Research On Analysis Methods For Non-probabilistic Reliability Of Structural Systems Using Ellipsoidal Model

Reliability methods have been widely used in the safety evaluation of mechanical structural systems with uncertainties.The traditional probabilistic reliability theory is more mature,but requires a large number of experimental samples.Compared with the probability model,the non-probabilistic convex model is more suitable for the problems with limited information.In this paper,by dealing uncertain variables with the ellipsoidal convex model,the reliability analyses of series and parallel structural systems are investigated.The main contents are as follows:(1)The optimal bounds method for non-probabilistic reliability analysis of series str uctural systems.The optimal bounds method is proposed to overcome the drawbacks of the non-probabilistic bounds method for series structural systems,in which the minimum upper bound is obtained by the maximal tree method while the maximum lower bound is solved by the optimization criterion method.Four examples are provided to demonstrate the effectiveness and feasibility of the proposed method.(2)Non-probabilistic equivalent planes method for reliability analyses of parallel structural systems:The non-probabilistic reliability model of parallel structural systems is first given.Based on the consideration that two limit state planes are equivalent to one limit state plane,the analytic formulas of equivalent non-probabilistic reliability index and equivalent unit normal vector are then given respectively.An adaptive combining strategy with a descending order of the correlation coefficients of two failure modes is further proposed to obtain a more precise solution.Finally,four examples are given for illustrating the validity of the proposed method.(3)Improved non-probabilistic equivalent planes method for reliability analyses of parallel structural systems:To avoid the error caused by the lack of correlation between failure modes,an improved version of the non-probabilistic equivalent planes method is proposed.Firstly,the model of failure modes in the standard space are established,and the change rule of joint failure of multiple failure modes is analyzed.Then the correlation analysis between multiple failure modes is converted into the problem of included angle,and the calculation method of correlation coefficient is given.Finally,the results of three numerical examples show that the proposed method is reasonable and effective,providing a higher precision than the non-probabilistic equivalent planes method.