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

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 numeric...

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Bibliographic Details
Published in:International journal of mechanics and materials in design 2020-03, Vol.16 (1), p.35-56
Main Authors: Zheng, Yonggang, Zhang, Hanbo, Lv, Jun, Zhang, Hongwu
Format: Article
Language:English
Subjects:
Accuracy
Characterization and Evaluation of Materials
Classical Mechanics
Coupling
Engineering
Engineering Design
Finite element analysis
Finite element method
Multiscale analysis
Nonlinear programming
Numerical analysis
Polygons
Solid Mechanics
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Summary: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.
ISSN:1569-1713
1573-8841
DOI:10.1007/s10999-019-09458-w