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Second-Order Two-Scale Computational Method for Nonlinear Dynamic Thermo-Mechanical Problems of Composites with Cylindrical Periodicity

Part of: Equations of mathematical physics and other areas of application Partial differential equations, initial value and time-dependent initial-boundary value problems Homogenization, determination of effective properties Approximations and expansions

Published online by Cambridge University Press:  08 March 2017

Hao Dong ,
Junzhi Cui ,
Yufeng Nie  and
Zihao Yang
Hao Dong*
Affiliation:
Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an 710129, P.R. China
Junzhi Cui*
Affiliation:
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P.R. China
Yufeng Nie*
Affiliation:
Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an 710129, P.R. China
Zihao Yang*
Affiliation:
Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi'an 710129, P.R. China
*
*Corresponding author. Email addresses:donghaonwpu@mail.nwpu.edu.cn (H. Dong), cjz@lsec.cc.ac.cn (J. Cui), yfnie@nwpu.edu.cn (Y. Nie), yangzihao@nwpu.edu.cn (Z. Yang)
*Corresponding author. Email addresses:donghaonwpu@mail.nwpu.edu.cn (H. Dong), cjz@lsec.cc.ac.cn (J. Cui), yfnie@nwpu.edu.cn (Y. Nie), yangzihao@nwpu.edu.cn (Z. Yang)
*Corresponding author. Email addresses:donghaonwpu@mail.nwpu.edu.cn (H. Dong), cjz@lsec.cc.ac.cn (J. Cui), yfnie@nwpu.edu.cn (Y. Nie), yangzihao@nwpu.edu.cn (Z. Yang)
*Corresponding author. Email addresses:donghaonwpu@mail.nwpu.edu.cn (H. Dong), cjz@lsec.cc.ac.cn (J. Cui), yfnie@nwpu.edu.cn (Y. Nie), yangzihao@nwpu.edu.cn (Z. Yang)
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Abstract

In this paper, a novel second-order two-scale (SOTS) computational method is developed for nonlinear dynamic thermo-mechanical problems of composites with cylindrical periodicity. The non-linearities of these multi-scale problems were caused by the temperature-dependent properties of the composites. Firstly, the formal SOTS solutions for these problems are constructed by the multiscale asymptotic analysis. Then we theoretically explain the importance of the SOTS solutions by the error analysis in the pointwise sense. In addition, a SOTS numerical algorithm is proposed in detail to effectively solve these problems. Finally, some numerical examples verify the feasibility and effectiveness of the SOTS numerical algorithm we proposed.

Keywords

Second-order two-scalenonlinear dynamic thermo-mechanical problemstemperature-dependent propertiescylindrical periodicity

MSC classification

Secondary: 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 35Q74: PDEs in connection with mechanics of deformable solids 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.) 74Q10: Homogenization and oscillations in dynamical problems
Type
Research Article
Information
Communications in Computational Physics , Volume 21 , Issue 4 , April 2017 , pp. 1173 - 1206
Copyright
Copyright © Global-Science Press 2017 

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