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Curvilinear fatigue crack reliability analysis by stochastic boundary element method
Author(s) -
Lua Yuan Jie,
Liu Wing Kam,
Belytschko Ted
Publication year - 1993
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620362206
Subject(s) - boundary element method , curvilinear coordinates , random variable , randomness , mathematics , monte carlo method , structural engineering , paris' law , sensitivity (control systems) , finite element method , mathematical analysis , fracture mechanics , geometry , engineering , statistics , crack closure , electronic engineering
In this paper, the stochastic boundary element method, which combines the mixed boundary integral equations method explored in Reference 1 with the first‐order reliability method, is developed to study probabilistic fatigue crack growth. Due to the high degree of complexity and non‐linearity of the response, direct differentiation coupied with the response‐surface method is employed to determine the response gradient. Three random processes, the mode I and mode II. stress intensity factors and the crack direction angle, are included in the expression of the response gradient. The sensitivity of these random processes is determined using a first‐order response model. An iteration scheme based on the HL‐RF method 2 is applied to locate the most probable failure point on the limit‐state surface. The accuracy and efficiency of the stochastic boundary element method are evaluated by comparing the cumulative distribution function of the fatigue life obtained with Monte Carlo simulation. The reliability index and the corresponding probability of failure are calculated for a fatigue crack growth problem with randomness in the crack geometry, defect geometry, fatigue parameters and external loads. The response sensitivity of each primary random variable at the design point is determined to show its role in the fatigue failure. The variation of each primary random variable at the design point with the change of probability of failure is also presented in numerical examples.