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The separation of alcoholsNieuwoudt, Traute 03 1900 (has links)
Thesis (MScEng)--Stellenbosch University, 2002. / ENGLISH ABSTRACT: Pure primary alcohols are very valuable as raw materials and solvents.
Close-boiling alcohol mixtures are produced as byproducts from the Fischer
Tropsch synthesis. These byproducts include the mixtures 1-butanol+2-
penta noI and 1-pentanol+2-hexanol. Due to the small difference in boiling
points these alcohols cannot be separated from one another by using
conventional distillation.
This study has been undertaken to determine whether primary and secondary
alcohols may be separated by exploitation of their chemical properties.
Esterification of the alcohols followed by distillation of the esters into cuts and
hydrolyses of the esters, has been attempted to separate the alcohols. This
however, was unsuccessful.
In this study the difference in dehydration rate of secondary and primary
alcohols in acidic media has also been investigated. Several acidic resins
and liquid catalysts have been used. The acidic resins gave no dehydration
or extremely low dehydration rates in the liquid phase. The liquid catalysts
H2S04, Oxalic Acid, NaHS04 and H3P04 were investigated. H3P04 gave
excellent results. Laboratory experiments were conducted at the boiling point
of the reaction mixture at atmospheric pressure. The reaction mixture was
sampled at varying time intervals and analysed. The secondary alcohol
dehydrated rapidly to the corresponding alkene. The primary alcohol formed
symmetrical ethers at a very low rate. The primary and secondary alcohol
also combined to form small amounts of unsymmetrical ethers. After the
dehydration reaction the organic products can be separated from the acid
with a'short path distillation unit. The primary alcohol can further be purified
by conventional distillation. Conceptual process designs were done for the
separation and purification of the reactor product streams of the alcohol
mixtures 1-butanol+2-pentanol and 1-pentanol+2-hexanol. n laboratory scale it was found that for the separation of 85% 1-butanol and
15% 2-pentanol (mass %), 90 % H3P04 (mass %) at an acid:alcohol ratio of
1,5: 1 results in suffcient dehydration of 2-pentanol. A reaction time of 70
minutes is required. A conceptual design on the purification of the 1-butanol
predicted a product quality of 99,5 % 1-butanol (mass %) and a 1-butanol
recovery of 75 %. The 1-butanol recovery is low, because a major part of the
1-butanol is lost in the purification as part of the ternary azeotrope with water
and n-butylether.
On laboratory scale it was also found that for the separation of 85 % 1-
pentanol+15 % 2-hexanol (mass %),90 % H3P04 (mass %) at an acid:alcohol
ratio of 1,5:1 gives sufficient dehydration of 2-hexanol. A reaction time of only
35 minutes is required. A conceptual design on the purification of the 1-
pentanol predicted a product quality of 99,9 % 1-pentanol and a 1-pentanol
recovery of > 98 %. The 1-pentanol recovery is excellent, only the 1-
pentanol that is converted to ethers is lost.
In this study it has been proven that a dehydration separation process can be
applied successfully to remove secondary alcohols from a primary+secondary
alcohol mixture. Especially the removal of 2-hexanol from a 1-pentanol+2-
hexanol mixture gave promising results. In order to assess the economic
viability of this dehydration process an economic evaluation should be done.
This could be part of subsequent studies.
The dehydration separation process should be investigated further. It is
believed that this dehydration separation process can be expanded to higher
alcohols, e.g. 1-hexanol+2-heptanol. It would be extremely advantageous if
a solid catalyst could be found for the separation. In this case the recovery of
the organics from the reaction mixture would be very much easier. If a solid
catatyst is not found, a continuous process using H3P04 as liquid catalyst
should be developed. / AFRIKAANSE OPSOMMING: Suiwer primêre alkohole is baie waardevolle rou materiale en oplosmiddels.
Alkohol mengsels, wat uit naby-kokende alkohole bestaan, word as neweprodukte
in die Fischer Tropsch Sintese gevorm. Hierdie newe-produkte sluit
alkohol mengsels soos 1-butanol+2-pentanol en 1-pentanol+2-hexanol in.
Weens die klein verskil in kookpunte van hierdie alkohole kan die alkohole nie
met konvensionele distillasie van mekaar geskei word nie.
Hierdie studie is onderneem om te bepaal of die chemiese eienskappe van
alkohole benut kan word om primêre en sekondêre alkohole van mekaar te
skei. 'n Poging is aangewend om die alkohole met behulp van esterifikasie te
skei. Die alkohole is eers ge-esterifiseer, daarna met behulp van distillasie in
verskeie snitte verdeel en die alkohol is vrygestel deur hidrolise van die
esters. Dit was egter onsuksesvol.
Die verskil in dehidrasie tempo van sekondêre en primêre alkohole in suur
mediums is ook ondersoek. Verskeie suur harse en vloeibare kataliste is
ondersoek. Die suur .harse het of geen dehidrasie of baie lae dehidrasie
tempo's in die vloeistoffase gegee. Die vloeistof kataliste H2S04, Oksaalsuur,
NaHS04 en H3P04 is ondersoek. H3P04 het uitstekende resultate gelewer.
Eksperimente is op laboratoriumskaal en onder atmosferiese druk uitgevoer.
Monsters is van die reaksiemengsels by verskillende tydsintervalle geneem
en geanaliseer. Die sekondêre alkohol het vinnig na die ooreenstemmende
alkeen gedehidreer. Die primêre alkohole het simmetriese eters teen 'n lae
tempo gevorm. Die primêre en sekondêre alkohole het ook gekombineer om
gemengde eters te vorm. Kort-pad-distillasie kan gebruik word om na die
dehidrase reaksie die organiese produkte van die suur te verwyder. Die
primêre alkohole kan verder met konvensionele distillasie gesuiwer word.
Konseptueie prosesontwerpe is uitgevoer vir die skeiding en suiwering van
die alkohol mengsels 1-butanol+2-pentanol en 1-pentanol+2-hexanol nadat
dehidrasie van die mengsels uitgevoer is. Op laboratoriumskaal is dit gevind dat vir die skeiding van 85% 1-butanol en
15% 2-pentanol (massa %), 90 % H3P04 (massa %) met 'n suur:alkohol
verhouding van 1,5:1 effektiewe dehidrase van 2-pentanol lewer. fn
Reaksietyd van 70 minute word benodig. fn Konseptueie ontwerp vir die
suiwering van die 1-butanol het fn produkkwaliteit van 99,5 % 1-butanol
(massa %) en fn 1-butanol opbrengs van 75 % voorspel. Die 1-butanol
opbrengs is laag aangesien fn groot deel van die 1-butanol verlore gaan as
deel van die ternêre azeotroop wat 1-butanol met n-butieleter en water vorm.
Dit is ook op laboratoriumskaal vasgestel dat vir die skeiding van 85 % 1-
pentanol+15 % 2-hexanol (massa %), 90 % H3P04 (massa %) met fn
suur:alkohol verhouding van 1,5:1 effektiewe dehidrase van 2-hexanollewer.
fn Reaksietyd van slegs 35 minute word benodig. fn Konseptueie ontwerp vir
die suiwering van die 1-pentanol het fn produkkwaliteit van 99,9 % 1-pentanol
en fn 1-pentanol opbrengs van > 98 % voorspel. Die 1-pentanol opbrengs is
uitstekend, en slegs die 1-pentanol wat omgeskakel word na eters gaan
verlore.
In hierdie studie is dit bewys dat fn dehidrasie skeidingsproses suksevol
aangewend kan word om sekondêre alkohole uit fn primêre+sekondêre
alkohol mengsel te verwyder. Veral die verwydering van 2-hexanol uit fn 1-
pentanol+2-hexanol mengsel het belowende resultate gelewer. Om die
ekonomiese lewensvatbaarheid van so fn skeidingsproses te bepaal moet fn
ekonomiese evaluasie van die proses gedoen word. Dit behoort deel van
verdere studies te vorm.
Die dehidrasie skeidingsproses behoort verder ondersoek te word. Dit word
verwag dat die proses na hoër alkohol mengsels, bv. 1-hexanol+2-heptanol
uitgebrei kan word. Dit sou baie voordelig wees indien fn geskikte soliede
katalis vir die skeiding gevind word. In so fn geval sou die herwinning van
die organiese produkte van die reaksiemengsel baie makliker wees. Indien fn
soliede katalis nie gevind word nie, behoort fn kontinu proses waarin H3P04
as vloeistof katalis gebruik word, ontwikkel te word.
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The storage of water in sand : an investigation of the properties of natural and artificial sand reservoirs and of methods of developing such reservoirsWipplinger, O. (Otto) January 1953 (has links)
Thesis (D.Sc.)--Stellenbosch University, 1953. / ENGLISH ABSTRACT: no abstract available / AFRIKAANSE OPSOMMING: geen opsomming
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Aspect of a hardware-in-the-loop integrated test systemGrungxu, Lungile Leonard 03 1900 (has links)
Thesis (MScEng)--University of Stellenbosch, 2003. / ENGLISH ABSTRACT: A multiprocessor hardware-in-the-Ioop operating system was developed for the Integrated
Test System (ITS) and is aimed at implementing the ITS as a space emulation vehicle. The
thesis contains a study of satellite orbits, Kepler elements, geomagnetic fields and
communication protocol between the processors.
The system structure consists of an orbit generator, a core-operating system and is presented
with a study of the satellite sensors. In implementing the orbit propagator, there was a need
to pay special attention to the Halving algorithm, the Newton Raphson method and the True
Solution. These algorithms were used to calculate the true anomaly angle as a function of
eccentric anomaly. The communications protocol was tested and all the errors, with their
solutions, have been discussed.
A concept of a geomagnetic field emulator has also been included in the hardware-in-theloop
operating system. The evaluation of those aspects of the system and the conclusion are
presented together with recommendations. / AFRIKAANSE OPSOMMING: 'n multiprosesseerder Hardeware in die lus bedryfstelsel is ontwikkel vir 'n Geintegreerde
Toets Stelsel (ITS) en poog om die ITS te implementeer as 'n ruimte emulasie stelsel. Die
tesis behels die studie van sateliet wentelbane, Kepler wentelbaan elemente, geomagnetiese
velde en kommunikasie protokolle tussen die prosesseerders.
Die stelsel struktuur betaal uit 'n wentelbaan propageerder, 'n kern bedryfstelsel en 'n studie
van satelliet instrumentasie. As 'n deel van die implementering van die wentelbaan
propageerder is die halveer algoritme, Newton-Raphson algoritme en die ware oplossing as
numeriese oplossings ondersoek. Die kommunikasie protokol is getoets en foute ondersoek
en word bespreek.
'n konsep vir 'n Geomagnetiese veld emulasie word die hardeware in die lus stelsel ingesluit.
Die stelsel word ge-ewalueer en die gevolgtrekkings en aanbevelings gemaak.
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Scheduling program based on the theory of constraintsMalherbe, Johannes Louw 03 1900 (has links)
Thesis (MEng)--Stellenbosch University, 2003. / ENGLISH ABSTRACT: The goal of this thesis is to provide a stepping-stone for the design and development of a software
package that implements the Goal System Algorithm, based on the Theory of Constraints (TOC).
This includes the complete description and explanation of the Goal System Algorithm (GS), as
well as the partial implementation of this algorithm using Microsoft Access as a Database
Management System (DBMS) and Microsoft Visual C++ as programming language. The main
development effort was put into the development of a scheduling algorithm and the
implementation of a data structure that lies at the core of this algorithm.
The reason for the development of such a package is that it will aid a production manager,
working in a small to medium size job-shop, in generating a schedule for production that
will increase throughput, while simultaneously reducing both inventory and operating
expense thereby generating profits and cash flow.
With regard to this thesis and the overall project goal the following have been achieved.
1. The complete project has been researched, scoped and each step has been explained.
2. The complete program structure has been defined and broken into two separate modules;
the Data Mining and Conversion Module and the TOC Scheduling Algorithm.
3. The database containing all the MRP data necessary for scheduling has been designed
and implemented using a MS Access database with an ODBC connection. An ODBC
connection to the database was used so that a smooth transmission to other database
management systems can be made.
4. The TOC Scheduling Algorithm has been developed and the following have been
implemented:
• A basic user interface has been created for the insertion of all the user input and to
display the constraint schedule.
• A data structure called a linked list has been developed and used to store the
scheduling data in memory.
• The complete GS algorithm had been researched and explained.
• The GS algorithm has been and implemented and tested up to the point where it
schedules the constraint.
• The pseudo code for the part of the GS algorithm that was not implemented has been
documented and included in this report.
More development needs to be done and a proper Graphical User Interface must also be created
to complete this project, but after completion a Toe software package will exist that is
completely unique in South Africa and the market potential for this package will be considerable. / AFRIKAANSE OPSOMMING: Die doel van hierdie tesis is om die grondslag te skep vir die ontwerp en ontwikkeling van 'n
sagteware pakket wat Goldratt se Doel Sisteem Algoritme, gebasseer op die 'Theory of
Constraints', implementeer. Dit sluit die gedetaileerde beskrywing van die Doel Sisteem
Algoritme in en 'n gedeeltelike implementasie van die algortime, deur gebruik te maak van 'n
Microsoft Access databasis as databasis bestuur sisteem en Microsoft Visual C++ as 'n
programerings taal. Die hoof klem is gelê op die ontwikkeling van die skedulerings algortime en
die implementasie van die strukture wat deel van die kern uitmaak van die algoritme.
Die hoof rede vir die ontwikkeling van so 'n pakket is sodat dit 'n produksie bestuurder van
'n klein to medium grootte vervaardigings besigheid sal help om 'n skedule vir produksie
the genereer wat die vloer se deurset sal verhoog, terwyl dit voorraad en operasionele kostes
sal verlaag. Met ander woorde dit sal die besigheid help om meer geld te maak huidiglik en
in die toekoms.
Met betrekking tot die tesis en die algehele projek doel is die volgende bereik:
1. Die hele projek is nagevors, uit een gesit en verduidelik.
2. Die hele program struktuur is gedefinieer en opgebreek in twee aparte modules; nl. die
'Data Mining and Conversion Module' en die 'TOC Scheduling Algorithm'.
3. Die databasis wat al die nodige MRP inligting bevat wat benodig word vir skedulering is
ontwerp en geimplementeer deur gebruil te maak van 'n MS Access databasis met 'n
ODBC konneksie. Daar is van 'n ODBC konneksie gebruik gemaak sodat as die nodig
is, daar sonder enige moeite na ander databasis bestuurs sisteme oorgeskakel kan word.
4. Die 'TOC Scheduling Algorithm' is onwikkel en die volgende is geimplementeer.
• A basisse gebruikers vlak is ontwikkel sodat al die nodig invoer data in die program
ingevoer kan word.
• 'n Geskakelde lys is ontwikkel en gebruik as die data struktuur om al die
skedulerings informasie in geheue te stoor.
• Die Doel Sisteem algorimte is in sy geheel verduidelik en gedokumenteer.
Die Doel Sisteem algoritme is geïmplementeer tot op die punt waar dit die primêre
bottelnek skeduleer.
• Die pseudo kode vir die deel van die GS algoritme wat nie geimplementeer is nie is
uitgelê in ingesluit as deel van die verslag.
Verdere ontwikkeling word nog benodig en 'n beter gebruikers vlak moet nog geskep word om
die projek te finaal afte handel, maar na dit gedoen is sal daar 'n TOe skedulering pakket bestaan
wat heeltemal uniek is tot Suid-Afrika en 'n groot mark potensiaal sal hê.
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'n Ondersoek na die geskiktheid van 'n datavloeiverwerker as 'n herstruktureerbare spesiale verwerkerLoubser, Nicolas Johan 11 1900 (has links)
Thesis (MEng.) -- Stellenbosch Universiteit, 1984. / AFRIKAANSE OPSOMMING: Hierdie tesis behels 'n ondersoek na die geskiktheid van 'n
datavloei-verwerker om as 'n herstruktureerbare spesiale verwerker
te dien.
Die werking van 'n datavloei-verwerkermodel word aan die hand
van datavloeikonsepte verduidelik. Die tekortkominge van die
model, naamlik die gebrek aan datastruktuur-hanterings,
toevoer/afvoer en hertoelatingsmeganismes wor-d uitgelig en
moontlike oplos~ings word gege••
'n Semodifiseerde datavloei-model, wat beide struktuurhantering
en toevoer/afvoermeganismes insluit, word voorgestel.
Hertoelating word met behulp van 'n datapakketbenamingsmetode
bewerkstellig. Om die programmeerbaarheid en
die herstruktureerbaarheid van die model te ondersoek, is
besluit om 'n datavloei-verwerker te simuleer.
Die model is met behulp van die hoevlaktaal PASCAL, en bedryfstelselroepe
op die VAX 11/780 rekenaar gesimuleer. ParallelIe
verwerkingskonsepte in beide programmatuur en argitektuur
word gedemonstreer.
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Parallel algorithms for electromagnetic moment method formulationsDavidson, David Bruce 12 1900 (has links)
Thesis (PhD) -- Stellenbosch University, 1991. / ENGLISH ABSTRACT: This dissertation investigates the moment method solution of electromagnetic
radiation and scattering problems using parallel computers. In particular,
electromagnetically large problems with arbitrary geometries are considered.
Such problems require a large number of unknowns to obtain adequate approximate
solutions, and make great computational demands. This dissertation
considers in detail the efficient exploitation of the potential offered by
parallel computers for solving such problems, and in particular the class of
local memory Multiple Instruction, Multiple Data systems.
A brief history of parallel computing is presented. Methods for quantifying
the efficiency of parallel algorithms are reviewed. The use of pseudo-code
for documenting algorithms is discussed and a pseudo-code notation is defined
that is used in later chapters.
A new parallel conjugate gradient algorithm, suitable for the solution
of general systems of linear equations with complex values, is presented.
A method is described to handle efficiently the Hermitian transpose of the
matrix required by the algorithm. Careful attention is paid to the theoretical
analysis of the algorithm's parallel properties (in particular, speed-up and
efficiency). Pseudo-code is presented for the algorithms. Timing results for a
moment method code, running on a transputer array and using this conjugate
gradient solver, are presented and compared to the theoretical predictions.
A parallel LU algorithm is described and documented in pseudo-code. A
new graphical description of the algorithm is presented that simplifies the
identification of the parallelism and the analysis of the algorithm. The use
of formal methods for extracting parallelism via the use of invariants is presented
and new examples given. The speed-up and efficiency of the algorithm
are analyzed theoretically, using new methods that are simpler than those described
in the literature. Techniques for optimizing the efficiency of parallel
algorithms are introduced, and illustrated with pseudo-code. New parallel
forward and backward substitution algorithms using the data distribution
required for the parallel LV algorithm are described, and documented with
pseudo-code. Results obtained with a Occam 2 moment method code running
on a transputer array using these parallel LU solver and substitution
algorithms are presented and compared with the theoretical predictions.
PARNEC, a new Occam 2 implementation of the thin-wire core of NEC2,
is discussed. The basic 'theory of NEC2 is reviewed. Problems with early attempts
at combining Occam and FORTRAN are reported. Methodologies
for re-coding an old code written in an unstructured language in a. modern
structured language are discussed. Methods of parallelizing the matrix generation
are discussed. The accuracy of large moment method formulations
is investigated, as is the effect of machine precision on the solutions. The use of the biconjugate gradient method to accelerate convergence is briefly
considered and rejected. The increased size of problem that can be handled
by PARNEC, running on a transputer array, is demonstrated.
Conclusions are dra.wn regarding the contributions of this dissertation to
the development of efficient parallel electromagnetic moment method algorithms. / AFRIKAANSE OPSOMMING: Hierdie proefskrif ondersoek die momentmetode oplossing van elektromagnetiese
straling- en strooiingprobleme d.m.v. multiverwerkers. In besonder,
elektromagneties groot probleme met arbitrere geometriee word beskou.
Sulke probleme vereis 'n groot aantal onbekendes om 'n voldoende benaderde
oplossing te kry, en stel groot berekenings vereistes. Hierdie proefskrif beskou
in detail die doeltreffende benutting van die potensiaal wat multiverwerkers
vir sulke problem hied, in besonder die klas van lokale geheue Veelvoudige
Instruksie, Veelvoudige Data stelsels.
'n Kort geskiedenis van multiverwerkers word gegee. Metodes vir die
kwantifisering van die effektiwiteit van multiverwerkers word hersien. Die
. gebruik van pseudokode vir die dokumentering van algoritmes word bespreek
en 'n pseudokode notasie word gedefinieer wat gebruik word in latere hoofstukke.
'n Nuwe parallelle toegevoegde helling-algoritme wat geskik is vir die
oplossing van algemene stelsels van lineere vergelykings word aangebied. 'n
Metode word beskryf om op 'n doeltreffende wyse die Hermitiese transponent
van die matriks, wat deur die algoritme benodig word, te hanteer.
Sorgvuldige aandag word aan die teoretiese analise van die paralleleienskappe
van die algoritme gegee (in die besonder, versnelling en doeltreffendheid).
Pseudokode word aangebied vir die algoritmes. Resultate vir die looptyd
van 'n momentmetode program, wat op 'n transputerskikking loop, word
gegee en vergelyk met die teoretiese voorspellings.
'n Parallelle L U algoritme word beskryf en gedokumenteer in pseudokode.
'n Nuwe grafiese beskrywing van die algoritme, wat die identifikasie van parallelisme
en die analise van die algoritme vergemaklik, word gegee. Die gebruik
van formele metodes vir die onttrekking van parallelisme d.m.v. invariante
word getoon en nuwe voorbeelde word gegee. Die versnelling en doeltreffendheid
van die algoritme word teoreties geanaliseer, d.m.v. nuwe metodes wat
eenvoudiger is as die wat in die literatuur beskryf word. Tegnieke vir die optimering
van die doeltreffendheid van parallelle algoritmes word ingevoer, en
gelllustreer met pseudokode. Nuwe parallelle voor- en truwaarts-substitusie
algoritmes wat die data verspreiding van die parallelle LU algoritme gebruik
word beskryf, en gedokumenteer met pseudokode. Resultate verkry met 'n
Occam 2 momentmetode program wat op 'n transputerskikking loop en die
parallelle L U en substit'usie algoritmes gebruik, word gegee en vergelyk met
teoretiese voorspellings.
PARNEC, 'n nuwe Occam 2 implementering van die dun-draad kern van
NEC2, word bespreek. Die basiese teorie van NEC2 word opgesom. Verslag
word gedoen oor probleme met vroee pogings orh Occam en FORTRAN
te kombineer. Metodes om 'n ou program, geskryf in 'n ongestruktureerde taal, in 'n moderne gestruktureerde taal te herskryf word bespreek. Metodes
om die matriksopwekking te paralleliseer word bespreek. Die akkuraatheid
van groot momentmetode formulerings word ondersoek, asook die effek van
masjienpresisie op die oplossings. Die gebruik van die dubbeltoegevoegde
helling-metode om konvergensie te versnel word kortliks beskou en verwerp.
Die vergrote probleemgrootte, wat met PARNEC op- 'n transputerskikking
uitgevoer kan word, word gedemonstreer.
Gevolgtrekkings word gemaak rakende die bydraes van hierdie proefskrif
tot die ontwikkeling van doeltreffende parallelle elektromagnetiese momentmetode
algoritmes.
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Simulation procedure for marker and camera placementVan der Merwe, Andre 12 1900 (has links)
Thesis (MScEng) -- Stellenbosch University, 2003. / INTRODUCTION: The Medical Radiation department at iThemba LABS provides proton beam therapy facilities for irradiation of intracranial, head and neck lesions. Proton radiation
treatment offers a number of advantages over alternative radiation therapy modal-
ities. The most significant advantage is the ability to localize the dose to the lesion
or target volume [16]. Lesions are located by means of medical imaging processes,
such as Computer Tomography (CT) or Magnetic Resonance Imaging (MRI) scans.
Patient treatment commences at the existing treatment facility of iThemba LABS.
The patient positioning system that is currently in use at this facility was designed
for only one horizontal beam delivery system and a limited number of treatment
positions. The possibility of acquiring an additional beam delivery system and im-
proving the utilization of the system resulted in plans to expand the current proton
therapy capabilities. These plans resulted in the development of a new treatment
vault, complete with a new patient positioning system. The new vault will cater
for two beam delivery systems and expand current treatment positions.
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Finite element analysis of a wing type structure with experimental verification of results.Baumgartner, Edward Michael Ernst 06 1900 (has links)
Thesis (MScEng) -- Stellenbosch University, 1976. / pt. A. Theory and computer program -- pt. B. Experimental. / INTRODUCTION: The advent of the high speed computer has revolutionized structural
design in all spheres of Engineering. Up till then structural stress
analysis was limited to over-simplification of the structure in question to comply with derived classical mathematical solutions.
In practice however the picture is very different, the structure
usually being complex and highly redundant in nature. The techniques
involving Energy Methods to solve such structures have been known for
a long time. However they required weeks of hand calculations to
solve only a small number of redundancies in a structure. Neville Shute
mentions this in his book Slide Rule.
The development of Matrix algebra and the finite element method has made
it possible to analyse, say, a complete aircraft structure in a matter
of days. using a large capacity high speed computer~
Experimental results have shown that finite element stress analysis comes
much closer to reality than the dated classical methods.
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