Vehicle–Bridge Interaction (VBI) refers to the dynamic responses generated during a vehicle's passage over a bridge, where both systems behave in a coupled manner, resulting in a unified dynamic response. As vehicles traverse the bridge, the mutual influence between the vehicle and the structure becomes critical for understanding the overall behavior. VBI analysis investigates how these interactions contribute to structural anomalies, fatigue damage, and long-term deterioration of the bridge system, making the comprehension of these effects essential for maintaining structural integrity.The literature commonly represents VBI using numerical models or approaches that combine analytical solutions for the vehicle dynamics with a numerical representation of the bridge. Bridge structures are typically discretized using finite elements of varying complexity, such as 2D or 3D beam elements, plate or shell elements, depending on the required modeling detail. Due to the higher computational cost of the surface models, beam representations are more prevalent, with Euler-Bernoulli kinematics the most widely used, although the Timoshenko beam model is also employed, as adopted in this study for greater generality. Vehicle models in existing VBI studies are simplified as mass-spring-damper systems that represent their mechanical components: truck, trailer and various axles. In this work, the vehicle is modeled in an alternative manner using strategically positioned plane frame finite elements that are mechanically equivalent to conventional mass-spring-damper systems.To address the nonlinear geometric effects, due to the large displacement of the vehicle regarding the bridge, the positional formulation of the finite element method is employed. Numerical solution of the nonlinear dynamical system is performed by the Newton-Raphson method with the generalized-alpha time integration scheme. Lagrange multipliers are used to account for the coupling between vehicle and bridge frame elements. The influence of pavement roughness is also considered along the vehicle path.Comparison of the simulated VBI dynamic responses with existing literature is conducted to evaluate the suitability of the proposed model in representing the problem.
