Numerical method of lines for analysis of vehicle-bridge dynamic interaction

Abstract In this paper, a finite element-based formulation and implementation of vehicle-bridge dynamic interaction problems are presented. A variety of vehicle models are considered. The problem formulation takes into account the dynamic effects of multiple vehicles traversing on multiple lanes, with arbitrary and variable speeds and directions. The consideration of various vehicle traversing conditions allows for the interaction between vehicles and the bridge superstructure, as well as among vehicles, to be represented in a more realistic manner. The spatial discretization of the governing partial differential equation of the vehicle-bridge system is based on the finite element method. The resulting matrix ordinary differential equation is then discretized with respect to time on the basis of the Newmark method. The process of reduction of a partial differential equation into a matrix ordinary differential equation through a spatial discretization procedure, and then solving this expression using a time integration technique is referred to as the numerical method of lines. Since the consideration of vehicle-bridge interaction introduces nonlinearity into the problem formulation, a multi-predictor-corrector scheme is adopted in the solution procedure to obtain accurate results. The solution algorithm is implemented into a computer code developed by the authors, and numerical examples are solved to illustrate the validity and efficiency of the proposed formulation and solution methodology. Furthermore, the numerical results are detailed in order to highlight the dynamic effects of multiple vehicles on the behavior of bridge superstructures.