Thesis (MScEng)-- Stellenbosch University, 2013. / 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 of
structures both in component and system level to take into account the uncertainties involved
in structural analysis and design. To the contrary, in practice, the (computerised) analysis of
structures is based on a deterministic analysis which fails to address the randomness of design
and analysis parameters. This means that an investigation on the algorithmic methodologies for
a component and system reliability analysis can help pave the way towards the implementation
of fully stochastic analysis of structures in a computer environment. This study is focused
on algorithm development for component and system reliability analysis based on the various
proposed methodologies. Truss structures were selected for this purpose due to their simplicity
as well as their wide use in the industry. Nevertheless, the algorithms developed in this study
can be used for other types of structures such as moment-resisting frames with some simple
modi cations.
For a component level reliability analysis of structures different methods such as First Order
Reliability Methods (FORM) and simulation methods are proposed. However, implementation
of these methods for the statistically indeterminate structures is complex due to the implicit
relation between the response of the structural system and the load effect. As a result, the
algorithm developed for the purpose of component reliability analysis should be based on the
concepts of Stochastic Finite Element Methods (SFEM) where a proper link between the finite
element analysis of the structure and the reliability analysis methodology is ensured. In this
study various algorithms are developed based on the FORM method, Monte Carlo simulation,
and the Response Surface Method (RSM). Using the FORM method, two methodologies are
considered: one is based on the development of a finite element code where required alterations
are 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 Sampling
Monte Carlo (ULHCSMC). Moreover, RSM is used together with simulation methods. Throughout the thesis, the effciency of these methods was investigated. A Fully Stochastic
Finite Element Method (FSFEM) with alterations to the finite element code seems the fastest
approach 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 seemed
to be the most efficient method followed by LHCSMC and DMCS. The response surface method
is 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: the ß-unzipping method
and the branch and bound method. The ß-unzipping method is based on a level-wise system
reliability evaluation where the structure is modelled at different damaged levels according to its
degree 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 identification
of different failure paths of the structure by the expansion of the structural failure tree. The
evaluation of the damaged states for both of the methods is the same. Furthermore, both of
the methods lead to the development of a parallel-series model for the structural system. The
only difference between the two methods is in the search approach used for the failure sequence
identification.
It was shown that the ß-unzipping method provides a better algorithmic approach for evaluating
the system reliability compared to the branch and bound method. Nevertheless, the branch and
bound method is a more robust method in the identification of structural failure sequences. One
possible way to increase the efficiency of the ß-unzipping method is to define bigger unzipping
intervals in each level which can be possible through a computerised analysis. For such an
analysis four major modules are required: a general intact structure module, a damaged structure
module, a reliability analysis module, and a system reliability module.
In this thesis different computer programs were developed for both system and component
reliability analysis based on the developed algorithms. The computer programs are presented
in the appendices of the thesis. / AFRIKAANSE OPSOMMING: Meeste van die veranderlikes betrokke by die ontwerp en analise van strukture is stogasties in
hul aard. Om die onsekerhede betrokke in ontwerp en analise in ag te neem is dit dus van
groot belang om 'n ten volle stogastiese analise te kan uitvoer op beide komponent asook stelsel
vlak. In teenstelling hiermee is die gerekenariseerde analise van strukture in praktyk gebaseer
op deterministiese analise wat nie suksesvol is om die stogastiese aard van ontwerp veranderlikes
in ag te neem nie. Dit beteken dat die ondersoek na die algoritmiese metodiek vir komponent en
stelsel betroubaarheid analise kan help om die weg te baan na die implementering van ten volle
rekenaarmatige stogastiese analise van strukture. Di e studie se fokus is op die ontwikkeling van
algoritmes vir komponent en stelsel betroubaarheid analise soos gegrond op verskeie voorgestelde
metodes. Vakwerk strukture is gekies vir die doeleinde as gevolg van hulle eenvoud asook hulle
wydverspreide gebruik in industrie. Die algoritmes wat in die studie ontwikkel is kan nietemin
ook vir ander tipes strukture soos moment-vaste raamwerke gebruik word, gegewe eenvoudige
aanpassings.
Vir 'n komponent vlak betroubaarheid analise van strukture word verskeie metodes soos die
"First Order Reliability Methods" (FORM) en simulasie metodes voorgestel. Die implementering
van die metodes vir staties onbepaalbare strukture is ingewikkeld as gevolg van die implisiete
verband tussen die gedrag van die struktuur stelsel en die las effek. As 'n gevolg, moet die algoritme
wat ontwikkel word vir die doel van komponent betroubaarheid analise gebaseer word
op die konsepte van stogastiese eindige element metodes ("SFEM") waar 'n duidelike verband
tussen die eindige element analise van die struktuur en die betroubaarheid analise verseker is. In
hierdie studie word verskeie algoritmes ontwikkel wat gebaseer is op die FORM metode, Monte
Carlo simulasie, en die sogenaamde "Response Surface Method" (RSM). Vir die gebruik van die
FORM metode word twee verdere metodologieë ondersoek: een gebaseer op die ontwikkeling
van 'n eindige element kode waar nodige verandering aan die eindige element kode self gemaak
word en die ander waar 'n kommersiële eindige element pakket gebruik word. Verskillende simulasie
metodes word ook geïmplimenteer naamlik Direkte Monte Carlo Simulasie (DMCS),
"Latin Hypercube Sampling Monte Carlo" (LHCSMC) en sogenaamde "Updated Latin Hypercube
Sampling Monte Carlo" (ULHCSMC). Verder, word RSM tesame met die simulasie
metodes gebruik. In die tesis word die doeltreffendheid van die bostaande metodes deurgaans ondersoek. 'n Ten volle stogastiese eindige element metode ("FSFEM") met verandering aan die eindige element
kode blyk die vinnigste benadering te wees omdat die koppeling tussen die eindige element
metode pakket en die betroubaarheid analise verhoed word. Simulasie metodes kan ook effektief
aangewend word vir die betroubaarheid evaluasie waar ULHCSMC as die mees doeltre end
voorgekom het, gevolg deur LHCSMC en DMCS. The RSM metode is die mees komplekse
metode vir algoritmiese komponent betroubaarheid analise. Die metode is egter nuttig vir
sisteem betroubaarheid analise.
Vir sisteem-vlak betroubaarheid analise is twee metodes oorweeg naamlik die "ß-unzipping"
metode and die "branch-and-bound" metode. Die "ß-unzipping" metode is gebaseer op 'n
sisteem-vlak betroubaarheid ontleding waar die struktuur op verskillende skade vlakke gemodelleer
word soos toepaslik vir die hoeveelheid addisionele las paaie. In elke vlak word die
sogenaamde "unzipping" intervalle gedefinieer vir die identifikasie van die kritiese elemente. Die
"branch-and-bound" metode is gebaseer op die identifikasie van verskillende faling roetes van
die struktuur deur uitbreiding van die falingsboom. The ondersoek van die skade toestande vir
beide metodes is dieselfde. Verder kan beide metodes lei tot die ontwikkeling van 'n parallelserie
model van die strukturele stelsel. Die enigste verskil tussen die twee metodes is in die
soek-benadering vir die uitkenning van falingsmodus volgorde.
Dit word getoon dat die "ß-unzipping" metode 'n beter algoritmiese benadering is vir die ontleding
van sisteem betroubaarheid vergeleke met die "branch-and-bound" metode. Die "branch-and-
bound" metode word nietemin as 'n meer robuuste metode vir die uitkenning van die falings
volgorde beskou. Een moontlike manier om die doeltre endheid van die "ß-unzipping" metode
te verhoog is om groter "unzipping" intervalle te gebruik, wat moontlik is vir rekenaarmatige
analise. Vir so 'n analise word vier hoof modules benodig naamlik 'n algemene heel-struktuur
module, 'n beskadigde-struktuur module, 'n betroubaarheid analise module en 'n sisteem betroubaarheid analise module.
In die tesis word verskillende rekenaar programme ontwikkel vir beide sisteem en komponent
betroubaarheid analise. Die rekenaar programme word in die aanhangsels van die tesis
aangebied.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/85710 |
| Date | 12 1900 |
| Creators | Hashemolhosseini, Sepehr |
| Contributors | Van Der Klashorst, Etienne., Stellenbosch University. Faculty of Engineering. Dept. of Civil Engineering. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | xxiii, 267 p. : ill. |
| Rights | Stellenbosch University |
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