Time-discontinuous stabilized space-time finite elements for timoshenko beams

摘要

In the present research stabilized space-time finite elenemt methods for the transient computational analysis of the elastodynamics of Timoshenko beams have been developed. The underlying time-discontinuous Galerkin formulation with interpolations continuous in space and discontinuous in time is higher order accurate, robust and efficient. In order to suppress spurious numerical oscillations near discontinuities or high gradients, Galerkin/leastsquares stabilization has been applied. Further improvement of the numerical representation of the transient elastic wave propagation phenomena has been achieved by specially designed Galerkin/gradient least-squares operators. Due to the reduced phase and amplitude errors of thses finite elements, much coarser spatial meshes may be used without loss of accuracy. The resulting reduction of the number of unknowns by a factor of 4 to 5 leads to a significant decrease of computer time. Furthermore, a global adaptive time-stepping strategy based on the temporal jump residual of the time finite element method has been employed. Numerical examples of transient elastic wave propagation in Timoshenko beams involving a wide spectrum of wave numbers and frequencies demonstrate the good performance of the developed methods.