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ARTICLE

Multiscale Nonlinear Thermo-Mechanical Coupling Analysis of Composite Structures with Quasi-Periodic Properties

Zihao Yang¹, Liang Ma², Qiang Ma³, Junzhi Cui^1,4, Yufeng Nie¹, Hao Dong¹, Xiaohong An⁵

1 Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China. E-mail: yangzihao@nwpu.edu.cn
2 State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi'an 710072, China
3 College of mathematics, Sichuan University, Chengdu 610065, China
4 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
5 Department of Mathematics and Physics, Xi'an Technological University, Xi'an 710032, China

Computers, Materials & Continua 2017, 53(3), 219-248. https://doi.org/10.32604/cmc.2017.053.235

Abstract

This paper reports a multiscale analysis method to predict the thermo-mechanical coupling performance of composite structures with quasi-periodic properties. In these material structures, the configurations are periodic and the material coefficients are quasi-periodic, i.e., they depend not only on the microscale information but also on the macro location. Also, a mutual interaction between displacement and temperature fields is considered in the problem, which is our particular interest in this study. The multiscale asymptotic expansions of the temperature and displacement fields are constructed and associated error estimation in nearly pointwise sense is presented. Then, a finite element-difference algorithm based on the multiscale analysis method is brought forward in detail. Finally, some numerical examples are given. And the numerical results show that the multiscale method presented in this paper is effective and reliable to study the nonlinear thermo-mechanical coupling problem of composite structures with quasi-periodic properties.

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Citations