A Dynamic Partitioning Method to solve the vehicle-bridge interaction problem

Abstract

This paper presents a Dynamic Partitioning Method (DPM) to solve the vehicle-bridge interaction (VBI) problem via a set of exclusively second-order ordinary differential equations (ODEs). The partitioning of the coupled VBI problem follows a localized Lagrange multipliers approach that introduces auxiliary contact bodies between the vehicle's wheels and the sustaining bridge. The introduction of contact bodies, instead of merely static points, allows the assignment of proper mass, damping and stiffness properties to the involved constrains. These properties are estimated in a systematic manner, based on a consistent application of Newton's law of motion to mechanical systems subjected to bilateral constraints. In turn, this leads to a dynamic representation of motion constraints and associated Lagrange multipliers. Subsequently, both equations of motion and constraint equations yield a set of ODEs. This ODE formulation avoids constraint drifts and instabilities associated with differential–algebraic equations, typically adopted to solve constrained mechanical problems. Numerical applications show that, when combined with appropriate numerical analysis schemes, DPM can considerably decrease the computational cost of the analysis, especially for large vehicle-bridge systems. Thus, compared to existing methods to treat VBI, DPM is both accurate and cost-efficient.