An algorithm for three-dimensional dynamic vehicle-track-structure interaction (VTSI) analysis is described in this paper. The algorithm is described in terms of bridges and high-speed trains, but more generally applies to multibody systems coupled to deformable structures by time-varying kinematic constraints. Coupling is accomplished by a kinematic constraint/Lagrange multiplier approach, resulting in a system of index-3 Differential Algebraic Equations (DAE). Three main new concepts are developed. (i) A corotational approach is used to represent the vehicle (train) dynamics. Reference coordinate frames are fitted to the undeformed geometry of the bridge. While the displacements of the train can be large, deformations are taken to be small within these frames, resulting in linear (time-varying) rather than nonlinear dynamics. (ii) If conventional finite elements are used to discretize the track, the curvature is discontinuous across elements (and possibly rotation, too, for curved tracks). This results in spurious numerical oscillations in computed contact forces and accelerations, quantities of key interest in VTSI. A NURBS-based discretization is employed for the track to mitigate such oscillations. (iii) The higher order continuity due to using NURBS allows for alternative techniques for solving the VTSI system. First, enforcing constraints at the acceleration level reduces an index-3 DAE to an index-1 system that can be solved without numerical dissipation. Second, a constraint projection method is proposed to solve an index-3 DAE system without numerical dissipation by correcting wheel velocities and accelerations. Moreover, the modularity of the presented algorithm, resulting from a kinematic constraint/Lagrange multiplier formulation, enables ready integration of this VTSI approach in existing structural analysis and finite element software.

翻译：本文描述了一种用于三维车辆-轨道-结构动态相互作用（VTSI）分析的算法。该算法以桥梁和高速列车为例进行阐述，但更一般地适用于通过时变运动学约束与可变形结构耦合的多体系统。耦合通过运动学约束/拉格朗日乘子法实现，最终形成指标为3的微分代数方程组（DAE）。本文发展了三个主要新概念：（i）采用共旋方法表征车辆（列车）动力学。参考坐标系拟合至桥梁未变形几何形状。虽然列车位移可能较大，但在此坐标系中变形被视为微小，从而产生线性（时变）而非非线性动力学。（ii）若采用传统有限元离散轨道，曲率在单元间不连续（对于曲线轨道，旋转也可能不连续）。这将导致计算接触力与加速度（VTSI关键参量）出现数值伪振荡。为此采用基于NURBS的轨道离散方法以抑制此类振荡。（iii）NURBS的高阶连续性为VTSI系统求解提供了替代技术。首先，在加速度层面施加约束将指标3的DAE降阶为指标1系统，可避免数值耗散求解；其次，提出约束投影法，通过修正车轮速度与加速度实现无数值耗散的指标3 DAE系统求解。此外，基于运动学约束/拉格朗日乘子公式的算法模块化特性，使该VTSI方法可便捷集成至现有结构分析与有限元软件中。