Non‐local dispersive model for wave propagation in heterogeneous media: multi‐dimensional case
Jacob Fish, Wen Chen, Gakuji Nagai · International Journal for Numerical Methods in Engineering · 2002
Abstract Three non‐dispersive models in multi‐dimensions have been developed. The first model consists of a leading‐order homogenized equation of motion subjected to the secularity constraints imposing uniform validity of asymptotic expansions. The second, non‐local model, contains a fourth‐order spatial derivative and thus requires C1 continuous finite element formulation. The third model, which is limited to the constant mass density and a macroscopically orthotropic heterogeneous medium, requires C0 continuity only and its finite element formulation is almost identical to the classical local approach with the exception of the mass matrix. The modified mass matrix consists of the classical mass matrix (lumped or consistent) perturbed with a stiffness matrix whose constitutive matrix depends on the unit cell solution. Numerical results are presented to validate the present formulations. Copyright © 2002 John Wiley & Sons, Ltd.