An improved multiscale eigenelement method of periodical composite structures

Multiscale eigenelement method (MEM) proposed by the authors and co-workers is based on the eigenvector expansion method and substructure approach. Using the idea of perturbation, two methods are proposed to improve the accuracy of the multiscale eigenelement method. One method is choosing a few interior nodes from the micro model of unit cell as additional macro nodes of eigenelement; the other is taking the first m modes of the unit cell with clamped edges into account in the displacement functions of eigenelement. The computational cost of MEM is compared with that of asymptotic expansion homogenization method. Numerical comparisons are conducted to validate the high accuracy of the improved MEM for static and dynamic problems.