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An arbitrary multi-node extended multiscale finite element method for thermoelastic problems with polygonal microstructures

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Abstract

A coupling extended multiscale finite element method (P-CEMsFEM) is developed for the numerical analysis of thermoelastic problems with polygonal microstructures. In this method, the polygonal microstructures are effectively represented by polygonal coarse-grid elements and the corresponding numerical base functions are constructed for the temperature and displacement fields, respectively, by a unified method with the corresponding equivalent matrices. To reflect the interaction of deformations among different directions, the additional coupling terms are introduced into the numerical base functions. In addition, an improved downscaling technique is proposed to directly obtain the satisfying microscopic solutions in the P-CEMsFEM. Moreover, an arbitrary multi-node strategy is developed to further improve the computational accuracy for the two-dimensional thermoelastic problems. Two types of representative numerical examples are presented. The first type examples are given to testify the proposed multiscale method and the results indicate that the P-CEMsFEM has high accuracy and efficiency for the thermoelastic analysis of heterogeneous multiphase materials and structures. The second type examples testify that the P-CEMsFEM is applicable for practical engineering problems.

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Acknowledgements

The supports from the National Natural Science Foundation of China (Nos. 11772082, 11672062 and 11772083), the LiaoNing Revitalization Talents Program (No. XLYC1807193), the 111 Project (No. B08014) and Fundamental Research Funds for the Central Universities (Nos. DUT17ZD307 and DUT17LK26) are gratefully acknowledged.

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Correspondence to Hongwu Zhang.

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Zheng, Y., Zhang, H., Lv, J. et al. An arbitrary multi-node extended multiscale finite element method for thermoelastic problems with polygonal microstructures. Int J Mech Mater Des (2019). https://doi.org/10.1007/s10999-019-09458-w

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Keywords

  • Extended multiscale finite element method
  • Thermoelastic analysis
  • Polygonal coarse-grid element
  • Heterogeneous multiphase material
  • Multi-node strategy
  • Improved downscaling technique