A multiscale eigenelement method and its application to periodical composite structures

This paper develops a multiscale eigenelement method based on multilevel substructure technology for the multiscale analysis of periodical composite structures, and provides a comparison study with user point of view for the multiscale methods including the mathematical homogenization method, the heterogeneous multiscale method, the multiscale finite element method and the generalized finite element method, laying emphasis on their ideas, implementations, adaptabilities and similarities. It is shown that the newly developed eigenelement method satisfies the two essential homogenization conditions, one is the strain energy equivalence which is crucial to the lower order frequencies, and the other is the deformation similarity which is crucial to the local or micro stresses. Numerical experiments validate the present method.