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Multiscale Computational Method for Dynamic Thermo-Mechanical Problems of Composite Structures with Diverse Periodic Configurations in Different Subdomains

  • Hao DongEmail author
  • Xiaojing Zheng
  • Junzhi Cui
  • Yufeng Nie
  • Zhiqiang YangEmail author
  • Zihao Yang
Article

Abstract

In this paper, a novel multiscale computational method is presented to simulate and analyze dynamic thermo-mechanical problems of composite structures with diverse periodic configurations in different subdomains. In these composite structures, thermo-mechanical coupled behaviors at microscale have an important impact on the macroscopic displacement and temperature fields. Firstly, the novel second-order two-scale (SOTS) solutions for these multiscale problems are successfully obtained based on multiscale asymptotic analysis. Then, the error analysis in the pointwise sense is given to illustrate the importance of developing the SOTS solutions. Furthermore, the error estimate for the SOTS approximate solutions in the integral sense is presented. In addition, a SOTS numerical algorithm is proposed to effectively solve these problems based on finite element method, finite difference method and decoupling method. Finally, some numerical examples are shown, which demonstrate the feasibility and effectiveness of the SOTS numerical algorithm we proposed. In this paper, a unified two-scale computational framework is established for dynamic thermo-mechanical problems of composite structures with diverse periodic configurations in different subdomains.

Keywords

Dynamic thermo-mechanical problems Multiscale asymptotic analysis Diverse periodic configurations Error estimate SOTS numerical algorithm 

Notes

Acknowledgements

This research was supported by the Fundamental Research Funds for the Central Universities (No. JB180703), the National Natural Science Foundation of China (Nos. 51739007, 11471262 and 11501449), the National Basic Research Program of China (No. 2012CB025904), the State Scholarship Fund of China Scholarship Council (File No. 201606290191), and also supported by the Key Technology Research of FRP-Concrete Composite Structure and Center for high performance computing of Northwestern Polytechnical University.

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Authors and Affiliations

  1. 1.School of Mathematics and StatisticsXidian UniversityXi’anPeople’s Republic of China
  2. 2.School of Mechano-Electronic EngineeringXidian UniversityXi’anPeople’s Republic of China
  3. 3.LSEC, ICMSEC, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingPeople’s Republic of China
  4. 4.Department of Applied Mathematics, School of ScienceNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China
  5. 5.Department of Astronautic Science and MechanicsHarbin Institute of TechnologyHarbinPeople’s Republic of China

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