An Explicit Integration Scheme for Solving Dynamic Problems of Solid and Porous Media

In this article, an explicit integration scheme for dynamic finite element analysis is developed and the formulations for linear elastic solid and two-phase porous media are derived. The accuracy and stability characteristics analyses show this scheme is second-order accurate, which is the same as the Central Difference Method (CDM), and possesses a broader scope of stability within the range of normal damping ratios of media. Comparing with the CDM, this explicit scheme requires no matrix factorization even if a non diagonal damping matrix is included. Therefore, the dynamic finite element equations can be integrated economically provided that the mass matrix is diagonal. To demonstrate the validity of the present scheme, three examples are provided. First, taking a single-degree-of-freedom system as an example, the results obtained by the proposed scheme are compared with the exact solutions. Second, the dynamic responses of half-space saturated porous media, subjected to a concentrated load pulse at the surface, are analyzed. Both examples show that the results obtained by the proposed scheme agree well with the analytical solutions. Finally, the dynamic responses of a plane strain plate due to a load pulse are analyzed, respectively, by the proposed procedure and the commercial code ABAQUS (both implicit module and explicit module), and the CPU costs are compared.