Research For The Method Of System Reliability Analysis Based On Truss Structures

With the continuous development of engineering technologies,more and more engineering structures have emerged in recent years.There tends to be numerous random factors influencing the performance of the structure during the process of its design,construction and service.This is likely to cause structural failure and further affect the production of society and safety of individuals.The truss is a typical engineering structure with high redundancy,whose failure is complicated to be analyzed due to multiple failure modes included.Therefore,it is of great significance for the system reliability analysis of a structure with high redundancy to investigate the method of system reliability analysis based on truss structures.This thesis proposes two methods to analyze the system reliability of truss structures via different metamodels.Also,a method for the analysis of small failure probability is proposed.The main research contents are as follows.(1)A method for the reliability analysis of truss structures based on the response surface method is proposed.At the level of component,the response surface method is performed to fit the stress of each member of a truss to construct the performance function.A optimization is built according to the geometric meaning of the reliability index and solved.Following identify the dominant failure modes by-unzipping method.At the system level,the differential equivalent recursion algorithm is applied to calculate the reliability indices of dominant failure modes,and PNET(Probability Network Estimation Technique)is conducted to calculate the system reliability index of the truss.The overall calculation is based on the co-simulation of MATLAB and ANSYS/APDL that realizes the automation of the analysis process.In addition,the proposed method is performed to analyze three examples and the relative errors are3.04%,1.42% and 3.48% respectively,which demonstrates the accuracy of this proposed method.(2)For the event with small probability,an adaptive two-stage algorithm based on PC-Kriging model is proposed.The first stage combines PC-Kriging and subset simulation,and integrates uniform design,K-means++ clustering and convergence criterion based on failure probability to quickly estimate the failure probability.The second stage generates new samples in terms of the estimated failure probability of the first stage to conduct further reliability analysis.Besides,an adaptive criterion is constructed to determine the initiation and termination of the second stage.Meanwhile,this method is verified through four examples.Meanwhile,the relative errors of four examples are smaller than 1%,which verifies the accuracy and efficiency of the proposed method.(3)Based on the first stage of the proposed adaptive two-stage algorithm,the second method for the system reliability analysis of truss structures is proposed.The global metamodel of the performance function of overall failure of the truss is constructed by the first stage to determine the dominant failure domain.Then representative failure modes are identified.Local metamodels can be built according to the corresponding samples of representative failure modes and performed active learning to further calculate the system failure probability and failure probabilities of representative failure modes.Eventually,three examples verify the second proposed method.The relative errors are 0.40%,2.93% and 1.76% respectively,and the numbers of calls to performance functions decrease in three examples.