The multiscale asymptotic expansion method for three-dimensional static analyses of periodical composite structures

The decoupled multiscale asymptotic expansion method (MsAEM) is applied to the static analyses of three-dimensional (3D) periodical composite structures in this paper, and we focus on the attributes of the method in application. By comprehensive analyses and comparisons with finite element method, it is concluded that, 1) MsAEM can be viewed as the superposition method of different-order admissible deformation modes represented by influence functions; 2) the second-order expansion term is very necessary for the structure with considerable strain gradients; 3) the super unit cell approach can improve the computational accuracy of influence functions; 4) highly accurate differential quadrature finite element method can improve the computational efficiency of homogenized displacement and its derivatives; 5) the total potential energy is an effective measure to evaluate the computational accuracy.