Moving internal node element method for dynamic analysis of beam structure under moving vehicle

This paper presents a new Moving Internal Node Element (MINE) method for the dynamic analysis of bridges/beam structure under a moving load/vehicle. By introducing a moving internal node within the standard beam element, the resulting MINE method eliminates the need for interpolation for the dynamic responses at the contact point between the moving load/vehicle and the beam structure. The governing equation of the moving internal node element is derived from the resulting bi-element with variable lengths but yet keeping the total length of the bi-element a constant. With this bi-element, the moving load/vehicle can be tracked easily as it is coincident with the moving internal node. This allows the reduction of the number of elements when compared to the conventional FEM needed to accurately predict the dynamic responses (e.g., displacement, velocity, and acceleration) of the moving load/vehicle (including at the contact point). Accuracy and computational efficiency are enhanced due to the smaller number of elements needed in the MINE method. The illustrative moving load/vehicle problems solved herein demonstrated the accuracy of the MINE method as well as its versatility and easy handling of any vehicle model.