Three-dimensional transient elastodynamic analysis by a space and time-discontinuous Galerkin finite element method

摘要

This study presents a space and time-discontinous Galerkin (TDG) finite element method for analyzing three-dimensional linear transient elastodynamic problems. This novel method uses both the displacements and velocities as basic unknowns and approximates them as piecewise linear functions which are continuous in space and discontinuous in time. The improved algorithm employs the Gauss-Seidel method to calculate itcratively the solutions that exist in the numerical implementation. Stability analyses of TDG method reveal that such a method retains the unconditionally stable behavior with greater efficiency than other direct time integration algorithms. In addition, numerical examples are presented, demonstrating that the proposed method is more accurate than several commonly used algorithms in structural dynamic applications.