MATLAB Guide to Finite Elements: An Interactive Approach

433 Pages·2007·2.13 MB·English

by  Peter I. Kattan

MATLAB Guide to Finite Elements

Peter I. Kattan
MATLAB Guide
to Finite Elements
An Interactive Approach
SecondEdition
With108Figuresand25Tables
PeterI.Kattan,PhD
P.O.BOX1392
Amman11118
Jordan
[email protected]
[email protected]
LibraryofCongressControlNumber:2007920902
ISBN-13 978-3-540-70697-7SpringerBerlinHeidelbergNewYork
Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis
concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,
reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublicationor
partsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,
initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violationsareliable
forprosecutionundertheGermanCopyrightLaw.
SpringerisapartofSpringerScience+BusinessMedia
springer.com
(cid:2)c Springer-VerlagBerlinHeidelberg2008
Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,
evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelaws
andregulationsandthereforefreeforgeneraluse.
Typesetting:IntegraSoftwareServicesPvt.Ltd.,Pondicherry,India
Coverdesign:ErichKirchner,Heidelberg
Printedonacid-freepaper SPIN:11301950 42/3100/Integra 5 4 3 2 1 0
DedicatedtoMyProfessor,GeorgeZ.Voyiadjis

Preface to the Second Edition
Soon after the first edition of this book was published at the end of 2002, it was
realized that a new edition of the book was needed. I received positive feedback
from my readers who requested that I provide additional finite elements in other
areaslikefluidflowandheattransfer.However,Ididnotwanttolengthenthebook
considerably.Therefore,Idecidedtoaddtwonewchaptersthusaddingnewmaterial
whilekeepingthesizeofthebookreasonable.
The second edition of the book continues with the same successful format that
characterizedthefirstedition–whichwassoldoutinlessthanfouryears.Icontinue
toemphasizetheimportantfeaturesofinteractivityofusingMATLAB1coupledwith
the simplicity and consistency of presentation of finite elements. One of the most
importantfeaturesalsoisbypassingtheuseofnumericalintegrationinfavorofexact
analytical integration with the use of the MATLAB Symbolic MathToolbox2.The
useofthistoolboxisemphasizedinChaps.12,13,14,and16.
Inthenewedition,twoimportantchangesareimmediatelynoted.First,Icorrected
the handful of typing errors that appeared in the first edition. Second, I added two
newchapters.Chap.16includesanothersolidthree-dimensionalelement(theeight-
nodedbrickelement)ingreatdetail.Thefinalchapter(Chap.17)providesareview
of the applications of finite elements in other areas like fluid flow, heat transfer,
geotechnical engineering, electro-magnetics, structural dynamics, plasticity, etc. In
this chapter, I show how the same consistent strategy that was followed in the first
sixteenchapterscanbeusedtowriteMATLABfunctionsintheseareasbyproviding
theMATLABcodeforaone-dimensionalfluidflowelement.
OneminordrawbackofthefirsteditionasIseeitistheabsenceofaconcluding
chapter. Therefore, I decided to remedy the situation by adding Chap. 17 as a real
concludingchaptertothebook.Itisclearthatthischapterisdifferentfromthefirst
sixteenchaptersandthusmaywellprovideawellwrittenconclusiontothebook.
ThesecondeditionstillcomeswithanaccompanyingCD-ROMthatcontainsthe
full set of M-files written specifically to be used with this book. These MATLAB
functions have been tested with version 7 of MATLAB and should work with any
1MATLABisaregisteredtrademarkofTheMathWorks,Inc.
2TheMATLABSymbolicMathToolboxisaregisteredtrademarkofTheMathWorks,Inc.
VIII PrefacetotheSecondEdition
laterversions.Inaddition,theCD-ROMcontainsacompletesolutionsmanualthat
includesdetailedsolutionstoalltheproblemsinthebook.Ifthereaderdoesnotwish
toconsultthesesolutions,thenabrieflistofanswersisprovidedinprintedformat
theendofthebook.
Iwouldliketothankmyfamilymembersfortheirhelpandcontinuedsupportwith-
outwhichthisbookwouldnothavebeenpossible.Iwouldalsoliketoacknowledge
thehelpoftheeditioratSpringer-Verlag(Dr.ThomasDitzinger)forhisassistancein
bringingthisbookoutinitspresentform.Finally,Iwouldliketothankmybrother,
Nicola,forpreparingmostofthelinedrawingsinbotheditions.Inthisedition,Iam
providingtwoemailaddressesformyreaderstocontactme([email protected]
and [email protected]).The old email address that appeared in the first edition was
cancelledin2004.
December2006 PeterI.Kattan
Preface to the First Edition
ThisisabookforpeoplewholovefiniteelementsandMATLAB3.Wewillusethe
popularcomputerpackageMATLABasamatrixcalculatorfordoingfiniteelement
analysis. Problems will be solved mainly using MATLAB to carry out the tedious
andlengthymatrixcalculationsinadditiontosomemanualmanipulationsespecially
whenapplyingtheboundaryconditions.Inparticularthestepsofthefiniteelement
methodareemphasizedinthisbook.Thereaderwillnotfindready-madeMATLAB
programsforuseasblackboxes.Insteadstep-by-stepsolutionsoffiniteelementprob-
lemsareexaminedindetailusingMATLAB.Problemsfromlinearelasticstructural
mechanicsareusedthroughoutthebook.Theemphasisisnotonmasscomputation
orprogramming,butratheronlearningthefiniteelementmethodcomputationsand
understanding of the underlying concepts. In addition to MATLAB, the MATLAB
SymbolicMathToolbox4isusedinChaps.12,13,and14.
Manytypesoffiniteelementsarestudiedinthisbookincludingthespringelement,
the bar element, two-dimensional and three-dimensional truss elements, plane and
spacebeamandframeelements,two-dimensionalelasticityelementsforplanestress
and plane strain problems, and one three-dimensional solid element. Each chapter
dealswithonlyonetypeofelement.Alsoeachchapterstartswithasummaryofthe
basic equations for the element followed by a number of examples demonstrating
the use of the element using the provided MATLAB functions. Special MATLAB
functionsforfiniteelementsareprovidedasM-filesontheaccompanyingCD-ROMto
beusedintheexamples.ThesefunctionshavebeentestedsuccessfullywithMATLAB
versions5.0,5.3,and6.1.Theyshouldworkwithotherlaterversions.Eachchapter
alsoendswithanumberofproblemstobeusedaspracticeforstudents.
Thisbookiswrittenprimarilyforstudentsstudyingfiniteelementanalysisforthe
firsttime.Itisintendedasasupplementarytexttobeusedwithamaintextbookfor
anintroductorycourseonthefiniteelementmethod.Sincethecomputationsoffinite
elements usually involve matrices and matrix manipulations, it is only natural that
studentsuseamatrix-basedsoftwarepackagelikeMATLABtodothecalculations.
3MATLABisaregisteredtrademarkofTheMathWorks,Inc.
4TheMATLABSymbolicMathToolboxisaregisteredtrademarkofTheMathWorks,Inc.