On Some Non-probabilistic Reliability Analysis Methods Of Structures

The probabilistic reliability method is one of the effective ways to deal with the common uncertainties in mechanical structures related to geometry,materials,assembly and manufacturing process.Compared with the probabilistic reliability method,the non-probabilistic reliability method only needs to know the range or boundary of uncertain samples to evaluate the safety of structures,which is more suitable for engineering problems with small samples.In this paper,aiming at the invariance problem of non-probabilistic reliability index and the solving problem of non-probabilistic reliability of series structural system,several non-probabilistic reliability analysis methods,namely the mean-value method,the design-point method,the non-probabilistic linear programming bounds method(NLPBM)and the improved non-probabilistic linear programming bounds method(INLPBM),are investigated.The main research contents are as follows:(1)Invariance problem of the non-probabilistic reliability index and its influence on first order approximation methods:The preconditions for the existence of the invariance problem of non-probabilistic reliability index of interval model are given.And the influence of the invariance problem on two first-order reliability approximation methods,namely the mean-value method and the design-point method,is discussed.Finally,the application scope of the two methods is given by comparing the accuracies of the mean-value method and the design-point method through three examples.(2)The non-probabilistic linear programming bounds method for the reliability of series structural system:A non-probabilistic reliability model of series structure system is established by using ellipsoid model to describe uncertain variables.The corresponding linear programming(LP)model is established to solve the bounds of the non-probabilistic failure measure of the series structure system,with the non-probabilistic measure of all the mutually exclusive collectively exhaustive(MECE)sub-regions divided by the system failure surface in the variable uncertainty domain as the design variables,the non-probabilistic failure degree of the series structure system as the objective function,and the non-probabilistic measures of the single failure mode failure areas,the joint failure areas of two failure modes and the whole uncertainty areas as the constraint conditions,And the implementation process of the proposed method is given.Finally,the results of four examples show that the proposed method has the advantages of avoiding ranking,improving accuracy,and having strong expansibility over the traditional non-probabilistic reliability bounds method.(3)The improved non-probabilistic linear programming bounds method for the reliability of series structural system:In order to effectively reduce the size of design variables of linear programming model,the series structural system is decomposed into several subsystems with two failure modes and three failure modes,and the identification criterion of empty sets is given by using the relative position relationship of failure modes and the ellipsoid.The empty sets of each subsystem is used to determine the distribution of zero design variables in linear programming.Then a new linear programming model is constructed by deleting the zero design variables to determine the bounds of the non-probabilistic failure degree of the series structure system,and the implementation process of the proposed method is given.Finally,the results of four examples show that,compared with the non-probabilistic linear programming bounds method,the improved non-probabilistic linear programming bounds method can effectively reduce the design variables and has higher accuracy.