A GENERALIZED MULTISCALE FINITE ELEMENT METHOD FOR DYNAMIC ANALYSIS OF HETEROGENEOUS MATERIAL

Almost all natural materials, as well as industrial and engineering materials, have multiscale features.This paper presents a generalized multiscale finite element method for dynamic analysis of heterogeneous materials.In this method, multiscale base functions, which can reflect the internal heterogeneity of materials within the coarse-scale element, are constructed by using the static condensation method and penalty function method.And these functions, which are different from those in the traditional extended multiscale finite element method(EMsFEM), are obtained by matrix operations analytically rather than solving elliptic problem many times on the sub-grid domain numerically.The main steps of this proposed method are described as follows.Firstly, a single heterogeneous unit cell will be equivalent into a macroscopic element by virtue of the constructed multiscale base functions.Then, the stiffness matrix of heterogeneous structure can be calculated on the macroscopic scale.Thus, the macroscopic nodal displacements of coarse-scale mesh can be obtained.Finally, the microscopic nodal displacements of sub grids within the unit cell can be calculated by using the numerical base functions once again.This generalized multiscale finite element method is a new expansion of the EMsFEM, which can simulate the mechanical behavior of heterogeneous unit cell with more complex geometric configurations. The static problem, generalized eigenvalue problem and transient response problem of the heterogeneous material are then simulated.It can be found that the calculation results of the generalized multiscale finite element method maintain highly consistent with those from the traditional FEM.Compared with the traditional FEM, the present multiscale method has significantly improved the computational efficiency while ensuring the computational accuracy, which has a good application potential.