A Partition of Unity Boundary Element Method for Fracture and Fatigue Analysis

该建议的目的是产生一种新的计算建模算法，用于分析含有裂纹的工程部件。最近发生的一些引人注目的事故清楚地表明，当断裂失效由于开裂而发生时，它们通常是突然的、灾难性的并且没有警告。在循环载荷下裂纹扩展到临界尺寸的过程称为疲劳。本文提出了一种新的断裂力学和疲劳裂纹扩展模拟方法，断裂和疲劳的模拟都是基于裂纹附近材料的应力和位移的确定。有完善的计算方法找到这种类型的解决方案，但在裂纹的存在下，传统的方法，传统的“有限元”和“边界元”的方法，可以变得繁琐和效率低下。近年来，为了克服这些困难，人们提出了一些新的边界元方法，其中包括“对偶边界元法”（DBEM）和“单位分解法”（PUM）。DBEM克服了对非常精细的计算模型的需要，尽管存在一些缺点使得该方法更难以实现。PUM预计将允许进一步减少所需的模型refinement.The PUM是基于在我们的近似模型中包含一组来自局部裂纹尖端的材料的理论行为的函数。这已成功地用于断裂力学的有限元法。然而，我们自己的小组在达勒姆已经取得了巨大的成功与PUM在边界元算法的波传播模拟。在这里，我们发现，与传统的边界元相比，误差减少了8个数量级，并允许相当大的问题规模的减少。由于PUM似乎非常适合边界元的实现，边界元是众所周知的，其适用于裂纹问题，我们预计这个项目有很好的成功概率。并且可能对机械和航空航天工程中的断裂和疲劳模拟产生重大影响。

The aim of this proposal is to produce a novel computational modelling algorithm for the analysis of engineering components containing cracks. A number of recent, high profile accidents clearly demonstrate that when fracture failures occur due to cracking, they often do so suddenly, catastrophically and without warning. The process of cracks growing to a critical size under cyclical loading is termed fatigue. The work proposes a new method of simulating both fracture mechanics and fatigue crack growth.Simulations in fracture and fatigue are based around the determination of the stresses and displacements in the material in the vicinity of the crack. There are well established computational methods of finding this type of solution, but in the presence of cracks the traditional approaches based on conventional 'finite element' and 'boundary element' methods can become cumbersome and inefficient. In recent years, a number of variants of these techniques have been proposed to overcome some of these difficulties.The proposed work involves the combination of two such strategies: the 'Dual Boundary Element Method' (DBEM) and the 'Partition of Unity Method' (PUM). The DBEM overcomes the need for a very refined computational model, though there are some drawbacks making the method more difficult to implement. The PUM is expected to allow for further reductions in the required model refinement.The PUM is based on the inclusion in our approximate model of a set of functions derived from the theoretical behaviour of the materials locally at the crack tip. This has been successfully used with the finite element method for fracture mechanics. However, our own group in Durham has achieved great success with the PUM in a boundary element algorithm for wave propagation simulation. Here we have found up to 8 orders of magnitude reduction in errors over conventional boundary elements and allows for a considerable reduction in the size of the problem.Since the PUM seems well suited to a boundary element implementation, and boundary elements are well known for their suitability for crack problems, we anticipate this project to have a good probability of success, and could have a significant impact on fracture and fatigue simulations in mechanical and aerospace engineering.