An unconditionally stable and high-accuracy finite element scheme for dynamic analysis of saturated poroelastic media

摘要

This paper presents a finite element scheme for analyzing the dynamic response of the saturated poroelastic media. The proposed scheme employs the standard finite element method for space domain discretization of the dynamic u-p equation system. We introduce the precise time step integration method as an explicit, direct integration algorithm for handling the time derivatives. The spectral radius analysis, the error and convergence analysis show that the proposed scheme is unconditionally stable as well as convergent with numerical solutions that are of any order accuracy to exact solutions. Compared with the Newmark scheme, the advantages of the proposed scheme are demonstrated by simulating five examples in both one- and two-dimensions. The proposed scheme yields high-precision results and exhibits good adaptability under large time step size, which remarkably outperforms the Newmark scheme.