An eigenelement method and two homogenization conditions

Abstract

Under inspiration from the structure-preserving property of symplectic difference schemes for Hamiltonian systems, two homogenization conditions for a representative unit cell of the periodical composites are proposed, one condition is the equivalence of strain energy, and the other is the deformation similarity. Based on these two homogenization conditions, an eigenelement method is presented, which is characteristic of structure-preserving property. It follows from the frequency comparisons that the eigenelement method is more accurate than the stiffness average method and the compliance average method.

Two-Scale Asymptotic Homogenization Method for Composite Kirchhoff Plates with in-Plane Periodicity

“…In recent decades, many multiscale homogenization methods have been proposed to deal with composite structures, such as the two-scale asymptotic homogenization method (AHM) [1][2][3], the multiscale eigenelement method (MEM) [4][5][6], the heterogeneous multiscale method (HMM) [7,8], the variational asymptotic method (VAM) [9,10], and for many other multiscale homogenization methods referred to [11,12] and the references cited therein. Among the above numerical homogenization methods [1][2][3][4][5][6][7][8][9][10], the AHM [1][2][3] is one of the most representative ones with a rigorous mathematical foundation and has been widely used in the homogenization analysis of periodic composite structures for statics [13][14][15][16][17][18] and dynamics [19][20][21][22]. However, the AHM [1][2][3][13][14][15][16][17][18][19]…”