A discontinuous Galerkin finite element method for dynamic and wave propagation problems in non-linear solids and saturated porous media

摘要

A time-discontinuous Galerkin finite element method (DGFEM) for dynamics and wave propagation in non-linear solids and saturated porous media is presented. The main distinct characteristic of the proposed DGFEM is that the specific P3-P1 interpolation approximation, which uses piecewise cubic (Hermite's polynomial) and linear interpolations for both displacements and velocities, in the time domain is particularly proposed. Consequently, continuity of the displacement vector at each discrete time instant is exactly ensured, whereas discontinuity of the velocity vector at the discrete time levels still remains. The computational cost is then obviously saved, particularly in the materially non-linear problems, as compared with that required for the existing DGFEM. Both the implicit and explicit algorithms are developed to solve the derived formulations for linear and materially non-linear problems. Numerical results illustrate good performance of the present method in eliminating spurious numerical oscillations and in providing much more accurate solutions over the traditional Galerkin finite element method using the Newmark algorithm in the time domain.