Presented herein is a novel computational approach using the moving element method (MEM) for simulating the dynamic response of Mindlin plate resting on a viscoelastic foundation and subjected to moving loads. The governing equations and the element mass, damping and stiffness matrices are formulated in a convected coordinate system in which the origin is attached to the point of the moving applied load. Thus, the method simply treats moving loads as ‘stationary’ at the nodes of the plate to avoid updating the locations of moving loads due to the change of the contact points on the plate. To verify the accuracy of the proposed computational approach, static and free vibration analyses of plates are investigated first. Next, the dynamic response of plate resting on a viscoelastic foundation subjected to a moving load is examined. A parametric study is performed to determine the effects of the load’s velocity, foundation damping and foundation stiffness on the dynamic response of a plate. Finally, the comparisons of the dynamic response of plates resting on viscoelastic foundation and subjected to moving vehicles with three models of load (single-wheel, single-axle and tandem-axle) are discussed.

In this article, the dynamic analysis of three-dimensional high-speed train-track model is carried out using moving element method. The train comprises a car-body supported by a secondary suspension system to a bogie. The bogie is in turn connected to wheel-sets through a primary suspension system. A total of 16 degrees of freedom is employed to describe the vertical, lateral, rolling, pitching, and yawing displacements of the car-body, the bogie, and the wheel-sets. The Hertzian contact and Kalker's linear theory are used to account for the vertical and lateral contact forces between the wheels and rails. Two rails are modeled as two Euler-Bernoulli beams resting on a viscoelastic foundation. The moving element method is extended to establish the coupling formulations of the mass, damping, and stiffness matrices in vertical and lateral directions, where the element matrices are formulated based on a convected coordinate system attached to the moving vehicle. The dynamic amplification factor is defined as the ratio of the maximum dynamic contact force to the static load at the contact point between the wheel and the rail. To illustrate the benefits of the proposed threedimensional train-track model, several numerical examples are performed in this study to present the effects of the train speed, the resonance phenomenon, the track irregularity, and track stiffness variations along the track and across the track width on the dynamic amplification factor of the high-speed train.

The diffraction of waves by two bottom-fixed vertical circular cylinders is investigated by using boundary element method. This method has been successfully applied to the isolated vertical circular cylinder and now is used to study the interaction between waves and two vertical cylinders. In this paper, a numerical analysis by boundary element method is developed by using linear potential theory. The numerical analysis by boundary element method is based on Green's theorem and introduced to an integral equation for the fluid velocity potential around the vertical circular cylinders. To verify this method, the wave-exciting forces on two transverse and tandem cylinders obtained in this study are compared with the results computed by the multiple scattering method. The comparisons show that the results of this study are strong agreement with their results. Also in this paper, several numerical examples are given to illustrate the effects of various parameters on the wave-exciting force such as the separation distance, the relative size of the cylinders and the incident wave angle. This numerical analysis developed by boundary element method will be applied for various offshore structures to be constructed in the future.