Influencing factors analysis of plane crack uncertainty based on stochastic finite element method

Taylor stochastic finite element method(TSFEM) is applied to analyze the uncertainty of plane crack stress intensity factor(SIF) considering the uncertainty of material properties and crack length and load. Finite element model of plane crack is presented. In the model, crack tip is meshed by using six node triangular quarter point elements; and other area is meshed by using six node triangular elements. The partial derivatives of displacement and the stiffness matrix used by TSFEM are derived. The mean and variance expressions of the SIF under uncertain factors are also derived. Compared with the Monte Carlo simulations, the effectiveness of the present method is proved. The calculation results indicate that the uncertainty of material elastic module and load and crack length markedly affect the uncertainty of SIF, meanwhile, the Poisson's ratio of material affect little. Among the three variables (E, P, a), the elastic module E has the greatest effect on the SIF uncertainty. The next is external load P. The crack length a has lower effect on SIF uncertainty than both E and P.