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 fracture problems. 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.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:527539 |
| Date | January 2010 |
| Creators | Huang, Xiyong |
| Contributors | Aliabadi, Ferri |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/6192 |
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