An efficent computing strategy based on the unconditionally stable explicit algorithm for the nonlinear train-track-bridge system under an earthquake

Abstract

Dynamic response analysis of a nonlinear train-track-bridge system under earthquakes is a time-consuming task. In this paper, a fast computing strategy is proposed to reduce the simulation time by solving the shortcomings of classical time integration algorithms in the computation of the coupled system. The core of the strategy focuses on completely explicit computational processes and unconditional stability. Based on the loosely coupling scheme, the model of the train-track-bridge system is divided into two parts, namely, the train substructure established using multibody dynamics and the track-bridge substructure established using the finite element method. Track-bridge substructure and train substructure are separately integrated by the unconditionally stable explicit algorithm, CQ3, and its degenerate form, respectively. The interaction of the two substructures depends on wheel-rail forces. The track-bridge substructure is further decoupled to describe its nonlinear behavior and to improve the speed of solving algebraic equations. The proposed strategy not only avoids the complex iterative process of the nonlinear train-track-bridge system but also eliminates the limitation of the integration time step caused by the minimum natural period of the track-bridge substructure. This paper first simulates the dynamic response of a train under a sinusoidal displacement excitation and extends the simulation strategy to analyze the vibration of the coupling system under an earthquake. The applicability, efficiency, and accuracy of the strategy are illustrated through three numerical analyses. The strategy proposed in this paper provides a convenient and greatly computationally efficient option for simulating the nonlinear dynamic response of a large-scale train-track-bridge system.