A practical three-dimensional wheel-rail interaction element for dynamic response analysis of vehicle-track systems

Liu, Yongdou; Montenegro, Pedro Aires; Gu, Qiang; Guo, Wei; Calçada, Rui; Pombo, João

doi:10.1016/j.compstruc.2021.106581

Cited by 17 publications

(15 citation statements)

References 42 publications

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“…The normal contact force F c n and tangential contact forces F c t1 and F c t2 are calculated using nonlinear Hertz theory, Kalker linear theory, and the Polach formulation [19]. After the contact force F is obtained, the resisting force on the wheel node, Rw and the resisting force on the virtual rail node Rr (in Figure 3) can be calculated respectively by where A denotes the transformation matrix of the coordinate system, Tw and Tr denote the transformation matrix that converts F to the wheel node and the virtual rail node, which is related to the vector from the wheel-rail contact point to the wheel node and that to the virtual rail node [7]. The superscript T denotes the transpose of the matrix.…”

Section: The Internal Resisting Force and Consistent Tangent Stiffnes...mentioning

confidence: 99%

“…where A denotes the transformation matrix of the coordinate system, Tw and Tr denote the transformation matrix that converts F to the wheel node and the virtual rail node, which is related to the vector from the wheel-rail contact point to the wheel node and that to the virtual rail node [7]. The superscript T denotes the transpose of the matrix.…”

Section: R T a Fat R T A Fatmentioning

confidence: 99%

“…( 4) Substituting the CTS with the BPTS, i.e., the mapping relationship in Equations ( 6) and ( 8), by software implementing the BPTS algorithm in the WRI element. In practice, the calculation to obtain input X and output Y in step 1 and the training process in step 3 can be performed simultaneously, i.e., at the beginning of the calculation, the CTS (or the tangent by the perturbation method that obtains the tangent by the perturbation of displacement [7]) is used, and the input and output obtained are used to train the ANN model. After the ANN model has been well trained, the BPTS is used instead of the CTS to continue the calculation process so as to realize the intelligent choice of the tangent stiffness.…”

Section: The Bp-based Tangent Stiffness (Bpts)mentioning

confidence: 99%

“…As mentioned in Section 2.2, for the ANN model for the tangent stiffness of WRI, the inputs X are the nodal displacement u and velocity v, while the outputs Y are the approximate of ∂R w ∂u and ∂R r ∂u obtained by perturbation [7] because its derivation and programming are quite simple. There are 36 inputs and 216 outputs (decomposed as 12 groups with 18 outputs in each group for fast training purposes).…”

Section: The Data For the Bp Neural Networkmentioning

confidence: 99%

“…Pombo [6] presented a general wheel-rail contact detection formulation and calculated the contact forces using Kalker linear theory, a heuristic nonlinear model, and the Polach formulation. 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. The WRI element has been demonstrated to be efficient and accurate, able to simulate complicated TTB systems, and is therefore used in the dynamic responses analysis of the TTB systems in this paper.…”

Section: Introductionmentioning

confidence: 99%

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

Pan

Liu

et al. 2022

Applied Sciences

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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.

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Section: The Internal Resisting Force and Consistent Tangent Stiffnes...mentioning

confidence: 99%

Section: R T a Fat R T A Fatmentioning

confidence: 99%

Section: The Bp-based Tangent Stiffness (Bpts)mentioning

confidence: 99%

Section: The Data For the Bp Neural Networkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Pan

Liu

et al. 2022

Applied Sciences

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Frequency veering of railway vehicle systems and its mapping to vibration characteristics

Liu,

Gong,

Zhou

et al. 2024

Multibody Syst Dyn

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On dynamic analysis method for large-scale train–track–substructure interaction

2022

Rail. Eng. Science

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Train–track–substructure dynamic interaction is an extension of the vehicle–track coupled dynamics. It contributes to evaluate dynamic interaction and performance between train–track system and its substructures. For the first time, this work devotes to presenting engineering practical methods for modeling and solving such large-scale train–track–substructure interaction systems from a unified viewpoint. In this study, a train consists of several multi-rigid-body vehicles, and the track is modeled by various finite elements. The track length needs only satisfy the length of a train plus boundary length at two sides, despite how long the train moves on the track. The substructures and their interaction matrices to the upper track are established as independent modules, with no need for additionally building the track structures above substructures, and accordingly saving computational cost. Track–substructure local coordinates are defined to assist the confirming of the overlapped portions between the train–track system and the substructural system to effectively combine the cyclic calculation and iterative solution procedures. The advancement of this model lies in its convenience, efficiency and accuracy in continuously considering the vibration participation of multi-types of substructures against the moving of a train on the track. Numerical examples have shown the effectiveness of this method; besides, influence of substructures on train–track dynamic behaviors is illustrated accompanied by clarifying excitation difference of different track irregularity spectrums.

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A practical three-dimensional wheel-rail interaction element for dynamic response analysis of vehicle-track systems

Cited by 17 publications

References 42 publications

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

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

Frequency veering of railway vehicle systems and its mapping to vibration characteristics

On dynamic analysis method for large-scale train–track–substructure interaction

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