Reliability Based Analysis with the Boundary Element Method

本研究的主要目的是发展用边界单元法分析复杂工程结构可靠性的技术。边界元是一种用于结构分析的数值计算方法，可用于模拟结构在荷载作用下的行为。有限元方法是结构分析的另一种数值计算方法。边界元与有限元相比有几个优点，使其在可靠性分析中非常有用，即它的速度和精度。这项研究将集中在BEM的使用上。结构的可靠性是结构成功满足一定标准的概率。例如，标准可能是结构不会断裂，或者在施加载荷时不会弯曲太多。因此，结构的可靠性是决定安全性的一个非常重要的因素。对于飞机来说尤其如此，因为结构故障的后果可能非常严重。结构的可靠性受到许多不确定因素的影响。例如，我们可能不知道将应用于结构的确切负荷量，或者我们可能不知道结构的确切尺寸。在进行可靠性分析时，重要的是要考虑到这些不确定因素。边界元还将被用来模拟结构中疲劳裂纹的扩展。疲劳是指材料因反复施加载荷而变弱的现象。它是飞机结构失效的主要原因，也是其他工程结构失效的最常见原因之一。通过更好地了解疲劳裂纹扩展背后的机理，可以更准确地估计结构的疲劳寿命(结构在疲劳严重削弱之前预计将保持多长时间)。因此，可以更准确地确定例行检查的时间，从而在安全和效率方面都有所改善。边界元在模拟裂纹扩展方面已被证明是非常有效的。它能够以一种非常有效的自动方式对裂纹扩展进行建模，既快速又准确。确定结构疲劳寿命的一个重要步骤是估计结构中裂纹的初始尺寸。这些初始裂纹被称为等效初始缺陷尺寸(EIF)，可以使用边界元来估计它们。还将通过应用代理建模来提高边界元的效率。代理建模涉及将计算昂贵的模型(如有限元模型或边界元模型)替换为廉价的“代理模型”。这些代理模型是从有限元或边界元模型创建的。这些代理模型在计算上非常便宜，但只能用于狭隘的目的。它们对于可靠性分析或估计EIF非常有用。多保真度模型是代理模型的一种高级形式，将在本工作中使用。本研究的新方面：-使用边界单元法(BEM)进行结构可靠性分析尚未被研究界考虑。将首次使用边界元法开发复杂工程结构的可靠性分析技术。由于边界元法的速度和精度，可以证明它比其他可靠性分析方法更有效。因此，可以用更少的计算成本来研究更复杂的工程结构。-以前从未用边界元法进行过EIFS的估计。考虑到它在模拟裂纹扩展方面的有效性，它在估计EIF方面可能比其他方法更有效。因此，可以用较小的计算量来确定更复杂的工程结构的等效域。-多保真模型将首次与BEM一起使用，它们也将首次用于估计EIF。

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.