Micropolar Theory of Shells and Plates

187 Pages·2021·2.675 MB·English

by  Sergey A. Ambartsumian

Foundations of Engineering Mechanics
Sergey A. Ambartsumian (posthumous)
Micropolar
Theory
of Shells and
Plates
Foundations of Engineering Mechanics
SeriesEditors
VladimirI.Babitsky,SchoolofMechanical,ElectricalandManufacturing
Engineering,LoughboroughUniversity,Loughborough,Leicestershire,UK
JensWittenburg,Karlsruhe,Germany
Moreinformationaboutthisseriesat http://www.springer.com/series/3582
Sergey A. Ambartsumian (posthumous)
Micropolar Theory of Shells
and Plates
SergeyA.Ambartsumian(posthumous)
Yerevan,Armenia
ISSN1612-1384 ISSN1860-6237 (electronic)
FoundationsofEngineeringMechanics
ISBN978-3-030-71325-6 ISBN978-3-030-71326-3 (eBook)
https://doi.org/10.1007/978-3-030-71326-3
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DedicatedtomylatewifeSedawhowas,and
remains,aconstantsourceofsupportand
inspiration inmylife,mywork,andmy
writings.
Preface
Thisbookfocusesontheappliedtheoryofshellsandplatesbasedontheunderlying
assumptionsandequationsofasymmetricalelasticitytheory.
This is not a new problem, but it has taken on a different meaning in recent
years due to the extensive use of polycrystalline and composite materials in the
micromechanicsofthinbodies.
The theories proposed in this book represent intermediate links in a long chain
of various theories on shells and plates. They have been constructed, on the one
hand, based on theequations of theclassicaltheory of elasticity,and on theother,
on equations that have thus far remained ‘untouched’ in their application to the
moleculartheoriesofsoliddeformablemedia.
This book has been written in one sitting, based on the results of the research
undertakenbyme.Unfortunately,Iwasunabletocollect,analyze,andsummarize
alltheknownresultsinthenamedareaofthetheoryofshellsandplates.Thisgaphas
beenpartiallyfilledbyabriefliteraturereviewthatisincludedwiththeintroduction.
The book contains certain unspecified and insufficiently rigorous provisions. I
hopethattheywillbecompletedatalaterdatebyeithermyselforbyreaderswho
areinterestedintheproblemslaidoutthroughout.IfinditonlyfittingtoquoteOliver
Heaviside,whosaid,‘WillIgiveupmylunchjustbecauseIdon’tfullyunderstand
digestion?’
Thebookconsistsofsixchapters.Thefirstchapterisareviewoftheessentialdata
onthenon-symmetrictheoryofelasticity.Thesecondandthirdchaptersaredevoted
tovarioustheoriesofplatebendingandsolutionstosomebasicproblems.Chapter
four refers to membrane or, so-called, momentary shell theory. Chapter five deals
withthetheoryofveryshallowshells.Finally,chaptersixpresentsthegeometryof
thenonlineartheoryofplatesandthetheoryofveryshallowshells.
Thebookisintendedforresearchers,postgraduatestudentsandengineersinter-
estedintheproblemsofmechanicsofdeformablebodies,inthetheoryofshellsas
wellasplatetheoryanditsapplicationsinmicromechanics.
The book was initially reviewed by Prof. M. V. Belubekyan, who made a few
valuablesuggestions,whichIgladlyaccepted.
vii
viii Preface
I consider it my duty to express my deep gratitude to I. R. Arutyunyan and
L.V.Melikyan,whoprovidedgreatassistanceinpreparingthebookforpublication.
Copenhagen,Denmark/ SergeyA.Ambartsumian(posthumous)
Yerevan,Armenia
March1999
Preface to the Second Edition
The main reason for publishing a new edition of this book is that the first edition
wasdedicatedtosomeoneIcaredeeplyabout,andduetoanoversightonbothmy
side and that of the publishers, the first version was published with some (mainly
typographical)omissions.
Asinthepreviousedition,Idedicatethisbooktomylatewife,Seda,towhomI
oweadeptofgratitude.
I would like to add that due to the limited printing and circulation of the first
edition, the elements presented in this book have been largely absent from the
field of academia and global mechanics. Taking advantage of this, some uneth-
ical researchers, who previously openly stated (and wrote) that the problem of
constructingmodelsofmicropolarthinbeams,slabsandshellswasfirstdiscovered
byS.A.Ambartsumian,stoppedreferencingthisbookandotherrelevantpublica-
tionswrittenbymeandmyco-authors.Assuch,theygavethefalseimpressionthat
theythemselveswerepioneersinthisfieldofscience.
In the new edition of the book, we seek to correct the inaccuracies and irregu-
laritiesofthefirsteditionandtoaddtheresultsofnewfindingsthatmyco-authors
and I discovered through our subsequent research. We have avoided making any
fundamentalchangestothetext.
Followingthepublicationofthisbookandotherarticles[1–5],M.V.Belubekyan,
andIwroteanadditionalbooktitled‘AppliedMicropolarTheoryofElasticShells’
[1].Thisbookismainlybasedonourpreviousworksanddoesnotinanywaylimit
thepossibilityofintroducingalternativetheoriesofmicropolarplatesandshells.
ProfessorM.V.Belubekyan’scontributiontothepublicationofthissecondedition
wassignificantandIwouldliketoexpressmysincerethankstohim.
I am also very grateful to my colleagues at the Institute of Mechanics of the
NationalAcademyofSciencesofArmeniaG.Z.GevorkyanandJ.A.Avdalyanfor
theirhelpinpreparingthebookforpublication.
Yerevan,Armenia SergeyA.Ambartsumian(posthumous)
March2013
ix
x PrefacetotheSecondEdition
References
1. Ambartsumian,S.A.&Belubekyan,M.V.(2010).Appliedmicropolartheoryofelasticshells.
Yerevan:“Gitutyun”NASofArmenia,136p.
2. Ambartsumian, S. A. & Belubekyan, M. V. (2008). Oscillation of elastic plates with the
accountofinternalrotation.YSUAS.Architectureandconstruction.Vol.3.pp.25–29.
3. Ambartsumian,S.A.&Belubekyan,M.V.(2009).Theproblemofaxisymmetricvibrations
ofamicropolarcircularcylindricalshell.Izv.NASofArmenia.Mechanics.Vol.62.No.3.
pp.11–16.
4. Ambartsumian,S.A.&Belubekyan,M.V.(2010).Onthemicropolartheoryofveryshallow
shells.Izv.NASofArmenia.Mechanics.Vol.63.No.3.pp.23–32.
5. Ambartsumian,S.A.&Belubekyan,M.V.(2012).Vibrationsofaveryshallowspherical
panelwiththeaccountofinternalrotation.BulletinoftheEngineeringAcademyofArmenia.
9(1),101–106.