  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.
