Development of optimal designs of insulated rail joints

Proper functioning of Insulated Rail Joints (IRJs) is essential for the safe operation of the railway signalling systems and broken rail identification circuitries. The Conventional IRJ (CIRJ) resembles structural butt joints consisting of two pieces of rails connected together through two joint bars on either side of their web and the assembly is held together through pre-tensioned bolts. As the IRJs should maintain electrical insulation between the two rails, a gap between the rail ends must be retained at all times and all metal contacting surfaces should be electrically isolated from each other using non-conductive material. At the gap, the rail ends lose longitudinal continuity and hence the vertical sections of the rail ends are often severely damaged, especially at the railhead, due to the passage of wheels compared to other continuously welded rail sections. Fundamentally, the reason for the severe damage can be related to the singularities of the wheel-rail contact pressure and the railhead stress. No new generation designs that have emerged in the market to date have focussed on this fundamental; they only have provided attention to either the higher strength materials or the thickness of the sections of various components of the IRJs. In this thesis a novel method of shape optimisation of the railhead is developed to eliminate the pressure and stress singularities through changes to the original sharp corner shaped railhead into an arc profile in the longitudinal direction. The optimal shape of the longitudinal railhead profile has been determined using three nongradient methods in search of accuracy and efficiency: (1) Grid Search Method; (2) Genetic Algorithm Method and (3) Hybrid Genetic Algorithm Method. All these methods have been coupled with a parametric finite element formulation for the evaluation of the objective function for each iteration or generation depending on the search algorithm employed. The optimal shape derived from these optimisation methods is termed as Stress Minimised Railhead (SMRH) in this thesis. This optimal SMRH design has exhibited significantly reduced stress concentration that remains well below the yield strength of the head hardened rail steels and has shifted the stress concentration location away from the critical zone of the railhead end. The reduction in the magnitude and the relocation of the stress concentration in the SMRH design has been validated through a full scale wheel – railhead interaction test rig; Railhead strains under the loaded wheels have been recorded using a non-contact digital image correlation method. Experimental study has confirmed the accuracy of the numerical predications. Although the SMRH shaped IRJs eliminate stress singularities, they can still fail due to joint bar or bolt hole cracking; therefore, another conceptual design, termed as Embedded IRJ (EIRJ) in this thesis, with no joint bars and pre-tensioned bolts has been developed using a multi-objective optimisation formulation based on the coupled genetic algorithm – parametric finite element method. To achieve the required structural stiffness for the safe passage of the loaded wheels, the rails were embedded into the concrete of the post tensioned sleepers; the optimal solutions for the design of the EIRJ is shown to simplify the design through the elimination of the complex interactions and failure modes of the various structural components of the CIRJ. The practical applicability of the optimal shapes SMRH and EIRJ is demonstrated through two illustrative examples, termed as improved designs (IMD1 & IMD2) in this thesis; IMD1 is a combination of the CIRJ and the SMRH designs, whilst IMD2 is a combination of the EIRJ and SMRH designs. These two improved designs have been simulated for two key operating (speed and wagon load) and design (wheel diameter) parameters that affect the wheel-rail contact; the effect of these parameters has been found to be negligible to the performance of the two improved designs and the improved designs are in turn found far superior to the current designs of the CIRJs in terms of stress singularities and deformation under the passage of the loaded wheels. Therefore, these improved designs are expected to provide longer service life in relation to the CIRJs.

Explicit finite element modelling of bridge girder bearing pedestals

Bridge girder bearings rest on pedestals to transfer the loading safely to the pier headstock. In spite of the existence of industry guidelines, due to construction complexities, such guidelines are often overlooked. Further, there is paucity of research on the performance of pedestals, although their failure could cause exorbitant maintenance costs. Although reinforced concrete pedestals are recommended in the industry design guidelines, unreinforced concrete and/ or epoxy glue pedestals are provided due to construction issues; such pedestals fail within a very short period of service. With a view to understanding the response of pedestals subject to monotonic loading, a three-dimensional nonlinear explicit finite element micro-model of unreinforced and reinforced concrete pedestals has been developed. Contact and material nonlinearity have been accounted for in the model. It is shown that the unreinforced concrete pedestals suffer from localised edge stress singularities, the failure of which was comparable to those in the field. The reinforced concrete pedestals, on the other hand, distribute the loading without edge stress singularity, again conforming to the field experience.

Experimental studies on the performance of rail joints with modified wheel/railhead contact

Rail joints are provided with a gap to account for thermal movement and to maintain electrical insulation for the control of signals and/or broken rail detection circuits. The gap in the rail joint is regarded as a source of significant problems for the rail industry since it leads to a very short rail service life compared with other track components due to the various, and difficult to predict, failure modes – thus increasing the risk for train operations. Many attempts to improve the life of rail joints have led to a large number of patents around the world; notable attempts include strengthening through larger-sized joint bars, an increased number of bolts and the use of high yield materials. Unfortunately, no design to date has shown the ability to prolong the life of the rail joints to values close to those for continuously welded rail (CWR). This paper reports the results of a fundamental study that has revealed that the wheel contact at the free edge of the railhead is a major problem since it generates a singularity in the contact pressure and railhead stresses. A design was therefore developed using an optimisation framework that prevents wheel contact at the railhead edge. Finite element modelling of the design has shown that the contact pressure and railhead stress singularities are eliminated, thus increasing the potential to work as effectively as a CWR that does not have a geometric gap. An experimental validation of the finite element results is presented through an innovative non-contact measurement of strains. Some practical issues related to grinding rails to the optimal design are also discussed.

On the dynamic contact angle in simulation of impinging droplets with sharp interface methods

Effects of dynamic contact angle models on the flow dynamics of an impinging droplet in sharp interface simulations are presented in this article. In the considered finite element scheme, the free surface is tracked using the arbitrary Lagrangian-Eulerian approach. The contact angle is incorporated into the model by replacing the curvature with the Laplace-Beltrami operator and integration by parts. Further, the Navier-slip with friction boundary condition is used to avoid stress singularities at the contact line. Our study demonstrates that the contact angle models have almost no influence on the flow dynamics of the non-wetting droplets. In computations of the wetting and partially wetting droplets, different contact angle models induce different flow dynamics, especially during recoiling. It is shown that a large value for the slip number has to be used in computations of the wetting and partially wetting droplets in order to reduce the effects of the contact angle models. Among all models, the equilibrium model is simple and easy to implement. Further, the equilibrium model also incorporates the contact angle hysteresis. Thus, the equilibrium contact angle model is preferred in sharp interface numerical schemes.

On concentrated loads and Green's functions in elastostatics

This investigation is concerned with the notion of concentrated loads in classical elastostatics and related issues. Following a limit treatment of problems involving concentrated internal and surface loads, the orders of the ensuing displacements and stress singularities, as well as the stress resultants of the latter, are determined. These conclusions are taken as a basis for an alternative direct formulation of concentrated-load problems, the completeness of which is established through an appropriate uniqueness theorem. In addition, the present work supplies a reciprocal theorem and an integral representation-theorem applicable to singular problems of the type under consideration. Finally, in the course of the analysis presented here, the theory of Green's functions in elastostatics is extended.

Singular stresses at the tip of a crack terminating at frictional interface of fibre reinforced composites

The stress singularities at the tip of a crack that terminates at a frictional interface between two layers in anisotropic composites are investigated. The order of stress singularities is determined by solving the characteristic equations obtained from the boundary conditions and the frictional interface conditions for the cases concerned. The interface is assumed to be governed by Coulomb's law of friction. Numerical results are presented for the cases with a crack terminating at a frictional interface of a fibre reinforced composite, and it is shown that there is a big difference of stress singularities between cases with and without considering friction along the interface.

Some theoretical aspects in computational analysis of adhesive lap joints

This paper is devoted to the numerical analysis of bidimensional bonded lap joints. For this purpose, the stress singularities occurring at the intersections of the adherend-adhesive interfaces with the free edges are first investigated and a method for computing both the order and the intensity factor of these singularities is described briefly. After that, a simplified model, in which the adhesive domain is reduced to a line, is derived by using an asymptotic expansion method. Then, assuming that the assembly debonding is produced by a macro-crack propagation in the adhesive, the associated energy release rate is computed. Finally, a homogenization technique is used in order to take into account a preliminary adhesive damage consisting of periodic micro-cracks. Some numerical results are presented.

Use of the energy-release rate in a 2 scale damage analysis of a bonded joint

Stress singularities appear at the extremities of an adhesive bond. They can produce a damage mechanism that we assimilate in this Note to a crack. The energy release rate permits to characterize its evolution. But a very refined mesh would be necessary for a real structure. Using an asymptotic method based on the small thickness of the bond a limit model with a different local behaviour is suggested. It leads to an approximation of the energy release rate

Computation of Thermal Stress Intensity Factors for Bimaterial Interface Cracks Using Domain Integral Method

The concept of domain integral used extensively for J integral has been applied in this work for the formulation of J(2) integral for linear elastic bimaterial body containing a crack at the interface and subjected to thermal loading. It is shown that, in the presence of thermal stresses, the J(k) domain integral over a closed path, which does not enclose singularities, is a function of temperature and body force. A method is proposed to compute the stress intensity factors for bimaterial interface crack subjected to thermal loading by combining this domain integral with the J(k) integral. The proposed method is validated by solving standard problems with known solutions.

On the stress analysis of cracked bodies by means of finite elements

The work described in this thesis deals with the development and application of a finite element program for the analysis of several cracked structures. In order to simplify the organisation of the material presented herein, the thesis has been subdivided into two Sections : In the first Section the development of a finite element program for the analysis of two-dimensional problems of plane stress or plane strain is described. The element used in this program is the six-mode isoparametric triangular element which permits the accurate modelling of curved boundary surfaces. Various cases of material aniftropy are included in the derivation of the element stiffness properties. A digital computer program is described and examples of its application are presented. In the second Section, on fracture problems, several cracked configurations are analysed by embedding into the finite element mesh a sub-region, containing the singularities and over which an analytic solution is used. The modifications necessary to augment a standard finite element program, such as that developed in Section I, are discussed and complete programs for each cracked configuration are presented. Several examples are included to demonstrate the accuracy and flexibility of the technique.

Does psychological stress mediate social deprivation in tooth loss?

It is unclear which theoretical dimension of psychological stress affects health status. We hypothesized that both distress and coping mediate the relationship between socio-economic position and tooth loss. Cross-sectional data from 2915 middle-aged adults evaluated retention of < 20 teeth, behaviors, psychological stress, and sociodemographic characteristics. Principal components analysis of the Perceived Stress Scale (PSS) extracted 'distress' (a = 0.85) and 'coping' (a =0.83) factors, consistent with theory. Hierarchical entry of explanatory variables into age- and sex-adjusted logistic regression models estimated odds ratios (OR) and 95% confidence intervals [95% CI] for retention of < 20 teeth. Analysis of the separate contributions of distress and coping revealed a significant main effect of coping (OR = 0.7 [95% CI = 0.7-0.8]), but no effect for distress (OR = 1.0 [95% CI = 0.9-1.1]) or for the interaction of coping and distress. Behavior and psychological stress only modestly attenuated socio-economic inequality in retention of < 20 teeth, providing evidence to support a mediating role of coping.