Research On Several Problems Of Structure Reliability Of Fatigue And Fracture Under Uncertain Parameters

In engineer practice, structures are always under dynamic loading which is changing all the time. Although the stress caused by the dynamic loading is under the yield stress and the strength stress, fatigue damage will happen to structures under the repeated dynamic loading. It was reported that about 80 percent failures of components and structures in modern industry fields such as axle, connecting rod, gear, steam turbine blade, bolt, spring, pressure vessel, pipe, vehicle, plane, offshore platform, submarine and jointed steel bridge are caused by fatigue.Most of the current models treat fatigue from a deterministic point of view. In these models, the working load and material parameters of the structure is deterministic. However, the external load of the structure is different form different work conditions and effected by several accidental factors. On the other hand, fatigue behavior scatters due to material inhomogeneities such as constituent particles and micropores, and extrinsic features like corrosion pits and surface scratches. In order to have a more accurate prediction of the reliability of structures, probabilistic characters should be introduced in the analysis of structure fatigue. To account for the uncertainty in the parameters and the random scatter found in experimental fatigue data, material properties, geometry dimensions and loads should be treated as random variables.From the view of economic and maintenance, the reliability analysis of fatigue and fracture make the failure probability of structures caused by fatigue and fracture decrease to the minimum extent under required work conditions and performance finishing. It is significant to predicate the failure probability of the structure , ensure the structure safety , increase the reliability of products, decrease the maintenance cost and enhance the market competition ability of products. However, most analysis of fatigue and fracture were carried out through experiments, which have hindered its practical application to a certain degree, especially for those expensive structures with complicated shapes under stochastic loads. In this thesis, finite element method is combined with fatigue and fracture analysis, material properties, geometry dimensions and loads are treated as random variables. The reliability of structure with single crack and multi-cracks , optimal inspection time for structural fatigue life, robust design of structure fatigue life, fatigue reliability analysis under fuzzy failure rules were studied.The main work of this thesis is as follows:1. Reliability of structures with cracks was studied. The expression of stress intensity factors is build according to least square method, the mode I-equivalent stress intensity factors is used as a fracture criterion. The model of reliability of structures with mode I crack , mode I-II composite crack and multi-cracks were presented by stochastic finite element method and first order reliability method.2. An optimal inspection time model for structural fatigue life based on stochastic finite element method and first order reliability method was presented. The uncertainties such as material parameters and loads which affect the fatigue life of the structure were regarded as random variables. Taylor expansion stochastic finite element method was introduced to simulate the material behavior of the fatigue life. Reliability analysis was made respectively for crack initiation life and crack propagation life. Take the crack initiation life as service life and the crack propagation life as inspection time, so the optimal inspection time can be easily obtained from the reliability function of the whole structure.3. To reduce the scatter of fatigue life, a robust design model of structural fatigue life is presented. The structural optimization theory is incorporated with stochastic finite element method. Under the condition of considering the effect for structural fatigue life due to the variance of design variables and other random variables, the problem is formulated as a multi-criteria optimization problem, in which both the mean structural fatigue life and the standard deviation of structural fatigue life are to be minimized. The structural fatigue life is limited between the low fatigue life and high fatigue life in the constrain functions.4. A reliability model of fatigue life considering fuzzy failure rules is presented. The fatigue life and the fatigue design life was treated as a random variable and a fuzzy random variable respectively. Reliability was analyzed when the fatigue design life obeys linear L-R distribution , normal distribution and parabola distribution. Results were compared with regular fatigue reliability analysis.