Physical interpretation of multiscale asymptotic expansion method

The multiscale asymptotic expansion method (MsAEM) up to any expansion order is formulated in a matrix form which is convenient for use as standard finite element method (FEM). Physical interpretations of the influence functions of different order are presented by analyzing the properties of self-balanced quasi load vectors used for solving the influence functions. The physical interpretation of MsAEM will lay the foundation for its applications. Numerical results validate the mathematical formulations and show that the second perturbation is necessary for micro analysis of periodical composite structures.