Stochastic meshless analysis of elastic?plastic cracked structures

Abstract

This paper presents a stochastic mesh-free method for probabilistic fracture-mechanics analysis of nonlinear cracked structures. The method involves enriched element-free Galerkin formulation for calculating the J-integral; statistical models of uncertainties in load, material properties, and crack geometry; and the first-order reliability method (FORM) for predicting probabilistic fracture response and reliability of cracked structures. The sensitivity of fracture parameters with respect to crack size, required for probabilistic analysis, is calculated using a virtual crack extension technique. Numerical examples based on mode-I fracture problems have been presented to illustrate the proposed method. The results from sensitivity analysis indicate that the maximum difference between sensitivity of the J-integral calculated using the proposed method and reference solutions obtained by the finite-difference method is about three percent. The results from reliability analysis show that the probability of fracture initiation using the proposed sensitivity and meshless-based FORM are very accurate when compared with either the finite-elementbased Monte Carlo simulation or finite-element-based FORM. Since all gradients are calculated analytically, the reliability analysis of cracks can be performed efficiently using meshless methods.Keywords Probabilistic fracture mechanics, Mesh-free method, Element-free galerkin method, J-integral, Sensitivity of J-integral, Probability of failure IntroductionProbabilistic fracture mechanics (PFM) is becoming increasingly popular for realistic evaluation of fracture response and reliability of cracked structures. The theory of fracture mechanics provides a mechanistic relationship between the maximum permissible load acting on a structural component to the size and location of a crackeither real or postulated -in that component. Probability theory determines how the uncertainties in crack size, loads, and material properties, when modeled accurately, affect the reliability of cracked structures. PFM, which blends these two theories, accounts for both mechanistic and stochastic aspects of the fracture problem, and hence, provides a more rational means to describe the actual behavior and reliability of structures than traditional deterministic methods [1].While development is ongoing, a number of methods have been developed for estimating statistics of various fracture response and reliability. Most of these methods are based on linear-elastic fracture mechanics (LEFM) and the finite element method (FEM) that employs the stressintensity factor (SIF) as the primary crack-driving force [1][2][3][4][5]. For example, using SIFs from an FEM code, Grigoriu et al. [2] applied first-and second-order reliability methods (FORM/SORM) to predict the probability of fracture initiation and a confidence interval of the direction of crack extension. The method can account for random loads, material properties, and crack geometry. However, the randomness in crack geometry was modeled by response surfa...

Immune algorithm-embedded stochastic meshless method for structural reliability

“…Probabilistic models using meshless methods have not received much attention. Hence, stochastic analysis involving meshless methods provides a rich, relatively unexplored area for future research in stochastic structures [ 32 – 34 ] and reliability analysis [ 35 ].…”