Probabilistic Simulation of Fracture by Meshless Methods

裂纹扩展是结构和机械系统中的重要失效机制，需要精确的数值模型来实现支持失效预测的基本模拟。 系统的不确定性和风险的存在，在负载，材料性能，和裂纹尺寸需要一个可靠性为基础的结构力学分析要考虑在内。 本文的目的是发展一种新的随机无网格方法，用于预测含裂纹缺陷的二维和三维结构的断裂响应特性和可靠性。 这项工作将基于：（1）断裂力学的成熟理论，包括线弹性和弹塑性模型，（2）用于确定裂纹尖端应力和应变场以及连续体设计灵敏度分析的无网格和集成无网格/有限元方法，（3）由随机变量和随机场引起的载荷、材料特性和裂纹尺寸的不确定性的概率模型，（4）裂纹结构断裂响应和可靠性的随机无网格和模拟方法。 对于集成无网格/有限元法，无网格法将用于模拟靠近裂纹区域的材料行为，而有限元法将用于模拟远离裂纹区域的材料行为。 这样的耦合有可能大大简化裂纹扩展分析，同时实现大幅提高的精度水平。 提出的研究代表了一种创新的和及时的方法，计算建模的断裂过程的无网格方法和随机场理论。 所提出的无网格方法在概率断裂力学领域具有重要的应用潜力。 特别是，这些方法可以用于断裂控制和寿命延长的和老化的结构仍然低于巨大的资本支出与设计和建造新的飞机，寿命延长的理念将继续下去。 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，先进的寿命和剩余强度预测工具，如本研究中提出的，是必要的。 这并不是航空航天工业所独有的。 同样的情况在其他行业也普遍存在，例如在化石和核能行业，这些行业也试图使用远远超过其预期设计寿命的老化发电厂。 因此，本研究中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，汽车和其他行业共同面临的许多现实问题。 迄今为止，涉及无网格方法的可靠性问题尚未得到解决。 随机无网格和集成无网格/有限元方法的发展，在此proorgram将显着推进国家的最先进的断裂力学领域，以及解决广泛的实际工程问题中遇到的概率结构力学。

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.