Formulation of equations of motion of finite element form for vehicle-track-bridge interaction system with two types of vehicle model

2005 ◽  
Vol 62 (3) ◽  
pp. 435-474 ◽  
Author(s):  
Ping Lou ◽  
Qing-yuan Zeng
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Vehicle Model ◽  
Interaction System ◽  
Track Bridge

scholarly journals Numerical Simulation of Vertical Random Vibration of Train-Slab Track-Bridge Interaction System by PEM

2014 ◽  
Vol 2014 ◽  
pp. 1-21 ◽  
Author(s):  
Zhi-ping Zeng ◽  
Zhi-wu Yu ◽  
Yan-gang Zhao ◽  
Wen-tao Xu ◽  
Ling-kun Chen ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Random Vibration ◽  
Equations Of Motion ◽  
Gaussian Stochastic Process ◽  
Random Load ◽  
Energy Principle ◽  
Slab Track ◽  
Interaction System ◽  
Rail Irregularity ◽  
Track Bridge

The paper describes the numerical simulation of the vertical random vibration of train-slab track-bridge interaction system by means of finite element method and pseudoexcitation method. Each vehicle is modeled as four-wheelset mass-spring-damper system with two-layer suspension systems. The rail, slab, and bridge girder are modeled by three-layer elastic Bernoulli-Euler beams connected with each other by spring and damper elements. The equations of motion for the entire system are derived according to energy principle. By regarding rail irregularity as a series of multipoint, different-phase random excitations, the random load vectors of the equations of motion are obtained by pseudoexcitation method. Taking a nine-span simply supported beam bridge traveled by a train consisting of 8 vehicles as an example, the vertical random vibration responses of the system are investigated. Firstly, the suitable number of discrete frequencies of rail irregularity is obtained by numerical experimentations. Secondly, the reliability and efficiency of pseudoexcitation method are verified through comparison with Monte Carlo method. Thirdly, the random vibration characteristics of train-slab track-bridge interaction system are analyzed by pseudoexcitation method. Finally, applying the 3σrule for Gaussian stochastic process, the maximum responses of train-slab track-bridge interaction system with respect to various train speeds are studied.

High Speed Rail Short Bridge-Track-Train Interaction Based on the Decoupled Equations of Motion in the Finite Element Domain

2016 ◽  
Author(s):  
Said I. Nour ◽  
Mohsen A. Issa
Keyword(s):  
Finite Element ◽  
High Speed ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Rotational Inertia ◽  
Force Model ◽  
Inertia Effects ◽  
Contact Points ◽  
Short Span ◽  
Track Bridge

The interaction between the train, track, and bridge was considered as an interaction between two decoupled subsystems. A first subsystem consisted of the train vehicle simulated as a four-wheelset mass-spring-damper system having two layers of suspensions and ten degrees of freedom. A second subsystem consisted of the track-bridge system assumed to be a top rail beam and a bottom bridge beam coupled by continuous springs and dampers representing the elastic properties of the trackbed smeared over the spacing of the railway ties. The bridge supports were assumed to be rigid or flexible. The equations of motion of a finite element form were derived for each subsystem independently by means of the Newton’s second law. The dynamic interaction between the moving vehicle of the first subsystem and the stationary underlying track-bridge structure of the second subsystem was established by means of a no-separation constraint equation in the contact points between the wheels and the rails. The proposed two-dimensional analysis was intended to accurately describe the vertical behavior of short span bridges subjected to high-frequency excitations due to the passage of high speed trains; therefore, shear deformations, rotational inertia effects, and consistent mass matrices were adopted in the mathematical model. Numerical solutions of the decoupled equations of motion for both subsystems were obtained with the step-by-step direct integration in the time domain using HHT alpha method with a special scheme in the contact interface. The solution accuracy of the proposed method was validated against responses obtained from a semi-analytical method of a train car travelling over a simply supported bridge. The practical engineering application was demonstrated with a case study investigating effects of key parameters in the behavior of a ballasted short span railway bridge. Compared with the moving force model, results showed that for bridges with rigid supports both the vehicle interaction and trackbed produce lower peak responses at resonance speeds with the latter being more significant. However an increase in support flexibility had a greater impact across all speeds in increasing the bridge responses.

The Influence of Loading Position in A Priori High Stress Detection using Mode Superposition

2020 ◽  
Vol 1 (1) ◽  
pp. 93-102
Author(s):  
Carsten Strzalka ◽  
◽  
Manfred Zehn ◽  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
High Stress ◽  
Von Mises Stress ◽  
Detailed Knowledge ◽  
Variable Loading ◽  
Numerical Effort ◽  
Von Mises

For the analysis of structural components, the finite element method (FEM) has become the most widely applied tool for numerical stress- and subsequent durability analyses. In industrial application advanced FE-models result in high numbers of degrees of freedom, making dynamic analyses time-consuming and expensive. As detailed finite element models are necessary for accurate stress results, the resulting data and connected numerical effort from dynamic stress analysis can be high. For the reduction of that effort, sophisticated methods have been developed to limit numerical calculations and processing of data to only small fractions of the global model. Therefore, detailed knowledge of the position of a component’s highly stressed areas is of great advantage for any present or subsequent analysis steps. In this paper an efficient method for the a priori detection of highly stressed areas of force-excited components is presented, based on modal stress superposition. As the component’s dynamic response and corresponding stress is always a function of its excitation, special attention is paid to the influence of the loading position. Based on the frequency domain solution of the modally decoupled equations of motion, a coefficient for a priori weighted superposition of modal von Mises stress fields is developed and validated on a simply supported cantilever beam structure with variable loading positions. The proposed approach is then applied to a simplified industrial model of a twist beam rear axle.

A New Approach to the Rigid Finite Element Method in Modeling Spatial Slender Systems

2018 ◽  
Vol 18 (02) ◽  
pp. 1850017 ◽  
Author(s):  
Iwona Adamiec-Wójcik ◽  
Łukasz Drąg ◽  
Stanisław Wojciech
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
New Approach ◽  
Static And Dynamic Analysis ◽  
Rigid Finite Element Method ◽  
Longitudinal Flexibility ◽  
Element Method

The static and dynamic analysis of slender systems, which in this paper comprise lines and flexible links of manipulators, requires large deformations to be taken into consideration. This paper presents a modification of the rigid finite element method which enables modeling of such systems to include bending, torsional and longitudinal flexibility. In the formulation used, the elements into which the link is divided have seven DOFs. These describe the position of a chosen point, the extension of the element, and its orientation by means of the Euler angles Z[Formula: see text]Y[Formula: see text]X[Formula: see text]. Elements are connected by means of geometrical constraint equations. A compact algorithm for formulating and integrating the equations of motion is given. Models and programs are verified by comparing the results to those obtained by analytical solution and those from the finite element method. Finally, they are used to solve a benchmark problem encountered in nonlinear dynamic analysis of multibody systems.

Consistent Tangent Stiffness of a Three-Dimensional Wheel–Rail Interaction Element

2021 ◽  
Author(s):  
Quan Gu ◽  
Jinghao Pan ◽  
Yongdou Liu
Keyword(s):  
Finite Element ◽  
Quadratic Convergence ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Light Rail ◽  
Software Framework ◽  
Tangent Stiffness ◽  
Rail Vehicle ◽  
Interaction Element ◽  
Nonlinear Equations Of Motion

Consistent tangent stiffness plays a crucial role in delivering a quadratic rate of convergence when using Newton’s method in solving nonlinear equations of motion. In this paper, consistent tangent stiffness is derived for a three-dimensional (3D) wheel–rail interaction element (WRI element for short) originally developed by the authors and co-workers. The algorithm has been implemented in finite element (FE) software framework (OpenSees in this paper) and proven to be effective. Application examples of wheelset and light rail vehicle are provided to validate the consistent tangent stiffness. The quadratic convergence rate is verified. The speeds of calculation are compared between the use of consistent tangent stiffness and the tangent by perturbation method. The results demonstrate the improved computational efficiency of WRI element when consistent tangent stiffness is used.

scholarly journals On the Stream Function-Vorticity Finite Element Formulation for Incompressible Flow in Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Abdellatif Agouzal ◽  
Karam Allali ◽  
Siham Binna
Keyword(s):  
Finite Element ◽  
Porous Media ◽  
Stream Function ◽  
Incompressible Flow ◽  
Equations Of Motion ◽  
Finite Element Formulation ◽  
Flow In Porous Media ◽  
Darcy Law ◽  
Element Formulation ◽  
Discrete Problem

Stream function-vorticity finite element formulation for incompressible flow in porous media is presented. The model consists of the heat equation, the equation for the concentration, and the equations of motion under the Darcy law. The existence of solution for the discrete problem is established. Optimal a priori error estimates are given.

scholarly journals Linear Vibration Analysis of Shells Using a Seven-Parameter Spectral/hp Finite Element Model

2020 ◽  
Vol 10 (15) ◽  
pp. 5102
Author(s):  
Carlos Valencia Murillo ◽  
Miguel Gutierrez Rivera ◽  
Junuthula N. Reddy
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Variable Thickness ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Element Model ◽  
Linear Elastic ◽  
Commercial Code ◽  
The Finite Element Model ◽  
Hp Finite Element

In this paper, a seven-parameter spectral/hp finite element model to obtain natural frequencies in shell type structures is presented. This model accounts for constant and variable thickness of shell structures. The finite element model is based on a Higher-order Shear Deformation Theory, and the equations of motion are obtained by means of Hamilton’s principle. Analysis is performed for isotropic linear elastic shells. A validation of the formulation is made by comparing the present results with those reported in the literature and with simulations in the commercial code ANSYS. Finally, results for shell like structures with variable thickness are presented, and their behavior for different ratios r/h and L/r is studied.

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