Time-discontinuous Galerkin quadrature element methods for structural dynamics

Three time-discontinuous Galerkin quadrature element methods (TDGQEMs) are developed for structural dynamic problems. The weak-form time-discontinuous Galerkin (TDG) statements, which are capable of capturing possible displacement and/or velocity discontinuities, are employed to formulate the three types of quadrature elements, i.e., single-field, singlefield/least-squares and two-field. Gauss-Lobatto quadrature rule and the differential quadrature analog are used to turn the weakform TDG statements into a system of algebraic equations. The stability, accuracy and numerical dissipation and dispersion properties of the formulated elements are examined. It is found that all the elements are unconditionally stable, the order of accuracy is equal to two times the element order minus one or two times the element order, and the high-order elements possess desired high numerical dissipation in the high-frequency domain and low numerical dissipation and dispersion in the lowfrequency domain. Three fundamental numerical examples are investigated to demonstrate the effectiveness and high accuracy of the elements, as compared with the commonly used time integration schemes.