Computational Statics and Dynamics: An Introduction Based on the Finite Element Method

723 Pages·2023·19.27 MB·English

by  Andreas Öchsner

Andreas Öchsner
Computational
Statics and
Dynamics
An Introduction Based on the Finite
Element Method
Third Edition
Computational Statics and Dynamics
Andreas Öchsner
Computational Statics
and Dynamics
An Introduction Based on the Finite Element
Method
Third Edition
AndreasÖchsner
EsslingenUniversityofAppliedSciences
EsslingenamNeckar,Baden-Württemberg,
Germany
ISBN 978-3-031-09672-3 ISBN 978-3-031-09673-0 (eBook)
https://doi.org/10.1007/978-3-031-09673-0
1stedition:©SpringerScience+BusinessMediaSingapore2016
2ndedition:©SpringerNatureSingaporePteLtd.2020
3rdedition:©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringer
NatureSwitzerlandAG2023
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DerVorteilderKlugheit bestehtdarin,
dassmansichdummstellenkann.Das
Gegenteilistschonschwieriger.
KurtTucholsky(1890–1935)
Preface to the Third Edition
The pedagogical methodology proposed in the first and second edition has been
wellacceptedbystudentsandthescientificcommunity.Thethirdeditionhasbeen
extended by approximately 250 pages compared to the first and by approximately
100pagescomparedtothesecondedition.Manyadditionalexamplestopracticethe
finiteelementapproachtoengineeringproblemshavebeenincluded.Inadditionto
manysimple(i.e.,handcalculation)examples,aconsiderablenumberofnumerical
examples, i.e., examples which should be solved with the help of any computer
algebra system, have been included. In the appendix, the section on the triangular
element formulation has been extended by including a theory on classical plate
elements. Last but not least, the entire content and the graphical illustrations have
beenthoroughlyrevisedandupdated.
Esslingen,Germany AndreasÖchsner
March2022
vii
Preface to the Second Edition
Thepedagogicalmethodologyproposedinthefirsteditionhasbeenwellaccepted
bystudentsandthescientificcommunity.Thesecondeditionhasbeenextendedby
approximately 150 pages. Many additional examples to practice the finite element
approach to engineering problems and a new chapter on shear deformable plate
elementshavebeenincluded.Furthermore,theweightedresidualmethodhasbeen
introduced and consistently applied to allow illustrating the same method for all
elementtypes.Intheappendix,anewsectiononthetriangularelementformulation
hasbeenincluded.Lastbutnotleast,theentirecontentandthegraphicalillustrations
havebeenthoroughlyrevisedandupdated.
Esslingen,Germany AndreasÖchsner
October2019
ix
Preface to the First Edition
This book results from the core course ‘Computational Statics and Dynamics’
(6522ENG) held at Griffith University, Australia, in the scope of the ‘Bachelor of
Engineering with Honours in Mechanical Engineering’ degree program. This 13-
weekcoursecomprisesthreehoursoflecturesandtwohoursoftutorialsperweek.
Anadditionallabcomponentbasedonacommercialfiniteelementprogramisnot
covered in this textbook. This course is based on the finite element method and
locatedinthethirdyearofthestudyprogram.Itreliesheavilyonthefundamental
knowledgeofthefirstyearsofengineeringeducation,i.e.highermathematics,mate-
rialsscience,appliedmechanics,design,andprogrammingskills.Thisisthereason
whymanystudentsfindthistopicdifficulttomasterandthistextbookshouldprovide
someguidanceforsuccessinthiscourse.
All derivations in the following chapters follow a common approach: First the
threefundamentalequationsofcontinuummechanics,i.e.,thekinematicsequation,
theconstitutiveequation,andtheequilibriumequation,arecombinedtoconstructthe
partialdifferentialequation.Subsequently,theweightedresidualmethod,auniversal
approachtoderiveanyoftheclassicalapproximationmethods,isappliedtoderive
theprincipalfiniteelementequationforeachelementtype.
Chapter 1 illustrates the finite element method in the context of engineering
practice and academic education. Chapter 2 covers the simplest one-dimensional
elementtype,i.e.therod/barelement.First,thiselementtypeisconsideredinpure
one-dimensional structures and then, the case of plane truss structures is covered.
Chapter 3 covers the simplest one-dimensional beam formulation according to
Euler-Bernoulli. This element is also generalized by superposition with a rod
element (so-called generalized beam element) and its arrangement in plane frame
structuresistreated.Chapter4introducesahigherbeambendingtheoryaccordingto
Timoshenko.Thistheoryconsidersthecontributionoftheshearforceonthedefor-
mation.Chapter5introducestwo-dimensionalplaneelasticityelementsfortheplane
stressandplanestrainstate.Chapter6coversclassicalplatebendingelementswhich
can be seen as the two-dimensional generalization of Euler-Bernoulli beams.
Chapter 7 treats three-dimensional solids on the example of hexaeder elements.
Chapters8and9brieflyintroducethetopicoftransientanalysis.
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xii PrefacetotheFirstEdition
Inordertodeepentheunderstandingofthederivedequationsandtheories,each
technicalchaptercollectsatitsendsupplementaryproblems.Thesesupplementary
problemsstartwithfundamentalknowledgequestionsonthetheoryofthechapterand
arefollowedbycalculationproblems.Intotalover80ofsuchadditionalcalculation
problemsareprovidedandashortsolutionforeachproblemisincludedinthisbook.
Itshouldbenotedthattheseshortsolutionscontainmajorstepsforthesolutionof
the problem and not only, for example, a numerical value for the final result. This
should ensure that students are able to successfully master these problems. I hope
thatstudentsfindthisbookausefulcomplementtomanyclassicaltextbooks.Ilook
forwardtoreceivetheircommentsandsuggestions.
January2016 AndreasÖchsner
GriffithUniversity
GoldCoast,Australia
Acknowledgements
It is important to highlight the contribution of many undergraduate and postgrad-
uatestudentswhichhelpedtofinalizethecontentofthisbook.Theirquestionsand
commentsduringdifferentlecturesandtheirworkinthescopeoffinalyearprojects
helpedtocompilethisbook.ThehelpandsupportofmytutorsandPh.D.students
LeonhardHitzlerandZiaJavanbakhtisalsogratefullyacknowledged.Furthermore,
I would like to express my sincere appreciation to the Springer-Verlag, especially
to Dr. Christoph Baumann, for giving me the opportunity to realize this book. A
professionalpublishingcompanywiththerightunderstandingwastheprerequisite
tocompletethiscomprehensiveproject.Finally,Iwouldliketothankmyfamilyfor
theunderstandingandpatienceduringthepreparationofthisbook.Iwouldliketo
especiallythankMarcoforhiscorrectionsandsuggestions.
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