Dual reciprocity BEM analysis of 2D transient elastodynamic problems by time-discontinuous Galerkin FEM

Abstract

This work applies the dual reciprocity boundary element method (DRBEM) to the transient analysis of two-dimensional elastodynamic problems. Adopting the elastostatic fundamental solution in the integral formulation of elastodynamics creates an inertial volume integral as well as the boundary ones. This volume integral is further transformed into a surface integral by invoking the reciprocal theorem. The analysis includes the quadratic three-noded boundary elements in the spatial domain. Importantly, the second-order ordinary differential equations in the time domain formulated by the DRBEM are solved using the time-discontinuous Galerkin finite element method. Particularly, both the displacement and velocity variables in the time domain are independently represented by quadratic interpolation functions that allow the unknown variables to be discontinuous at the discrete time levels. This method can filter out the spurious high modes and provide solutions with a fifth-order accuracy. Numerical examples are presented, confirming that the proposed method is more stable and accurate than widespread direct time integration algorithms, such as the Houbolt method.