Algorithmic component and system reliability analysis of truss structures

[摘要] ENGLISH ABSTRACT: Most of the parameters involved in the design and analysis of structures are of stochastic nature.This is, therefore, of paramount importance to be able to perform a fully stochastic analysis ofstructures both in component and system level to take into account the uncertainties involvedin structural analysis and design. To the contrary, in practice, the (computerised) analysis ofstructures is based on a deterministic analysis which fails to address the randomness of designand analysis parameters. This means that an investigation on the algorithmic methodologies fora component and system reliability analysis can help pave the way towards the implementationof fully stochastic analysis of structures in a computer environment. This study is focusedon algorithm development for component and system reliability analysis based on the variousproposed methodologies. Truss structures were selected for this purpose due to their simplicityas well as their wide use in the industry. Nevertheless, the algorithms developed in this studycan be used for other types of structures such as moment-resisting frames with some simplemodi cations.For a component level reliability analysis of structures different methods such as First OrderReliability Methods (FORM) and simulation methods are proposed. However, implementationof these methods for the statistically indeterminate structures is complex due to the implicitrelation between the response of the structural system and the load effect. As a result, thealgorithm developed for the purpose of component reliability analysis should be based on theconcepts of Stochastic Finite Element Methods (SFEM) where a proper link between thefiniteelement analysis of the structure and the reliability analysis methodology is ensured. In thisstudy various algorithms are developed based on the FORM method, Monte Carlo simulation,and the Response Surface Method (RSM). Using the FORM method, two methodologies areconsidered: one is based on the development of afinite element code where required alterationsare made to the FEM code and the other is based on the usage of a commercial FEM package.Different simulation methods are also implemented: Direct Monte Carlo Simulation (DMCS),Latin Hypercube Sampling Monte Carlo (LHCSMC), and Updated Latin Hypercube SamplingMonte Carlo (ULHCSMC). Moreover, RSM is used together with simulation methods.Throughout the thesis, the effciency of these methods was investigated. A Fully StochasticFinite Element Method (FSFEM) with alterations to thefinite element code seems the fastestapproach since the linking between the FEM package and reliability analysis is avoided. Simulation methods can also be effectively used for the reliability evaluation where ULHCSMC seemedto be the most efficient method followed by LHCSMC and DMCS. The response surface methodis the least straight forward method for an algorithmic component reliability analysis; however,it is useful for the system reliability evaluation.For a system level reliability analysis two methods were considered: theß-unzipping methodand the branch and bound method. Theß-unzipping method is based on a level-wise systemreliability evaluation where the structure is modelled at different damaged levels according to itsdegree of redundancy. In each level, the so-called unzipping intervals are defined for the identification of the critical elements. The branch and bound method is based on the identificationof different failure paths of the structure by the expansion of the structural failure tree. Theevaluation of the damaged states for both of the methods is the same. Furthermore, both ofthe methods lead to the development of a parallel-series model for the structural system. Theonly difference between the two methods is in the search approach used for the failure sequenceidentification.It was shown that theß-unzipping method provides a better algorithmic approach for evaluatingthe system reliability compared to the branch and bound method. Nevertheless, the branch andbound method is a more robust method in the identification of structural failure sequences. Onepossible way to increase the efficiency of theß-unzipping method is to define bigger unzippingintervals in each level which can be possible through a computerised analysis. For such ananalysis four major modules are required: a general intact structure module, a damaged structuremodule, a reliability analysis module, and a system reliability module.In this thesis different computer programs were developed for both system and componentreliability analysis based on the developed algorithms. The computer programs are presentedin the appendices of the thesis.

[发布机构] Stellenbosch University