Analysis of transient wave propagation dynamics using the enriched finite element method with interpolation cover functions

Abstract

To improve the performance of the low-order linear triangular element for solving transient wave propagation problems, this paper presents a novel enriched finite element method (EFEM) for wave analysis. The original linear nodal shape functions are enriched by using the additional interpolation cover functions over patches of elements. To effectively solve the wave problems, the used interpolation cover function is constructed by using the Lagrangian functions plus the harmonic trigonometric functions. The present approach can be regarded as a combination of the classical finite elements and the spectral techniques, but individual strengths of the two methods are synergized, so more accurate results can be obtained compared to the standard finite elements. In this work the root of the linear dependence (LD) issue in the present EFEM is investigated detailedly, and then an effective approach is proposed to completely eliminate the LD problem. By performing the dispersion analysis, it is found that the present EFEM possesses the attractive monotonic convergence property for transient wave propagations, that is the obtained numerical solutions will monotonically converge to the exact solutions with the decreasing time steps for time integration as long as the reasonably fine meshes are used. Several typical numerical examples are solved to illustrate the capacities of the present method.