Shakedown Limits of Slab Track Substructures and Their Implications for Design

This paper presents an approach to shakedown of slab track substructures subjected to train loads. The train load is converted into a distributed moving load on the substructure surface using a simplified track analysis. Based on the lower-bound dynamic shakedown theorem, shakedown solutions for the slab track substructures are obtained over a range of train speeds between zero and the critical speed of the track. It is found the shakedown limit is largely influenced by the ratio of layer elastic moduli and the ratio of train speed to critical speed rather than their absolute values. An attenuation factor, as a function of the critical speed and the friction angle of subsoil, is proposed to effectively obtain the shakedown limit of the slab track substructure at any train speed. In light of the shakedown solutions, improvements to the existing design and analysis approaches are also suggested

Linear matching methods for shakedown analysis

An understanding of the load bearing capacity of road pavements requires insight into the load levels at which incremental plastic strains occur under rolling contact. A number of authors have described solutions of this problem in terms of shakedown limits, assuming particular simple classes of plastic deformation patterns and using the upper bound shakedown theorem. In this paper we describe a general numerical technique, the Linear Matching Method, for evaluating the shakedown limit under rolling contact including surface friction where the mechanism at the shakedown limit may be described by any finite element discretization

Extension of the Linear Matching Method to frame structures made from a material that exhibits softening

This paper considers the problem of evaluating the maximum load that an elastic-plastic frame structure can withstand when material or element softening is present. Here we propose an extension of the Linear Matching Method to take into account material softening. The technique has two major steps: reduction of the total potential energy to obtain the solution of a linear problem and scaling of the resulting mechanism of deformation to maximize the load. Two procedures are evaluated for the second of these steps; a direct approach which simply examines how the solution evolves along a radial path in degree of freedom space, and an incremental method which takes into account how the solution might evolve along paths away from this radial line. It is demonstrated that the incremental approach is more robust and provides stable solutions for high and low levels of softening, but numerical instabilities in the procedure can occur for intermediate degrees of softening. © 2011 Elsevier Masson SAS. All rights reserved

The Linear Matching Method applied to composite materials: A micromechanical approach

The paper considers a Direct Method for the evaluation of the maximum load corresponding to pre-assigned limits on the non-linear behaviour of the matrix and fibres in a laminate structure. This is achieved by combining a consistent micro-macro model for linear behaviour with an extension of the Linear Matching Method (LMM), previously extensively applied to Direct Methods in plasticity. The method is developed with assumptions that allow the methodology to be displayed in its simplest form. Applications to examples of laminate elements and a laminate plate containing a hole are described, assuming a matrix with a limit on ductility. © 2010

Evaluation of the convergent properties of the Linear Matching Method for computing the collapse of structural components

The paper considers the application of the Linear Matching Method to the limit analysis of perfectly plastic portal frames. This allows the display of the characteristic features of this method to a class of structural problems that have been studied by several other methods. The convergence of both upper and lower bounds is proven and a simple geometric interpretation displays the nature of the programming method. Through a sequence of examples the convergence properties of the method are displayed, showing that complete convergence can sometimes be delayed by the proximity of mechanisms with near equal limit loads. © 2009 Elsevier Masson SAS. All rights reserved