Performance of the quadrilateral overlapping elements combined with implicit time integration method in solving the transient wave propagations

In the analyses of transient wave propagations, a numerical method with the monotonic convergence property is favored by analysts. However, the classic finite element method does not possess this attractive property due to pronounced numerical dispersions and can generate severe spurious oscillations by using a small time step. In this work, the novel quadrilateral overlapping element is extended into the investigation of transient wave propagations by using the standard implicit Bathe time integration method. Since the local field approximation in overlapping elements can be a function, the performances of different basis functions in transient wave propagation problems are studied. Detailed analyses regarding the numerical dispersion error caused by spatial and temporal discretization are conducted. Then several numerical experiments with different types of excitation loading are investigated to show the performance of the quadrilateral overlapping elements. It is shown that the overlapping element with the trigonometric functions and the bilinear Lagrange polynomials has the monotonic convergence property and can perform well in handling various transient wave propagation problems.