An advanced time-discontinuous Galerkin finite element method for structural dynamics

This study presents a novel computational method for implementing the time finite element formulation for the equations of linear structural dynamics. The proposed method adopts the time-discontinuous Galerkin method, in whic h both the displacement and velocity variables are represented independentl y by second-order interpolation functions in the time domain. The solution algorithm derived utilizes a predictor/multi-corrector technique that can e ffectively obtain the solutions for the resulting system of coupled equatio ns. The numerical implementation of the time-discontinuous Galerkin finite element method is verified through several benchmark problems. Numerical re sults are compared with exact and accepted solutions from previous literatu re. Since a fifth-order accurate algorithm ensues by using quadratic interp olations for displacement and velocity, numerical results significantly imp rove in stability and accuracy for structural dynamics problems.