Shell-like Structures: Advanced Theories and Applications PDF
Preview Shell-like Structures: Advanced Theories and Applications
CISM International Centre for Mechanical Sciences 572 Courses and Lectures Holm Altenbach Victor Eremeyev Editors Shell-like Structures Advanced Theories and Applications International Centre for Mechanical Sciences CISM International Centre for Mechanical Sciences Courses and Lectures Volume 572 Series editors The Rectors Friedrich Pfeiffer, Munich, Germany Franz G. Rammerstorfer, Vienna, Austria Elisabeth Guazzelli, Marseille, France The Secretary General Bernhard Schrefler, Padua, Italy Executive Editor Paolo Serafini, Udine, Italy Theseriespresentslecturenotes,monographs,editedworksandproceedingsinthe field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences. More information about this series at http://www.springer.com/series/76 Holm Altenbach Victor Eremeyev (cid:129) Editors Shell-like Structures Advanced Theories and Applications 123 Editors HolmAltenbach Victor Eremeyev Faculty of MechanicalEngineering Department ofMechanical Engineering Otto-von-Guericke-University Magdeburg andAvionics Magdeburg RzeszówUniversity ofTechnology Germany Podkarpacie,Rzeszów Poland ISSN 0254-1971 ISSN 2309-3706 (electronic) CISMInternational Centre for MechanicalSciences ISBN978-3-319-42275-6 ISBN978-3-319-42277-0 (eBook) DOI 10.1007/978-3-319-42277-0 LibraryofCongressControlNumber:2016945776 ©CISMInternationalCentreforMechanicalSciences2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland Preface Shell-like structures are widely used in engineering as basic structural elements. Such structures are also used in other branches of science as a model of analysis, e.g., in medicine, biology, nanotechnology, etc. New applications are primarily relatedtonewmaterials—forexample,insteadofsteelorconcrete,nowonehasto analyze laminates, foams, functionally graded materials, shape memory thin films, fullerenes, nanofilms, biological membranes, soft tissues, etc. The new trends in applications demand the improvements of the theoretical foundations of shell the- ory, since new effects must be taken into account. For example, in the case of small-size shell-like structures (thin films, multi-walled nanotubes), the surface effect plays an important role in the mechanical analysis of these structural ele- ments.Ontheotherhand,thetheoreticalachievementsmustbesupplementedwith the development of consistent numerical tool. The aim of the CISM course, Shell-like Structures—Advanced Theories and Applications, was to present together mathematical aspects of the theory of plates and shells, applications in civil, aerospace and mechanical engineering, as well as other areas. The focus of the course relates to the following problems: (cid:129) comprehensive review of the most popular theories of plates and shells; (cid:129) relation between 3D and 2D theories; (cid:129) presentationofrecentlydevelopednewrefinedplatesandshellstheoriessuchas for example, micropolar theory, or gradient-type theories; (cid:129) applications in modeling of complex structures (multi-folded, branching and/or self-intersecting shells, plates and shells made of foams, functionally graded materials, etc.); (cid:129) modeling of coupled effects in shells and plates related to electromagnetic and temperature fields, phase transitions, diffusion, etc.; (cid:129) applications in modeling of non-classical objects as thin- and nanofilms, nan- otubes, and nanoparticles, and biological membranes; (cid:129) presentation of actual numerical tools based on finite elements approach. v vi Preface (cid:129) During the course the following lectures were presented: (cid:129) Holm Altenbach: Thin-walled Structural Elements—Classification, Classical and Advanced Theories, New Applications; (cid:129) Victor Eremeyev: Mechanics and Thermodynamics of Micropolar Shells; (cid:129) Gennady Mikhasev: Non-Classical Problems on Localized Vibrations and Waves in Thin Shells; (cid:129) Paolo Podio-Guidugli: How to Deduce Structure Theories from 3D Elasticity; (cid:129) KaramSab:TheBending-GradientTheoryforHeterogeneousIn-PlanePeriodic Plates; (cid:129) Krzysztof Wisniewski: Selected Topics on Finite Elements for Finite Rotation Shells In this sense the course was an overview about the theories of plate and shells, the history, and some new developments. In the following chapters the basic material of thecourse was slightly changed. The chapter names are not always the same like the lecture names. Finally, the authors of these proceedings acknowledge Prof. Paolo Serafini and Mrs. Silvia Schilgerius from Springer-Austria for supporting the publication and last but not least, Mrs. Paola Agnola from the CISM Secretariat fulfilling all organizing duties. Magdeburg, Germany Holm Altenbach Rzeszów, Poland Victor Eremeyev Contents Thin-Walled Structural Elements: Classification, Classical and Advanced Theories, New Applications. . . . . . . . . . . . . . . 1 Holm Altenbach and Victor Eremeyev Basics of Mechanics of Micropolar Shells. . . . . . . . . . . . . . . . . . . . . . . 63 Victor Eremeyev and Holm Altenbach The Bending-Gradient Theory for Laminates and In-Plane Periodic Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 Arthur Lebée and Karam Sab Some Problems on Localized Vibrations and Waves in Thin Shells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Gennadi Mikhasev Six Lectures in the Mechanics of Elastic Structures . . . . . . . . . . . . . . . 211 Paolo Podio-Guidugli Selected Topics on Mixed/Enhanced Four-Node Shell Elements with Drilling Rotation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 K. Wisniewski and E. Turska vii Thin-Walled Structural Elements: Classification, Classical and Advanced Theories, New Applications HolmAltenbachandVictorEremeyev Abstract Thinstructureswereexistingfromtheancienttime.Fromobservationsof thenaturethepeopleunderstoodthatthinnermeanslighter,butstiffnessandstability problemsarose.Thiswasthestartingpointfortheelaborationoftheoriesanalyzing thesestructures.Atthattimeapplicationswerelimitedtocivilengineering.Atpresent theyareusedinaerospaceengineeringasbasicelements.Suchstructuresareapplied as a model of analysis in other branches too, e.g. mechanical engineering. With thenecessitytosubstituteclassicalmaterialbynew(advanced)materials—instead ofsteelorconcrete,nowlaminates,foams,nano-films,biologicalmembranes,etc. are used. The new trends in applications demand improvements of the theoretical foundationsoftheplateandshelltheories,sinceneweffects(forexample,transverse shear or surface effects) must be taken into account. This contribution is mainly anintroductiontotheCISM-CourseSHELL-LIKESTRUCTURES:ADVANCED THEORIESANDAPPLICATIONS. After some introduction to the history some examplesconcerningnewapplicationsarediscussed.Afterthatmaindirectionsin thetheoryofplatesandshellsarepresented.Finally,variousadvancedtheoriesare brieflyintroduced.Otheradvancedtheoriesarepresentedinthefollowingchapter. B H.Altenbach( ) ChairofEngineeringMechanics,FacultyofMechanicalEngineering, Otto-von-Guericke-UniversityMagdeburg,Magdeburg,Germany e-mail:[email protected] V.Eremeyev DepartmentofMechanicalEngineeringandAvionics, RzeszówUniversityofTechnology,Podkarpacie,Rzeszów,Poland e-mail:[email protected] V.Eremeyev SouthScientificCenterofRussianAcademyofScience,RostovonDon,Russia V.Eremeyev DepartmentofMathematics,MechanicsandComputerScience, SouthFederalUniversity,RostovonDon,Russia ©CISMInternationalCentreforMechanicalSciences2017 1 H.AltenbachandV.Eremeyev(eds.),Shell-likeStructures, CISMInternationalCentreforMechanicalSciences572, DOI10.1007/978-3-319-42277-0_1 2 H.AltenbachandV.Eremeyev Fig.1 First(simplest)beamtheory:aDanielBernoulli,bLeonhardEuler 1 Introduction:HistoricalRemarks Thestartingpointforthedevelopmentofanyplateorshellanalysiswasgivenbytwo mathematicians: Daniel Bernoulli1 and Leonhard Euler2 (Fig. 1). They presented a beam theory containing all necessary elements: kinematics, reaction to external loadings and equilibrium statements based on the balances of momentum and of momentofmomentum.Atthesametimetheyintroducetwocrucialitems – geometricallinearizationandkinematicalhypothesesand – independenceofforcesandmoments(botharethestressresultants)resultingin theindependenceoftheabovementionedbalanceequations.3 By this way the first engineering theory was formulated. This is an approximate theoryandapplicationboundsarenotclear.Butatthesametimetheresultingbeam equationorthesetofcoupledequationsallowsanalyticalsolutions. Anymechanicaltheoryisrelatedalsotosomeexperimentalinvestigations.Inthe caseofplatesandshellsthestudiesofErnstFlorensFriedrichChladni4(Fig.2)were 1∗January29(jul.)/February8(greg.)1700inGroningen,†March17,1782inBasel. 2∗April15,1707inBasel,†September18,1783inSt.Petersburg. 3ThiswasanalyzedbyCliffordAbmbroseTruesdellIII(∗February18,1919,†January14,2000) inTruesdell1964. 4∗November30,1756inWittenberg,†April3,1827Breslau.
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