicationCOMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
ISSN0045-7825
Volume317Pages:1068-1101
AbstractA 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.
KeywordAsymptotic expansion homogenization method SOTS finite element algorithm Modal analysis Eigenvalue problem Axisymmetric and spherical symmetric structure Periodic configuration
DOI10.1016/j.cma.2017.01.013
Language英语
Funding ProjectNational 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 Research AreaEngineering ; Mathematics ; Mechanics
WOS SubjectEngineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics
WOS IDWOS:000398373500043
PublisherELSEVIER SCIENCE SA
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/25106
Collection计算数学与科学工程计算研究所
Corresponding AuthorLi, Z. H.
Affiliation1.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
Recommended Citation
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.
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