A Methodology to Control Numerical Dissipation Characteristics of Velocity Based Time Discontinuous Galerkin Space‐Time Finite Element Method

Direct time integration schemes are an integral part of the FEM simulation of structural dynamics problems. Such schemes should be at least second-order accurate, unconditionally stable, and numerically dissipates the high-frequency components. To this end, this article develops a time integration scheme, called modified v-ST/FEM, which is based on the time-discontinuous Galerkin method. The proposed method employs an unsymmetric triangular bubble function for relating the displacement field to the velocity field. The modified v-ST/FEM contains two-parameter alpha is an element of(0,0.5)$$ \alpha \in \left(0,0.5\right) $$ and beta is an element of(-1,beta c)$$ \beta \in \left(-1,{\beta}_c\right) $$ for controlling the dissipation of high-frequency components. A comprehensive study of the influence of alpha$$ \alpha $$ and beta$$ \beta $$ on the numerical performance of the proposed method is conducted. It is found that the error in the solution increases when the value of alpha$$ \alpha $$ increases. However, for all practical purposes, beta$$ \beta $$ has a negligible influence on the accuracy of the proposed method. The modified v-ST/FEM is second-order accurate for alpha not equal 0.0$$ \alpha \ne 0.0 $$, and third-order accurate for alpha=0.0$$ \alpha =0.0 $$. The numerical efficacy of the modified v-ST/FEM is demonstrated by solving some benchmark problems and comparing its result to those obtained by other popular methods such as Trapezoidal rule, HHT-alpha$$ \alpha $$, and Bathe's scheme.