Table Of ContentMATLAB 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
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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.
Description:This successful textbook explores the numerical implementation of Finite Element Analysis using the computer program MATLAB, which is very popular today in engineering and engineering education. The book contains a short tutorial on MATLAB as well as a systematic strategy for the treatment of finite
