Fast simulation of 3D elastic response for wheel–rail contact loading using Proper Generalized Decomposition

Abstract

To increase computational efficiency, we adopt Proper Generalized Decomposition (PGD) to solve a reduced-order problem of the displacement field for a three-dimensional rail head exposed to different contact scenarios. The three-dimensional solid rail head is modeled as a two-dimensional cross-section, with the coordinate along the rail being treated as a parameter in the PGD approximation. A novel feature is that this allows us to solve the full three-dimensional model with a nearly two-dimensional computational effort. Additionally, we incorporate the distributed contact load predicted from dynamic vehicle–track simulations as extra coordinates in the PGD formulation, using a semi-Hertzian contact model. The problem is formulated in two ways; one general ansatz which considers the treatment of numerous parameters, some of which exhibit a linear influence, and a linear ansatz where multiple PGD solutions are solved for. In particular, situations where certain parameters become invariant are handled. We assess the accuracy and efficiency of the proposed strategy through a series of verification examples. It is shown that the PGD solution converges toward the FE solution with reduced computational cost. Furthermore, solving for the PGD approximation based on load parameterization in an offline stage allows expedient handling of the wheel–rail contact problem online.