Tensor algebra and tensor analysis for engineers : with applications to continuum mechanics PDF
Preview Tensor algebra and tensor analysis for engineers : with applications to continuum mechanics
Tensor Algebra and Tensor Analysis for Engineers Mathematical Engineering SeriesEditors: Prof.Dr.ClausHillermeier,Munich,Germany(volumeeditor) Prof.Dr.-Ing.Jo¨rgSchro¨der,Essen,Germany Prof.Dr.-Ing.BernhardWeigand,Stuttgart,Germany Forfurthervolumes: http://www.springer.com/series/8445 Mikhail Itskov Tensor Algebra and Tensor Analysis for Engineers With Applications to Continuum Mechanics 3rd Edition 123 Prof.Dr.-Ing.MikhailItskov DepartmentofContinuumMechanics RWTHAachenUniversity Eilfschornsteinstr.18 D52062Aachen Germany ISSN2192-4732 ISSN2192-4740(electronic) ISBN978-3-642-30878-9 ISBN978-3-642-30879-6(eBook) DOI10.1007/978-3-642-30879-6 SpringerHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2012945179 (cid:2)c Springer-VerlagBerlinHeidelberg2013 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer. PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations areliabletoprosecutionundertherespectiveCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Moim roditel(cid:2)m • Preface to the Third Edition This edition is enriched by new examples, problems, and solutions, in particular concerned with simple shear. I have also added an example with the derivation of constitutive relations and tangent moduli for hyperelastic materials with the isochoric-volumetric split of the strain energy function. Besides, Chap.2 has somenewfiguresillustratingsphericalcoordinates.Thesefigureshaveagainbeen preparedbyUweNavrath.IalsogratefullyacknowledgeKhieˆmNgocVuforcareful proofreading of the manuscript. At this opportunity, I would also like to thank the Springer-Verlag and in particular Jan-Philip Schmidt for the fast and friendly supportingettingthiseditionpublished. Aachen,Germany MikhailItskov vii • Preface to the Second Edition Thissecondeditionhasanumberofadditionalexamplesandexercises.Inresponse tocommentsandquestionsofstudentsusingthisbook,solutionsofmanyexercises have been improvedfor a better understanding.Some changes and enhancements are concerned with the treatment of skew-symmetric and rotation tensors in the firstchapter.Besides,thetextandformulaehavebeenthoroughlyreexaminedand improvedwherenecessary. Aachen,Germany MikhailItskov ix
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