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 Complementarity 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.

翻译：本工作的目标是开发一种稳健且易于实现的动态车-轨-结构相互作用（VTSI）分析算法，适用于列车通过桥梁的场景。该算法可便捷地集成到现有桥梁分析软件中，仅需对代码进行最小修改。其核心思路是分别对桥梁与列车建模，并通过运动学约束将两者耦合。在此方法中，轮轨接触力作为拉格朗日乘子出现。直接实现该算法会导致接触力出现伪振荡。为抑制这些伪振荡，本文提出两种方法：（a）对运动学约束进行三次B样条时间插值，以及（b）采用Bathe最初提出的改进型时间积分方案。通过通用微分代数方程（DAE）求解器验证了该算法所得解的准确性。由于列车高速运行及轨道可能存在不平顺，车轮可能瞬时脱离轨道。本文将这种接触分离问题建模为线性互补问题（LCP）。基于此建模，分析中引入接触分离仅需将调用线性方程组求解器替换为调用LCP求解器，即仅需修改算法流程中的两个步骤。本文重点阐述VTSI分析的计算流程，主要贡献在于识别与时变运动学约束相关的计算难题，明确其成因并提出解决方案。