An algorithm for dynamic vehicle-track-structure interaction analysis for high-speed trains

Abstract

The objective of the present work is to develop a robust, yet simple-to-implement algorithm for dynamic vehicle-track-structure-interaction (VTSI) analysis, applicable to trains passing over bridges. The algorithm can be readily implemented in existing bridge analysis software with minimal code modifications. It is based on modeling the bridge and train separately, and coupling them together by means of kinematic constraints. The contact forces between the wheels and the track become Lagrange multipliers in this approach. A direct implementation of such an approach results in spurious oscillations in the contact forces. Two approaches are presented to mitigate these spurious oscillations – (a) a cubic B-spline interpolation of the kinematic constraints in time, and (b) an adaptation of an alternate time-integration scheme originally developed by Bathe. Solutions obtained using this algorithm are verified using a generic differential algebraic equation (DAE) solver. Due to high train speeds and possible track irregularities, wheels can momentarily lose contact with the track. This contact separation is formulated as a Linear Complementary Problem (LCP). With this formulation, including contact separation in the analysis amounts to replacing a call to a linear equation solver by a call to an LCP solver, a modification of only two steps of the procedure. The focus of this paper is on the computational procedure of VTSI analysis. The main contribution of this paper is recognizing computational issues associated with time-varying kinematic constraints, clearly identifying their cause and developing remedies.