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International Journal for Multiscale Computational Engineering
Facteur d'impact: 1.016 Facteur d'impact sur 5 ans: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimer: 1543-1649
ISSN En ligne: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v8.i6.40
pages 597-613

Extended Multiscale Finite Element Method for Mechanical Analysis of Periodic Lattice Truss Materials

Hongwu Zhang
Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, P. R. China
J. K. Wu
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, China
Zhendong Fu
State Key Laboratory of Structure Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, China

RÉSUMÉ

An extended multiscale finite element method (EMsFEM) is developed to study the equivalent mechanical properties of periodic lattice truss materials. The underlying idea is to construct the numerical multiscale base functions to reflect the heterogeneity of the unit cell of periodic truss materials. To consider the coupled effect among different directions in the multidimensional problems, the coupled additional terms of base functions for the interpolation of the vector fields are introduced. Numerical results show that the base functions constructed by linear boundary conditions will induce nonequilibrium of the boundary nodal forces and thus lead to a strong scale effect of the unit cell in the multiscale computation. Thus, more reasonable oscillatory boundary conditions are introduced by using the oversampling technique in the construction of the multiscale base functions of the unit cell. A special algorithm is introduced to improve the properties of the equivalent stiffness matrix of the unit cell to make the numerical results more accurate. The advantage of the developed method is that the downscaling computation could be realized easily and the stress and strain in the unit cell can be obtained simultaneously in the multiscale computation. Therefore, the developed method has great potential for strength analysis of heterogeneous materials.

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