The safe transportation of new and spent nuclear fuel is an essential part of the nuclear fuel cycle. The aim of this thesis was to obtain a more thorough understanding of the mechanical loading acting on heavy nuclear packages during rail transportation. There were two motivating factors for this study. Firstly, the design of equipment used to tie down a package to its conveyance has become more challenging with the recent trend of increasing package mass; often exceeding 100 tonnes. This difficulty is due to the advisory acceleration factors recommended for design. Despite widespread acceptance that the factors ensure safety, it is also recognised that for heavier packages they can be prohibitive and result in over engineered tie down systems. Secondly, transportation imparts complex dynamic mechanical loading on packages and the fuel assemblies within them. There have been no reported instances in the UK of problems caused by fuel vibrations. However international studies have prompted this investigation. A rail wagon and tie down system for a 100 tonne package were instrumented with accelerometers and strain gauges. The measurements were taken during a routine rail journey from Barrow-in-Furness to Sellafield. Continuous data was digitally recorded with a sampling rate sufficient to capture shock and vibrations up to 100 Hz. Accelerometers were selected to measure very low frequencies to capture quasi-static loading. Investigation of the frequency content of the accelerations indicated that digital filtering of the data is necessary to determine the magnitudes of the structural loading on tie downs. A method for designing a suitable filter has been developed. A sensitivity analysis of different filters indicated there is a possibility for over estimating loads based on measured data due to poor filter design. Industrial design of tie downs using FEA requires pragmatic run times. This motivated a comparison of the measured strain time histories with the results of a linear static FEA model. The correlation between measured and predicted strains, was strong at frequencies < 3.5 Hz. A residuals analysis indicated that the model predicted the underlying strain process accurately. The methods described are generic and adaptable. They will aid any future experimental work, to characterise shock, vibration and quasi-static loads acting on nuclear packages and their ancillary equipment.

Ph. D.

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The form of the energy function (i.e. Total, Hellinger-Reissner, Hu-Washizu or Complementary energy functions) has a significant influence on FEM performance. Motivated by the ability of the force-based method to satisfy the equilibrium equation and ability of the displacement-based method to satisfy compatibility equation, this thesis proposes a mathematical framework, namely the ‘Hybrid Force-Based Method’ which employs two physical concepts; the Total and Complementary Potential Energy functions. Satisfaction of both the Total and Complementary Potential Energy function is critical to the success of the Hybrid Force-Based Method. The Hybrid Force-Based Method is constructed using these two independent energy functions in order to perform inelastic structural analyses. The method has been proposed, implemented and evaluated across the entire structure, element, section and material domains first considering each domain separately and then in combination. The equilibrium and compatibility equations are satisfied simultaneously by discretisation of these two equations, and accuracy is controlled by specifying the upper and lower bounds of the results. Outcomes following evaluation of the proposed method can be classified into the following three categories: (i) structure-level performance (see Chapter 2), (ii) material-level performance (see Chapter 3), and (iii) element level performance (see Chapter 4). The proposed Hybrid Force-Based Method is constructed by deriving the governing equations directly from the Total and Complementary Potential Energy functions, leading to two distinct variants of the hybrid approach (i) the so-called ‘augmented Hybrid Force-Based Method’, and (ii) the so-called ‘unaugmented Hybrid Force-Based Method’. A number of numerical posterior process tests were devised and used to demonstrate the performance of these two variations of the hybrid method (see Sections 2.9.4.1 and 2.9.5.1) to demonstrate those methods ability in convergence in contrast to the Large Increment Method. Due to the occurrence of numerical instabilities experienced when using various established solution algorithms in solving the fundamental equations at the material level, within implicit approach (such as the Standard Implicit Method, the Cutting Plane Method, and the Closest Point Projection Method). A new form of the constitutive equation solver is proposed in Sections 3.9, referred to as the General Implicit Method (GIM). It is shown that the GIM can be implemented both in the strain and stress domains, and is therefore appropriate for use in both the displacement- and the force-based solution family of methods. The GIM is then evaluated by comparing its predictions to those of other common solution algorithms for inelastic analysis. Performance evaluation involves the use of a new error indicator that guarantees the uniqueness and accuracy of a solution in both the stress and the strain domains. Three iso-error maps serve to emphasis the accuracy, reliability, and computational performance of the General Implicit Method as a solution method compared to those are evaluated for the defined Stress Increment Ratio. The fundamental equations at the element level are followed, based on structured fibre discretisation. The decomposition of the various degrees of freedom into deformational and rigid-body motion serve as a mechanism by which independent equilibrium equations can be determined for each element. The subsequent equation is able to involve axial force, torsion, and both in and out of plane moments while a general form of shear strain distribution is also involved. The original form of the solution at the cross section of the elements leads to novel governing equations that are based on the characteristics of the hybrid force-based approach. The numerical evaluation in Section 4.11.7.1 demonstrates the performance of the proposed method. The newly defined error indicators demonstrate the accuracy and computational performance of the method and the uniqueness of the solution in satisfying both the equilibrium and compatibility equations for Euler-Bernoulli, Timoshenko, and Reddy strain distributions across the element section. Further to the structured fibre, distributed, semi-distributed and concentrated inelastic approach elements, as a simplified form of the element are implemented and evaluated. Although performance of those original formulations is evaluated independently in in comparison with the conventional approaches, compatibility of those as an important issue is followed as well. The numerical evaluation demonstrates higher accuracy and reliability by following the proposed method, further to the higher computational performance respect to the conjugate approaches.

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Accidents involving passenger trains happen regularly in India. The reasons for such accidents could be many; such as weather and flooding, faulty tracks, bridge collapse, collisions caused by signaling errors, mechanical failures, driver error, sabotage etc. The annual accident-related deaths as a percentage of the total number of passengers carried by Indian Railway may seem to be negligible, but the aim should be to achieve zero fatality as every single person killed is an irreplaceable loss to his/her family. It needs to be mentioned that in addition to fatalities for which exact numbers are not available, serious injuries and permanent disabilities caused by train accidents in India at present stand completely unaccounted for. In the absence of a large scale renovation and crash avoidance measures coupled with the propensity to increase the number of trains every year, enhancing passive safety is crucial i.e. crashworthiness and occupant safety of passenger coaches of Indian trains. In the current work, crashworthiness and occupant safety of the existing typical three-tier cabin passenger coach of Indian Railway in an event of collision accident are assessed with the aid of a finite element analysis. In the light of the published work on research in railroad equipment crashworthiness, the current work is intended to envisage the methodology to assess the Indian Railway passenger coach from the point of view of the crashworthiness and occupant safety using CAE (Computer aided engineering) based approach. It is involved with an extensive study of the structural crush behavior of an individual passenger coach car and its effect on the interaction between occupants and the coach interior. Here the structural crush behavior of a typical three-tier cabin passenger coach is evaluated for the head-on impact against a fixed and rigid barrier. The occupant response for the same scenario is also studied which can be viewed as a component of the actual occupant response due to the structural crush behavior of the passenger coach. This can give useful estimates of injury severity and fatalities that may occur in actual accidents. An FE model of the passenger coach structure was built and validated using International Railway Union (UIC) specified code OR 567-design requirements in terms of static loads constituting structural proof cases. These proof cases specify the static load values the coach body structure should withstand without any permanent deformation or failure when applied at the specified locations on the structural ends across the longitudinal axis. In addition, a favorable correlation between the simulation and actual experiment for drop impact behavior of the open section specimens, namely C-section and I-section, was obtained to validate the simulation methodology. LS-DYNA a nonlinear dynamic explicit FE solver was used to carry out all the dynamic impact simulations involved in the current work. The material modeling takes into account the strain rate effect which is essential for the material impact behavior study. The contact modeling was done using penalty contact method. The degrading effect of the buffer on the structural crush patterns which induced the undesirable global bending and jackknifing of the whole coach structure was demonstrated with the help of dynamic impact simulations of the coach structure. The quantification of occupant injury was done by occupant safety simulations using the Hybrid III 50th percentile male dummy FE model. The dummy having been designed for simulating automobile accident scenarios, its contacts had to be adapted to suit the excessive mobility conditions in the coach interior. The dummy was revalidated successfully for the head drop test, pendulum chest impact test, neck flexion and extension test and knee impact test. Impact simulations for three different speeds were performed by positioning the dummy close to the impact point. Injury criteria such as Head Injury Criterion, Chest Deceleration, Knee force level and Neck extension-flexion moments were used to estimate the injury severity level and fatality rate.