Probabilistic fracture mechanics by Galerkin meshless methods – part I: rates of stress intensity factors

This is the first in a series of two papers generated from a study on probabilistic meshless analysis of cracks. In this paper (Part I), a Galerkin-based meshless method is presented for predicting first-order derivatives of stress-intensity factors with respect to the crack size in a linear-elastic structure containing a single crack. The method involves meshless discretization of cracked structure, domain integral representation of the fracture integral parameter, and sensitivity analysis in conjunction with a virtual crack extension technique. Unlike existing finite-element methods, the proposed method does not require any second-order variation of the stiffness matrix to predict first-order sensitivities, and is, consequently, simpler than existing methods. The method developed herein can also be extended to obtain higher-order derivatives if desired. Several numerical examples related to mode-I and mixed-mode problems are presented to illustrate the proposed method. The results show that firstorder derivatives of stress-intensity factors using the proposed method agree very well with reference solutions obtained from either analytical (mode I) or finite-difference (mixed mode) methods for the structural and crack geometries considered in this study. For mixed-mode problems, the maximum difference between the results of proposed method and finite-difference method is less than 7%. Since the rates of stress-intensity factors are calculated analytically, the subsequent fracture reliability analysis can be performed efficiently and accurately.