Probabilistic fracture mechanics analysis of linear-elastic cracked structures by spline fictitious boundary element method

The inherent uncertainties in crack geometry, material properties and loadings have large influence on fracture response characteristics of cracked structures. This paper presents the probabilistic fracture mechanics analysis of linear-elastic cracked structures subjected to mixed-mode loading conditions using the spline fictitious boundary element method (SFBEM). The response surface method (RSM) is used to predict the fracture probability of the cracked structure. To determine the unknown coefficients of the response surface function, the SFBEM based on the Erdogan fundamental solutions for infinite cracked plates is adopted to perform deterministic analyses of stress intensity factors (SIFs) corresponding to different test points with given parameters. Numerical examples based on mode-I and mixed-mode crack problems are presented to illustrate the present method. The results show that the predicted failure probability obtained by the present approach is accurate in comparison with the Monte Carlo simulation (MCS) results. Since a much lesser number of numerical tests are required in RSM as compared with that needed in MCS, and since the SFBEM based on the Erdogan fundamental solutions has been used to conduct the numerical tests, reliability analysis of cracked structures can be performed efficiently using the present method.