An Advanced Time-Discontinuous Galerkin Finite Element Method for Structural Dynamics
Chyou-Chi Chien, Tong-Yue Wu

doi:10.3970/cmes.2001.002.213
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 2, No. 2, pp. 213-226, 2001
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Keywords Time-discontinuous Galerkin method, finite element method, stability, accuracy, structural dynamics.
Abstract 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 which both the displacement and velocity variables are represented independently by second-order interpolation functions in the time domain. The solution algorithm derived utilizes a predictor/multi-corrector technique that can effectively obtain the solutions for the resulting system of coupled equations. The numerical implementation of the time-discontinuous Galerkin finite element method is verified through several benchmark problems. Numerical results are compared with exact and accepted solutions from previous literature. Since a fifth-order accurate algorithm ensues by using quadratic interpolations for displacement and velocity, numerical results significantly improve in stability and accuracy for structural dynamics problems.
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