Uncertainty analysis of reliability prediction for cracked structure

Abstract

The uncertainties inherent in the loading and the properties of mechanical systems necessitate a probabilistic approach as a realistic and rational platform for analysis. Therefore, this paper presents a probabilistic approach in order to model the uncertainties in fracture mechanics analysis. The main focus is on uncertainties aspect which relates the nature of crack in materials. The objective of this work is to calculate the rigidity of cracked structures based on failure probability by using simulation technique. The methodology consists of cracked structures modelling, finite element calculation, generation of adaptive mesh, sampling of cracked structure including uncertainties factors and probabilistic analysis using Monte Carlo method. Probabilistic analysis represents the priority of proceeding either suitable to repair the structures or it can be justified that the structures are still in safe condition. Therefore, the hybrid finite element and probabilistic analysis represents the failure probability of the structures by operating the sampling of cracked structures process. The uncertainty in the crack size can have a significant effect on the probability of failure, particularly for the crack size with large coefficient of variation. The probability of failure caused by uncertainties relates to loads and material properties of the structure are estimated using Monte Carlo simulation technique. Numerical examples are presented to show that probabilistic analysis based on Monte Carlo simulation provides accurate estimates of failure probability. Verification of the predicted failure probability is validated with analytical solutions and relevant numerical results obtained from other previous works. The comparison show that the combination between finite element analysis and probabilistic analysis based on Monte Carlo simulation provides a simple and realistic of quantify the failure probability.