On Non-probabilistic Reliability Analysis And Optimal Design Method Of Structure

Compared with the traditional probabilistic reliability model,the non-probabilistic reliability model based on convex model is more suitable for reliability analysis and optimal design of mechanical structures with small samples,poor information and high reliability requirements.In this paper,the non-probabilistic reliability analysis methods and the shape optimization design method of mechanical structures are studied.The main contents are as follows:(1)The wide and narrow non-probabilistic reliability methods for non-probabilistic reliability analysis:Using the ellipsoid convex model to describe the uncertainties in the series structural systems,two approximation methods to calculate the non-probabilistic dangerous degree of the structural systems are given by using the bounds estimation technology.Firstly,a wide non-probabilistic bounds method based on the volumes of failure domain of all single failure modes is proposed.Then,based on the volume of failure domain of all single failure modes and joint failure domain of any two failures modes,a narrow non-probabilistic bounds method with higher accuracy is presented,meanwhile,the analytical solution of the joint failure volume of two failure modes is deduced for improving the calculating efficiency of the narrow non-probabilistic bounds method.Finally,four examples are given for demonstrating the validity of the proposed methods.(2)Step-by-step equivalent planes method for non-probabilistic reliability analysis:Firstly,the non-probabilistic reliability index and normal vector of failure plane corresponding to the equivalent failure mode are derived based on the principle of step-by-step equivalent technology.Then,two strategies,namely the adaptive equivalent process and removing the redundant failure modes,are proposed to improve the precision of the step-by-step equivalent planes method.Finally,the correctness of the proposed method and the effectiveness of the strategies are verified through four examples.(3)Non-probabilistic reliability shape optimization of truss structure:A non-probabilistic reliability-based shape optimization design method of truss structure is proposed by representing uncertain parameters as interval variables.A non-probabilistic reliability-based shape optimization model is conducted,in which cross-sectional area and node coordinate,structural weight and non-probabilistic reliability indexes determined by homologous performance functions are used as design variables,objective function and constraints,respectively.To overcome the convergence deterioration caused by the coupling of two kinds of design variables,the strategy of dimensional normalization is introduced.The analytical solution of the non-probabilistic reliability index is given,in which the midpoint is selected as the linearization point of the limit-state function,and then the optimization model is solved by the sequential quadratic programming algorithm.The results of three numerical examples indicate that the solutions according with the design experiences for engineering structures can be obtained efficiently and stably,which is provided to demonstrate the accuracy and effectiveness of the proposed method.