Transmission Lines Stochastic Finite Element Reliability Analysis

AS an important part of transmission tower-line system,transmission lines is the guarantee of long-distance transportation of the power energy.As the precise research of the transmission line tower system,the reliability of the transmission lines which has the character of geometric nonlinearity has important theoretical significance and engineering significance.In this paper,based on the stochastic finite element theory,the link element of Co-rotational Formulation and reliability theory are combined to set up the force molding and calculate the reliability of the transmission lines which has the character of geometric nonlinearity.Specifically,the research mainly and conclusion including the following aspects.(1)The basic concept of structural reliability and basic algorithm of stochastic finite element method were introduced.On the basis of comparing the stochastic finite element method,according to the deformation of transmission lines,the Taylor expansion stochastic finite element method was used to calculate the reliability of transmission lines.(2)The initial state and axial tension calculation results of transmission lines will directly affect the precision of transmission lines' reliability analysis.Considering the initial form of transmission lines and the feasibility of the calculation method,the parabolic equation was used to describe the initial form of transmission lines.Then exploring the calculation method of Cable structures geometric nonlinear problem.In order to calculate the internal force and deformation of the transmission lines,the tangent stiffness matrix of the space link element was deduced on the fundament of the Co-rotational Formulation's basic assumptions,and the Newton-Raphson method was used to solve the nonlinear equation.The engineering examples were combined to verify the accuracy of this algorithm.(3)Based on the behavior controlling equation of CR,the controlling equation of behavior about the transmission lines was set up.This paper inferred to the reaction gradient of element displacement about random variable,set foundation to making use of random finite element method to find the degree of reliability in suspension structure.Then using the first order Taylor expansion(direct differentiation method)to derive the gradient of the cable structure displacement response.The first-order reliability method(FOSM)is used for the calculation and analysis of the reliability of the transmission lines under the combination of ice,wind load which has considering the basic random variables of mechanical properties,size and load.The computed results show that the reliability of suspension point and the lowest point is 3.883 and 3.885.Both of them is higher than the ultimate limit state in "Unified standard for reliability design of engineering structures"(GB 50153-2008)and "Eurocode-basis of structural design".The results can provide theoretical basis and technical support for reliability analysis of the transmission lines and other cable structure.(4)To verify the rationality and correctness of the result,the Monte Carlo Simulation method(MCS)and the Monte Carlo Simulation Based Optimization principle(MCOP)have been implemented.Compared with MCS the error of them is-0.438%and-0.463%,Compared with MCOP the error is between 2.961%with 0.412%and between 2.677%with 0.412%.With times added,the relative error became smaller and smaller.So this paper is correct and believable.