The Study Of Several Issues Of Reliability Analysis Of Structural System

Reliability analysis of structural systems is the basis and premise of carrying outpractical engineering structure safety assessment and conducting structure design andoptimization, and it is also the strong guarantee and technical support of improving structuresafety level and upgrading engineering structure economy. The need for reliability analysis ofstructural systems is urgent in engineering practice. But the main reason why it is not widelyused in practical engineering is that parts of emphasis and difficulty in the reliability theory ofstructural systems have not been solved completely.The paper mainly focuses on the study of the reliability calculation of serial(parallel)system, the function establishment of serial (parallel)system, the correlation analysisbetween failure modes and the effectively recognition of main failure modes, etc. Thecalculation accuracy of serial (parallel) system reliability is improved effectively byintroducing new theory, improving old method and putting forward new method, etc. Theexplicit expression of equivalent function for serial (parallel) system has been deduced; theproblem of correlation coefficients calculation between failure modes has been solvedreasonably; the recognition efficiency of main failure modes has been increased vastly. Theproblems which effects engineering application have been focused on, like poor calculationaccuracy, low computational efficiency and the difficulty in establishing function of serial(parallel) system.Through the comparison for existing methods, the calculation method of reliability basedon equivalent plane method is relatively suitable for reliability analysis of structural systems.But for parallel system, the calculation is limited and the accuracy is not enough. The mainreason is that the calculation of correlation coefficient is lack of theoretical basis in theprocess of equivalent, specifically for parallel system. Therefore, the concept of multiplecorrelations was introduced to reliability analysis of structural systems, to solve correlationcoefficients between one element and multiple elements, and multiple correlation-equivalentplane method was presented. The method uses multiple correlation coefficients to express thecorrelation between equivalent plane and other ultimate state surfaces. It solves thenon-correlation problem in equivalent principles, and overcomes the shortcoming of greaterror when equivalent plane method was used to analyze the reliability of parallel system. By comparing the relative error of this method and numerical integration, Monte Carlo method, itproves that this method has high calculation accuracy and speed for series (parallel) system.The advantages and disadvantages were analyzed between this method and the traditionalmethod by the typical examples, which proved that this method is suitable for the reliabilityanalysis of large structural system.Equivalent function was put forward to solve the problems of difficulty in establishingfunction of serial (parallel) system and low computational efficiency. Based on multiplecorrelation-equivalent plane method, equivalent function was deduced by equivalent principle.The explicit expression of equivalent function with constant coefficient which only involvestwo-dimension integral operation was given. Reliability of series (parallel) system andequivalent function could be solved by adequate multiple correlation-equivalent plane methodand equivalent function could be neglected to calculate reliability with high computationalefficiency. It was proved to be credible to solve equivalent function by multiplecorrelation-equivalent plane method through examples analysis. Equivalent function canreflect the acuteness of reliability for random variables accurately, and it can meet theapplication requirements of structure design and optimization based on reliability.Canonical correlation analysis was introduced into structural reliability analysis for theproblems that calculations of correlation coefficients between the failure modes are lack oftheoretical basis and the correlation between failure modes could not be described bycorrelation coefficients in the process of solving failure probability. The correlation betweenfailure modes has been explained reasonably; it has been proved that the correlation betweenfailure modes could be described accurately by the second canonical correlation coefficients.The correctness and the feasibility have been checked by typical numerical examples; it wasproved that the calculation accuracy of structural system reliability has been improved.On the base of analyzing the existing two kinds of identification methods of main failuremode, the problem that the reserved candidate failure elements are not all the necessaryelements of failure modes has been studied. According to the basic theory of structuralmechanics, the effect of failure elements on structure remained internal force has beenanalyzed, and the formula has been deduced; According to the formula, failure modes withthe same basic failure elements have been proved linerly correlated; Based on probabilitytheory, it can be concluded that the main failure modes only contain basic failure elements, and the necessary elements of main failure modes are the basic elements has been proved;Failure modes of structural system have been analyzed, and the failure range of structuralsystem has been discussed; Based on the thoughts of building structure gradually, the dividedmethod of minimum existence range including basic elements has been proposed to makesure main failure mode will not be left out; A new method of identifying main failure mode oftrusswork has been put forward combined with the branch bounding method. According toexamples analysis, it can be proved that this method is rational and high-efficient.