Application of multiscale asymptotic expansion method to three dimensional periodical composite structures

GAO Yahe; XING Yufeng; LI Min

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Application of multiscale asymptotic expansion method to three dimensional periodical composite structures

GAO Yahe #,XING Yufeng *,LI Min

Institute of Solid Mechanics, Beihang University (BUAA), Beijing 100191, China

*Correspondence author

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Funding: Research Fund for the Doctoral Program of Higher Education of China （No.20131102110039）, National Natural Science Foundation of China （No.11672019，11372021, 37686003）

Opened online:11 May 2017

Accepted by: none

Citation: GAO Yahe,XING Yufeng,LI Min.Application of multiscale asymptotic expansion method to three dimensional periodical composite structures[OL]. [11 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4732461

The decoupled Multiscale Asymptotic Expansion Method (MsAEM) is applied to the static analyses of three-dimensional (3D) periodical composite structures. The effects of perturbation orders, boundary conditions of unit cell problems and the derivatives of homogenized displacements on the accuracy are studied, the physical interpretation of the petrubation terms is revealed. By comprehensive results and comparisons, it is concluded that, 1) MsAEM can be viewed as the superposition method of different orders of admissible deformation modes represented by influence functions; 2) the second expansion term is leading in theoretical sense; 3) super unit cell approach and highly accurate differential quadrature method can improve the computational accuracy of influence functions and macro displacement derivatives; 4) the total potential energy functional is an effective method to evaluate the computational accuracy of displacements.

Keywords:Periodical composite; Multiscale asymptotic expansion; Boundary condition; Super unit cell; Differential quadrature

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