Rectangular shell elements based on the absolute nodal coordinate formulation

170 Pages·2015·1.6 MB·English

Rectangular shell elements based
on the absolute nodal coordinate
formulation
Department of Engineering
Per Hyldahl
PhD Thesis
Rectangular shell elements based
on the absolute nodal coordinate
formulation
PhD Dissertation
Per Hyldahl
July 2015

AU
AARHUS
UNIVERSITY
DEPARTMENT OF ENGINEERING
ISBN: 978-87-7507-354-2
DOI: 10.7146/aul.97.90
Thesissubmitted: July31,2015
PhDSupervisor: SeniorAssociateProfessorPhDOleBalling
DepartmentofEngineering,AarhusUniversity
Denmark
PhDCommittee: ProfessorPhDJoséLuisEscalonaFranco
Department of Mechanical and Materials Engineering,
UniversityofSeville
Spain
ProfessorPhDErikLund
Department of Mechanical and Manufacturing Engi-
neering(M-Tech),AalborgUniversity
Denmark
ProfessorDr. techn. HenrikMyhreJensen
DepartmentofEngineering,AarhusUniversity
Denmark
PhDSeries: FacultyofScience&Technology,
AarhusUniversity
Publishedby:
RiverPublishers
NielsJernesVej10
9220Aalborg
Denmark
http://riverpublishers.com/
c CopyrightbyPerHyldahl
(cid:13)
PrintedinDenmarkbySUN-TRYK,2015

Abstract
This thesis concerns the development of tools that are useful for designing
machine systems and components in an virtual environment using flexi-
ble multibody dynamics. Initially, flexible multibody dynamics is briefly
reviewed to explain available formalisms and possible applications of this
method. Subsequently, attention is turned towards the analysis of structures
that undergo large deformations and rotations using shell finite elements
basedontheabsolutenodalcoordinateformulation,ANCF.Thistopicisthe
focusfortheremainderofthethesis.
The thesis is divided into three main parts. The first part acts as a gen-
eralintroductiontoANCFbasedshellfiniteelementsandsumsupavailable
elements found in the research literature. In the end, a new ANCF element
developed during this PhD project is presented which gives enhanced mod-
elingcapabilitiesofproblemsincludinge.g. movingboundaryconditions.
Thesecondpartconcernstheperformanceandbehaviorofacertainclass
of ANCF shell elements that are developed for analysis of thin shell struc-
tures. Thisincludesdiscussionsondifferencesconcerningtheirkinematicde-
scriptionsanddisclosureofcertainissuesregardingtheirperformance. Those
being sensitivity to irregular mesh, pour representation of curved structures
andloaddependentconvergencewhenanalyzingcurvedstructures.
ThefinalpartconcernsthedevelopmentofanewversatileANCFshellel-
ement. Thiselementisdistinguishedbybeingabletodescribeboththinand
thick curved structures. This part contains a thorough derivation of its kine-
matics and stiffness description, as well as numerical examples to demon-
strateitsperformance. However,thispartofthestudyisnotyetcomplete.
Finally, the findings of this PhD project are summed up in a conclusion
andpossibilitiesforfurtherstudiesandperspectivesareoutlined.
v

Resumé
Denne afhandling omhandler udviklingen af værktøjer, som er nyttige til at
designe maskiner og maskindele i et virtuelt miljø vha. fleksibel flerlegeme-
dynamik. Indledningsvist gives der en kort gennemgang af den fleksible
flerlegeme-dynamik, for at give et overblik over metoden og dens mulige
anvendelser. Dernæst flyttes opmærksomheden over på analyse af struk-
turersomudsættesforstoredeformationerogrotationervha. endeligeskal-
elementer(eng: shellfiniteelements)baseretpåabsolutteknudekoordinater
(eng: absolute nodal coordinate formulation, ANCF). Dette emne vil være
fokusirestenafafhandlingen.
Afhandlingen er inddelt i 3 dele. Den første del giver en general in-
troduktion til ANCF skal-elementer, og opsummerer de forskellige element-
klassersomkanfindesilitteraturen. Modslutningenintroduceresderetnyt
ANCFskal-element,somerudvikletunderdetteph.d.-projekt. Detteelement
muliggørforbedretmodelleringafproblemermedmobilerandbetingelser.
Andendelomhandlereffektivitetenogegenskabernehosensærligklasse
af ANCF skal-elementer, som er udviklet specielt til analyse af tynde skal-
strukturer. Heri diskuteres der forskelle i deres kinematiske beskrivelser og
der fremhæves nogle uheldige egenskaber vedrørende deres adfærd. Det
væresigfølsomhedoverforuensartedeelementstørrelser,ringebeskrivelseaf
kurvedestruktureroglastafhængigkonvergensiforbindelsemedanalyseaf
kurvedestrukturer.
Den sidste del omhandler udviklingen af et nyt alsidigt ANCF skal-ele-
ment. Dette element udmærker sig ved at være anvendeligt til at beskrive
bådetyndeogtykkeskalstrukturer. Dennedelindeholderengrundigudled-
ning af elementets kinematik og stivhed, samt numeriske eksempler som
demonstrerer dets effektivitet. Denne del af studiet er dog ikke færdiggjort
endnu.
Slutteligt opsummeres resultaterne af ph.d.-studiet og der nævnes mu-
lighederforfremtidigearbejderogperspektiver.
vii

Preface
This thesis is submitted to the Graduate School of Science and Tech-
nology (GSST) at Aarhus University in a partial fulfillment of the re-
quirementsforthedegreeofDoctorofPhilosophy. Theworkhasbeen
carried out during the period from August 2011 to July 2015 at the
Department of Engineering at Aarhus University.
Thethesisconcernsinvestigationswithinandfurtherdevelopment
of rectangular shell finite elements based on the absolute nodal coor-
dinate formulation. The thesis is written as a monograph based on
published research papers, and the papers are attached in their origi-
nal form as appendices.
It has not been possible to complete this thesis without the help
and support of several people, to whom I am deeply grateful. I would
like to thank my supervisor Senior Associate Professor Ole Balling for
considering me for the PhD project, and for valuable discussions and
guidance during the project. Furthermore, I owe many thanks to Pro-
fessorAkiMikkola,LappeenrantaUniversityofTechnology,andAsso-
ciateProfessorHiroyukiSugiyama, UniversityofIowa, forhostingme
during visits at their respective research groups. In that connection,
special thanks go to the members of their research groups for making
my stays pleasant and enjoyable. I would also like to thank Adminis-
tratorMetteStigHansenatAarhusUniversityforalwaysbeinghelpful
withpracticalmattersandforvaluableassistancewithproofreadingof
this thesis.
My fellow PhD students at the Mechanical Engineering section,
Department of Engineering Alex Møberg, Mads Krabbe, Søren Stef-
fensen, Kennet Olesen and Jens Wind, I also owe great thanks for pro-
viding a great working environment and good company. Especially
Jens Wind deserves special acknowledgment, as he has been a great
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