A direct method for analyzing the nonlinear vehicle–structure interaction

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

A wheel-rail contact formulation for analyzing the train-structure nonlinear interaction that takes into account the wheel and rail geometry is proposed. Most of the existing methods treat the contact forces as external forces, whereas the present formulation uses a finite element to model the behavior in the contact interface, based on Hertz's theory and Kalker's laws. The equations of motion are complemented with constraint equations that relate the displacements of the vehicle and structure, being the complete system solved directly using an optimized algorithm. The formulation is validated with experimental data from a test performed on a rolling stock plant

A direct method for analyzing the vertical vehicle-structure interaction

A new method for the dynamic analysis of the vertical vehicle-structure interaction is presented. The vehicle and structure systems can be discretized with various types of finite elements and may have any degree of complexity. The equations of both systems are complemented with additional compatibility equations to ensure contact between the vehicles and the structure. The equations of motion and the compatibility equations form a single system that is solved directly, thus avoiding the iterative procedure used by other authors to satisfy the compatibility between the vehicle and structure. For large structural systems the proposed method is usually more efficient than those that frequently update and factorize the system matrix. Some numerical examples have shown that the proposed formulation is accurate and efficient