Interval Reliability Analysis Of Structural Fatigue And Fracture

Fatigue fracture damage is one of the main reasons for the failure of engineering structures.Although the probabilistic analysis method has been able to meet the design accuracy requirements well.But sometimes the sample data of experiment results is not enough,so it is difficult to get the probability density distribution of the variables.As a non-probabilistic analysis method,the interval analysis method does not need to consider the specific distribution of the parameters.Only a small amount of sample information can obtain the boundary of the uncertain problem,which effectively avoids the solution error caused by the insufficient number of samples.This paper presents the study of the uncertain fatigue fracture reliability of structures and put interval analysis method into usage to deal with the interval structure parameter.Combining the S-N curve method and the displacement extrapolation method,the upper and lower limits of the fatigue life and stress intensity factor(SIF)of the structure are solved.At last,the interval reliability indexes of fatigue and fracture of structures are solved by using the shortest distance method.The main research content and completed work of the thesis are as follows:(1)Based on interval mathematics,Taylor method and dimension reduction algorithm are used to expend the formulas of objective function.The expressions reserved to the first two order terms are given,and the upper and lower limits of the objective function are obtained.(2)Structural fatigue life based on interval analysis method is discussed.Using the S-N curve method,linear Miner’s cumulative damage theory and considering the effect of the mean stress,uncertainties(such as materials and loads)are treated as interval variables.The Taylor method interval formula and dimension reduction algorithm interval formula of structural fatigue life under random load are derived,and the upper and lower limits of structural fatigue life are given.(3)The interval analysis method of fracture of structures with cracks is studied,and the displacement extrapolation formulas of stress intensity factor of structures with cracks are given.Based on Taylor method,the interval formulas of model-I and model-II stress intensity factors are given by relating to interval finite element method,and then the upper and lower limits of equivalent stress intensity factor are obtained.The comparison between this method and interval Monte Carlo method is made.(4)Based on the shortest distance method,the interval reliability of structural fatigue and fracture is studied.Through interval reliability analysis,the structural reliability indexes under a certain design life range and the maximum design life within the safety range are obtained.At the same time,the influence of the coefficient of deviation on the fatigue reliability index is compared,taking the uncertainty of the information of structural material and load into consideration.Then,the interval reliability model of structural fracture is established,and the structural reliability index under the uncertain fracture toughness of a certain material is obtained,and then the equivalent stress intensity factor that guarantees the maximum structural reliability index under this material is solved.Considering the structural size and load uncertainty,the influence of deviation coefficient on structural fracture reliability index is studied.