|Abstract: ||In this work, a new boundary element method is presented for the Probabilistic Fracture Mechanics analysis. The method developed allows the probabilistic
analysis of cracked structure accomplished by the dual boundary element method
(DBEM), in which the traction integral equation is used on one of the crack faces
as opposed to the usual displacement integral equation. The stress intensity factors and their first order derivatives are evaluated for mode-I and mixed-mode
A new boundary element formulation is derived and implemented to evaluate
the design variables sensitivities. This method involves the solution of matrix
systems formed by the direct differentiation of the discretised dual boundary element equations with respect to the each random parameter. The derivatives of
fracture parameters with respect to design variables are calculated using implicit
differentiation method (IDM) in DBEM for mode-I and mixed-mode fracture
problems. The gradient of performance function is determined analytically and
the total derivative method (TDM) is used in probabilistic fatigue crack growth
problems. The randomness in the geometry, material property and the applied
stress are considered in 2-D fracture problems; while initial crack size, final crack
size, material property and applied stress are considered in fatigue crack growth.
Uncertainties in other aspects of the problem can be included. First-Order Reliability Method (FORM) is used for predicting the reliability of cracked structures.
The Hasofer Lind Rackwitz Fiessler algorithm is used to find the most probable
point, referred as reliability index.
Finally, the validation and applications of the stochastic boundary element
coupled with FORM are presented. Numerical calculations are shown to be in
good agreement either with the analytical solution or Monte Carlo Simulation.|