Probabilistic Simulation of Fracture by Meshless Methods

裂纹扩展是结构和力学系统中一种重要的失效机制，需要精确的数值模型来进行必要的模拟来支持失效预测。系统在载荷、材料特性和裂纹尺寸方面的不确定性和风险的存在要求考虑基于可靠性的断裂力学分析。该建议的目的是发展一种新的随机无网格法，用于预测含裂纹类缺陷的二维和三维结构的断裂响应特征和可靠性。这项工作将基于：(1)成熟的断裂力学理论，包括线弹性和弹塑性模型；(2)确定裂纹尖端应力和应变场的无网格和集成无网格/有限元方法以及连续体设计灵敏度分析；(3)随机变量和随机场对载荷、材料特性和裂纹尺寸的不确定性的概率模型；以及(4)裂纹结构断裂响应和可靠性的概率表征的随机无网格和模拟方法。对于无网格/有限元一体化方法，将无网格方法用于模拟裂纹附近区域的材料行为，而有限元方法则用于远离裂纹区域的材料行为模拟。这种耦合有可能极大地简化裂纹扩展分析，同时实现大幅提高的精度水平。该研究为无网格法和随机场理论在断裂过程计算模拟中的应用提供了一种创新和及时的途径。所提出的无网格法在概率断裂力学领域显示出巨大的应用潜力。特别是，这些方法可以用于骨折控制和延长寿命，而且老化结构仍然低于与设计和制造新飞机相关的巨额资本支出，延长寿命的理念将继续下去。然而，为了确定老化飞机的维护要求，以确保其持续的结构完整性和安全性，有必要使用先进的寿命和剩余强度预测工具，如本研究中提出的工具。这并不是航空航天行业独有的。同样的情况在其他行业也很普遍，比如化石和核电行业，这些行业也在试图使用老化的发电厂，远远超出其预期的设计寿命。因此，本文提出的随机无网格方法可以帮助解决飞机、民用、核能、航空航天、汽车等行业中许多与断裂相关的实际问题。到目前为止，涉及无网格法的可靠性问题尚未得到解决。在该程序下发展的随机无网格法和集成无网格法/有限元方法将极大地推动断裂力学领域的最新发展，并解决概率结构力学中遇到的广泛的实际工程问题。

Crack propagation is an important failure mechanism in structural and mechanical systems requiring accurate numerical models to implement essential simulation supporting failure prediction. The existence of system uncertainty and risk in loads, material properties, and crack size requires a reliability-based fracture-mechanics analysis to be taken into account. The objective of this proposal is to develop a new stochastic meshless methodoloy for predicting fracture response characteristics and reliability if two-and three-dimensional structures containing crack-like defects. This effort will be based on: (1) well-established theories of fracture mechanics involving both linear-elastic and elastic-plastic models, (2) meshless and integrated meshless/finite element methods for determining crack-tip stress and strain fields and continuum design sensitivity analysis, (3) probabilistic models of uncertainties in loads, material properties, and crack size by random variables and random fields, and (4) stochastic meshless and simulation methods for probabilistic characterization of fracture response and reliability of cracked structures. For the integrated meshless/finite element method, the meshless method will be used to model material behavior in areas close to cracks and the finite element method in areas further away from cracks. Such a coupling has the potential to greatly simplify crack-growth analysis while simultaneously achieving a substantially improved level of accuracy. The proposed research represents an innovative and timely approach to computational modeling of fracture process by meshless methods and random field theory. The proposed meshless methods demonstrate significant potential for application in the field of probabilistic fracture mechanics. In particular, these methods can be used for fracture control and life extension of and aging structure remains lower than the huge capital expenditures associated with designing and building a new aircraft, the life extension philosophy will continue. However, in order to define maintenance requirements of an aging aircraft to ensure it's continued structural integrity and safety, advanced predictive tools for life and residual strength, such as the ones proposed in this study, are necessary. This is not unique to the aerospace industry. Identical conditions prevail in others, such as in fossil and nuclear power industries, which are also attempting to use aging power plants far beyond their intended design lives. As such, the stochastic meshless methods proposed in this study can help solve many real-world fracture-related problems shared by aircraft, civil, nuclear, aerospace, automotive, and other industries. To date, reliability problems involving meshless methods have yet to be solved. The development of stochastic meshless and integrated meshless/finite element methods under this prorgram will significantly advance the state-of-the-art in the field of fracture mechanics as well as address a wide range of practical engineering issues encountered in probabilistic structural mechanics.