A direct method for analyzing the nonlinear vehicle–structure interaction

Abstract

This article presents an accurate, efficient and stable algorithm to analyze the nonlinear vertical vehicle-structure interaction. The governing equilibrium equations of the vehicle and structure are complemented with additional constraint equations that relate the displacements of the vehicle with the corresponding displacements of the structure. These equations form a single system, with displacements and contact forces as unknowns, that is solved using an optimized block factorization algorithm. Due to the nonlinear nature of contact, an incremental formulation based on the Newton method is adopted. The vehicles, track and structure are modeled using finite elements to take into account all the significant deformations. The numerical example presented clearly demonstrates the accuracy and computational efficiency of the proposed method.

Wheel–rail contact formulation for analyzing the lateral train–structure dynamic interaction

“…Neves et al [13] developed an accurate and efficient algorithm, referred to as the direct method, in which the governing equilibrium equations of the vehicle and structure are complemented with additional constraint equations that relate the displacements of the contact nodes of the vehicle with the corresponding nodal displacements of the structure. These equations form a single system, with displacements and contact forces as unknowns, that is solved directly using an optimized block factorization algorithm.…”

“…The constraint equations that relate the displacements of these nodes are imposed using the direct method [13], which is extended to deal with three-dimensional contact problems. Since in the proposed contact element there are no moments transmitted across the contact interface, the constraint equations only relate the translational displacements in the three directions.…”

“…According to the α method, the following approximations for the acceleration and velocity at the current time step can be obtained [13].…”

“…An extension of the formulation described in [12][13] that takes into account the lateral dynamic effects between railway vehicles and structures is proposed in the present article. Most of the existing methods treat the contact forces in the normal and tangential directions as external forces, whereas the proposed formulation uses a finite element to model the behavior in the contact interface.…”

Nonlinear modeling of the vehicle/structure interaction on a skewed highway bridge using an iterative uncoupled approach

“…Therefore, a large number of the previous investigations were focused on simplifying the complex dynamic interaction problem. Some have used simplified beam models to represent a highway bridge [2], [5], [6] and [7]. Others have simulated a bridge using an assembly of grillage members which consist of a combination of longitudinal beams and transverse elements [3], [4].…”