Research On Discrete Stress-Strength Interference Models Based On Universal Generating Function

The stress-strength interference (SSI)model is a basic tool for structural reliabilityanalysis.In this model,the structural reliability is defined as the probability thatstrength is larger than stress,where stress and strength of a structure are generallyregarded as two independent random variables.However,owing to the complexity andvariety of statistic characteristics of stress and strength in practical engineering,theconventional SSI model has shown its limitations in analyzing structural reliabilityunder some specified conditions.Considering the engineering characteristics of stress and strength,the discretizationof continuous random variables is adopted as a basic research approach in thisdissertation and the universal generating function is introduced,which is a fundamentaltool to calculate probability of discrete random variables.Several discrete SSI modelsare proposed,which extend the theoretical system and application range of theconventional SSI models.The contributions of this dissertation are summarized as follows:(1)The discrete SSI modelProbability calculation is one of the fundamental problems that the SSI model hasto deal with.In this dissertation,the universal generating function is used to calculatethe probability of a function with discrete random stress and strength and a discrete SSImodel is proposed.Through comparison with conventional methods (numerical integraland parameter estimation),the proposed model provides a unified algorithm forreliability analysis of structures under different conditions.(2)The SSI model with stress-dependent strengthThe unilateral dependency of strength on stress exists in engineering application.Inthis dissertation,the unilateral dependency is represented by the conditionaldistributions of strength under different stress levels.Assuming the stress as a discreterandom variable,a SSI model with stress-dependent strength can be built through theprobability computation of a function with stress and strength.(3)The SSI model under multi-operating conditions In the conventional SSI model,the structure stress is regarded as a single randomvariable,which does not fully represent the actual stress state of structures undermulti-operating conditions.In this dissertation,multiple discrete random variables aredefined based on the actual range of structure stress,which are used to represent themulti-operating conditions of the structure.The structural reliabilities under differentoperating conditions are calculated respectively,and then the total probability formula isused to evaluate the structure reliability synthetically.(4)The dynamic SSI model with strength degradation following a Gamma processStructure strength may degrade with time in engineering.In this dissertation,aGamma process is utilized to describe the strength degradation and the residual strengthof a structure is defined as the difference between initial strength and strengthdegradation.The probability of a function constituted by stress,initial strength andstrength degradation is calculated under the assumption that the structure stress is arandom variable.Then a time-dependent SSI model with strength degradation followingGamma process is proposed.(5)The dynamic SSI model under shock load conditionShock load widely exists in engineering application.Their characteristics can bedescribed by random change of load amplitude and reiteration of load action.Underreiterative shock load condition,the model of equivalent load is derived according to theproperties of order statistic.By treating the strength as an arbitrary random variable andcalculating the probability characteristics of the function of equivalent load and strength,a dynamic SSI model is proposed.