含裂结构脆性断裂的失效概率计算

摘要

采用随机有限元法研究结构脆性断裂的失效概率问题，借助于能描述裂尖奇异应变场的裂尖元，将随机有限元法扩展到概率断裂力学的研究领域，简化了应力强度因子对各随机变量的求导过程，针对各随机变量的不确定性，计算了应力强度因子的统计矩，并利用优化方法确定了可靠性指标，采用一阶可靠性方法给出脆性断裂的失效概率。Ⅰ型断裂的算例表明了计算模型和方法的有效性。%We extended the probabilistic finite element method to probabilistic fracture mechanics using a singular element that embeds the near crack-tip singular strain field. The computation procedures for derivatives of the stress intensity factors with respect to the various random variables were simplified through the adjoint approach. We calculated statistical moments of stress intensity factors for various uncertainties. We also determined the probability of fracture by using an optimization procedure to perform a first-order reliability analysis. The results on a mode I fracture example show the effectiveness of computation procedures for the established model. This makes the method useful for estimating the safety and the probability of fracture of a flawed structure.