Dynamic analysis of the train-bridge interaction: an accurate and efficient numerical method

The dynamic behavior of railway bridges carrying high-speed trains can be analyzed with or without the consideration of the vehicle's own structure. However, due to the amount of kinetic energy carried at high speeds, the train may interact significantly with the bridge, especially when resonance occurs. Equally important is the riding comfort and the stability of the track and train cars, which are usually the most critical limit states in the design of this type of structures. With the aim of studying this problem a computer code was developed, being the interaction between the bridge and the train implemented by means of contact conditions between each train wheel (nodal point) and the structure (point inside a finite element). The treatment of the interaction between a train wheel and a point on the surface of a finite element is directly and efficiently implemented by means of an extended stiffness matrix, which includes stiffness, flexibility and additional terms that stem from the compatibility equations between the displacements of the vehicle and the bridge. This methodology was applied to the study of the dynamic behavior of a bowstring arch bridge and proved to be very accurate and efficien

Development of an efficient finite element model for the dynamic analysis of the train-bridge interaction

The design of high-speed railway bridges comprises a set of demands, from safety and serviceability aspects, to new types of equipment and construction solutions. In order to perform an accurate and realistic evaluation of the corresponding dynamic behavior, adequate analysis tools that take into account the complexity of the train-bridge system are required. These computational tools must be based on efficient algorithms to allow for the completion of detailed dynamic analyses in a reasonable amount of time. The classical methods of analysis may be unsatisfactory in the evaluation of the dynamic effects of the train-bridge system and fully assessment of the structural safety, track safety and passenger comfort. A direct and versatile technique for the simulation of the train-bridge interaction was implemented in the FEMIX code, which is a general purpose finite element computer program. The presented case study is an application of the proposed formulation, which proved to be very accurate and efficient

Nonradial solutions for the H\'enon equation in RNR^N

In this paper we consider the problem {ll} -\Delta u=(N+\a)(N-2)|x|^{\a}u^\frac{N+2+2\a}{N-2} & in R^N u>0& in R^N u\in D^{1,2}(R^N). where $N\ge3$. From the characterization of the solutions of the linearized operator, we deduce the existence of nonradial solutions which bifurcate from the radial one when $\alpha$ is an even integer

Dynamic analysis of the vehicle-structure interaction: a direct and efficient computer implementation

The simulation of the dynamic behavior of a structure subjected to sets of moving loads originated by vehicles whose structural behavior is also considered corresponds to a task not efficiently addressed by standard finite element packages. The capability of solving this type of problems has been introduced in the FEMIX 4.0 computational code by means of an integrated formulation, which includes equilibrium and compatibility equations, with unknowns that consist on displacements and interaction forces. Each system of linear equations is efficiently solved by considering the characteristics of each submatrix of the coefficient matrix

A nonlinear vehicle-structure interaction methodology with wheel-rail detachment and reattachment

. A vehicle-structure interaction methodology with a nonlinear contact formulation based on contact and target elements has been developed. To solve the dynamic equations of motion, an incremental formulation has been used due to the nonlinear nature of the contact mechanics, while a procedure based on the Lagrange multiplier method imposes the contact constraint equations when contact occurs. The system of nonlinear equations is solved by an efficient block factorization solver that reorders the system matrix and isolates the nonlinear terms that belong to the contact elements or to other nonlinear elements that may be incorporated in the model. Such procedure avoids multiple unnecessary factorizations of the linear terms during each Newton iteration, making the formulation efficient and computationally attractive. A numerical example has been carried out to validate the accuracy and efficiency of the present methodology. The obtained results have shown a good agreement with the results obtained with the commercial finite element software ANSY

Impact of wheel shape on the vertical damage of cast crossing panels in turnouts

Impact forces generated in the load transfer area of railway crossing panels lead to a range of degradation modes from wear and fatigue of the contacting materials, fatigue of supporting components to ballast/subgrade deterioration. A simplified modelling approach has been developed to first analyse the geometrical problem of the axle rolling through the crossing geometry, and in a second step to predict the vertical dynamic force produce from the interaction between the wheel unsprung mass and the track system. The force is analysed in the frequency domain to estimate the level of damage in different parts of the track system. A parametric analysis of wheel shapes was carried out showing that the axle lateral displacement has a significant influence on the produced level of damage and also that characteristics such as the wheel flange thickness and the equivalent slope in the area of contact also leads to increased damage. It is suggested that such a measure in combination with the simplified algorithms developed here could be used, possibly in combination with track side monitoring system, to highlight traffic instances leading to increased asset damage

Optimization of support stiffness at a railway crossing panel

Turnouts are a key element of the railway system. They are also one part of the railway system with the highest number of degradation modes and failures for a number of reasons, including dynamic loads generated from non-linearities in the rail geometry and track support stiffness. It is therefore necessary to optimise the performance of the system in terms of its dynamic behaviour taking into account effects on long-term term damage evolution. The main aim of this study is to optimise the rail-pad stiffness in the crossing panel in order to achieve a decrease in the main indicator for ballast settlement, which is ballast pressure. A three-dimensional vehicle/track interaction model has been established, considering a detailed description of the crossing panel support structure. Genetic algorithm has been applied to find the optimum rail-pad combination for a specific case where variation in travelling speed and support conditions have been considered