An Effective Tangent Stiffness of Train–Track–Bridge Systems Based on Artificial Neural Network

Quan Gu,Jianguo Zhang,Yongdou Liu,Jinghao Pan,Minhong Fu

doi:10.3390/app12052735

Quan Gu, Jianguo Zhang + Show 3 more

Open Access

https://doi.org/10.3390/app12052735

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Journal: Applied Sciences	Publication Date: Mar 7, 2022
Citations: 5	License type: CC BY 4.0

Affiliation: Xiamen University, Qinghai University

Abstract

Dynamic response analysis of a train–track–bridge (TTB) system is a challenging task for researchers and engineers, partially due to the complicated nature of the wheel–rail interaction (WRI). When Newton’s method is used to solve implicit nonlinear finite element equations of a TTB system, consistent tangent stiffness (CTS) is essential to guarantee the quadratic convergence rate. However, the derivation and software implementation of CTS for the WRI element require significant efforts. Artificial neural network (ANN) can directly obtain a potentially good tangent stiffness by a trained relationship between input nodal displacement/velocity and output tangent stiffness. In this paper, the backpropagation neural-network-based tangent stiffness (BPTS) of the WRI element is derived and implemented into a general finite element software, OpenSees, and verified by dynamic response analysis of a high-speed train running on a seven span simply supported beam bridge. The accuracy and efficiency are compared between the use of BPTS and CTS. The results demonstrate that BPTS can not only save the significant efforts of deriving and software implementing CTS but also improve computational efficiency while ensuring good accuracy.

Highlights

Dynamic response analysis of a train–track–bridge (TTB) system is a challenging task for researchers and engineers, partially due to the strong nonlinearity and complex contact conditions of the wheel–rail interaction (WRI)
Montenegro et al [5] proposed a wheel–rail contact formulation for analyzing the nonlinear train–structure interaction that takes into account wheel and rail geometry and used a WRI element to model the behavior of the contact interface based on Hertz’s theory and Kalker’s laws
Liu et al [7] developed a 3D WRI element by wrapping the WRI into an element where the contact force is obtained by using Kalker linear theory, nonlinear Hertz theory, and the Polach formulation

Summary

Introduction

Dynamic response analysis of a train–track–bridge (TTB) system is a challenging task for researchers and engineers, partially due to the strong nonlinearity and complex contact conditions of the wheel–rail interaction (WRI). The element internal resisting force R consists of the forces on the nodes Ow, bi, and bi+1, i.e., R= [Rw, Rbi , Rbi+1 ] and can be obtained based on the nodal displacement u and velocity v, i.e., R = R(u, v), where the nodal displacement u consists of the displacements of the wheel node and two rail nodes, i.e., u= [uw, ubi , ubi+1 ], while the velocity v is a function of u, i.e., v = v(u). The element internal resisting force R can be calculated based on the contact force F between wheel node Ow and virtual rail node Or, which consists of the normal contact force Fn and the tangential contact force Ft, i.e.,. The derivation and implementation of Equation (5) require significant efforts, and the detailed derivation formula can be found in [13]

The BP-Based Tangent Stiffness (BPTS)

The Data foofr tthhee BWPRNIeuerleaml Neenttwiosrkreplaced by the BPTS

Verification of BPTS in the Wheelset Example

Conclusions

Findings

Methods