Dual reciprocity BEM applied to transient elastodynamic problems with differential quadrature method in time Original Research Article

This paper is concerned with numerical analysis of the transient elastodynamic problems by the dual reciprocity BEM (DRBEM) in space combined with the differential quadrature method (DQM) in time. Emphasis is placed on a comparative study of various time-marching schemes. Three numerical examples considered are for the longitudinal forced vibration of plates and the transverse free vibration of membranes. To authors’ best knowledge, this is the first attempt to apply the DQM to the second-order time derivative in the DRBEM elastodynamic formulations. A recent approach using boundary conditions in the DQM was here extended to handle the initial conditions of elastodynamic problems. The resulting algebraic formulation is a Lyapunov matrix equation, which can be very efficiently solved by the Bartels–Stewart algorithm. It is revealed that the DQM is an unconditionally stable algorithm and gives much better accuracy than the standard finite difference schemes such as the Wilson θ, Newmark and Houbolt methods, for the same time step size for the cases considered.