Reliability Based Analysis with the Boundary Element Method

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The main aim of this research is to develop techniques for analysing the reliability of complex engineering structures using the boundary element method (BEM). The BEM is a numerical computational method for structural analysis that can be used to model the behaviour of structures subjected to loads. The Finite Element Method (FEM) is another numerical computational method for structural analysis. The BEM has several advantages over the FEM that make it very useful for reliability analysis, namely its speed and accuracy. This research will focus on the use of the BEM.The reliability of a structure is the probability that the structure successfully meets certain criteria. For example, the criteria could be that the structure doesn't break, or that it doesn't bend too much when a load is applied. The reliability of a structure is therefore a very important factor in determining safety. This is especially true for aircraft, since the consequences of structural failure can be very significant. The reliability of a structure is influenced by many sources of uncertainty. For example, we might not know the exact amount of load that will be applied to the structure, or we might not know the exact dimensions of the structure. When performing reliability analyses, it is important to take into account these sources of uncertainty. The BEM will also be used to model the growth of cracks in structures due to fatigue. Fatigue is the weakening of a material due to repeatedly applied loads. It is the leading cause of structural failure in aircraft, and among the most common causes of failure in other engineering structures. By better understanding the mechanics behind fatigue crack growth, the fatigue life (how long the structure is expected to remain in service before fatigue severely weakens it) of a structure can be more accurately estimated. The timing of routine inspections can therefore be more accurately determined, providing improvements in both safety and efficiency. The BEM has proven to be very effective at modelling crack growth. It is able to model crack growth in a very effective automatic manner that is both quick and accurate. An important step in determining the fatigue life of a structure is to estimate the initial sizes of the cracks in the structure. These initial cracks are called Equivalent Initial Flaw Sizes (EIFS), and the BEM can be used to estimate them.Work will also be undertaken to improve the efficiency of the BEM through the application of surrogate modelling. Surrogate modelling involves replacing computationally-expensive models (such as a FEM or BEM model) with a cheap 'surrogate model'. These surrogate models are created from the FEM or BEM model. These surrogate models are very computationally-cheap but can only be used for narrow purposes. They are very useful for reliability analyses or for estimating EIFS. Multi-fidelity models are an advanced form of surrogate models and will be used in this work.Novel aspects of this research:- Structural reliability analysis using the boundary element method (BEM) has not been considered by the research community. Techniques for the reliability analysis of complex engineering structures will be developed for the first time using the BEM. Due to the speed and accuracy of the BEM, it could prove to be more effective that other methods for reliability analysis. Therefore, more complex engineering structures can be investigated for less computational cost.- The estimation of EIFS has not been carried out before with the BEM. Given its effectiveness in modelling crack growth, it could be more effective than other methods for estimating EIFS. Therefore, the EIFS for more complex engineering structures can be determined for less computational cost. - Multi-fidelity models will be used for the first time with the BEM, and they will also be used for the first time for estimating EIFS.