Accuracy and physical interpretation of multiscale asymptotic expansion method

The multiscale asymptotic expansion method (MsAEM) can be implemented by using weighted residual method etc. The authors have studied the accuracy and physical interpretation of MsAEM for years. This paper reviewed the authors' previous works, further demonstrated the relationships of element order and perturbation order with exact solution for one-dimensional periodical structures; revealed the physical interpretations of different orders of influence functions and self-balanced quasi loads; and emphasized that the second order of expansion is essential for the accuracy of MsAEM from the physical perspective. It also presented an outlook of future work.