Simulation of vertical dynamic vehicle–track interaction using a two-dimensional slab track model

The vertical dynamic interaction between a railway vehicle and a slab track is simulated in the time domain using an extended state-space vector approach in combination with a complex-valued modal superposition technique for the linear, time-invariant and two-dimensional track model. Wheel–rail contact forces, bending moments in the concrete panel and load distributions on the supporting foundation are evaluated. Two generic slab track models including one or two layers of concrete slabs are presented. The upper layer containing the discrete slab panels is described by decoupled beams of finite length, while the lower layer is a continuous beam. Both the rail and concrete layers are modelled using Rayleigh–Timoshenko beam theory. Rail receptances for the two slab track models are compared with the receptance of a traditional ballasted track. The described procedure is demonstrated by two application examples involving: (i) the periodic response due to the rail seat passing frequency as influenced by the vehicle speed and a foundation stiffness gradient and (ii) the transient response due to a local rail irregularity (dipped welded joint).     

A simplified grounding damage prediction method and its application in modern damage stability requirements

This paper presents the analyses and results aimed at developing damage stability requirements which take into account the structural vulnerability to grounding damage, i.e. the kinetic energy available to generate damage and the structural resistance. The paper presents analysis of new damage statistics in order to determine impact scenarios, in particular in terms of impact speed, impact location, and width and height of damage. Furthermore a new empirical damage prediction formula is developed based on a combination of full-scale testing and extensive non-linear finite element analyses. This deterministic prediction method is validated against grounding experiments and then used in a probabilistic (Monte Carlo) simulation framework. First the simulation method is calibrated and validated against the real statistical damage data for conventional ships and then it is used to generate damage statistics for high-speed craft. It turns out that the grounding damage statistics for all ships can be characterized by a single parameter; the Grounding Damage Index, GDI, which includes the ship kinetic energy and its structural resistance to grounding damage. Simple, closed-form expressions are developed for the GDI and it is shown how the probability of exceeding a box-shaped damage is a simple function of the GDI and the size of the box. The paper therefore gives the background and the results for a new generation of damage stability rules where the structural crashworthiness is taken into account and where the passive safety level is explicitly expressed. It furthermore gives simplified prediction tools and data for actual ships, i.e. a toolbox that is readily available for risk analysis regarding grounding damage.