tensor analysis with applications in mechanics

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1、TensorAnalysiswithApplicationsinMechanicsTensorAnalysiswithApplicationsinMechanicsLeonidP.LebedevNationalUniversityofColombiaSouthernFederalUniversity,RussiaMichaelJ.CloudLawrenceTechnologicalUniversity,USAVictorA.EremeyevMartin-Luther-UniversityHalle-Wittenberg,GermanySouthernScientif

2、icCenterofRussianAcademyofScienceSouthernFederalUniversity,RussiaWorldScientificNEWJERSEY•LONDON•SINGAPORE•BEIJING•SHANGHAI•HONGKONG•TAIPEI•CHENNAIPublishedbyWorldScientificPublishingCo.Pte.Ltd.5TohTuckLink,Singapore596224USAoffice:27WarrenStreet,Suite401-402,Hackensack,NJ07601UKoffice

3、:57SheltonStreet,CoventGarden,LondonWC2H9HEBritishLibraryCataloguing-in-PublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary.TENSORANALYSISWITHAPPLICATIONSINMECHANICSCopyright©2010byWorldScientificPublishingCo.Pte.Ltd.Allrightsreserved.Thisbook,orpartsthereof,mayn

4、otbereproducedinanyformorbyanymeans,electronicormechanical,includingphotocopying,recordingoranyinformationstorageandretrievalsystemnowknownortobeinvented,withoutwrittenpermissionfromthePublisher.Forphotocopyingofmaterialinthisvolume,pleasepayacopyingfeethroughtheCopyrightClearanceCente

5、r,Inc.,222RosewoodDrive,Danvers,MA01923,USA.Inthiscasepermissiontophotocopyisnotrequiredfromthepublisher.DeskEditor:TjanKwangWeiISBN-13978-981-4313-12-4ISBN-10981-4313-12-2PrintedinSingapore.ForewordEveryscienceelaboratestoolsforthedescriptionofitsobjectsofstudy.Inclassicalmechanicswem

6、akeextensiveuseofvectorialquantities:forces,moments,positions,velocities,momenta.Confiningourselvestoasinglecoordinateframe,wecanregardavectorasafixedcolumnmatrix.Thedefinitivetraitofavectorquantity,however,isitsobjectivity;avectordoesnotdependonourchoiceofcoordinateframe.Thismeansthatass

7、oonasthecomponentsofaforcearespecifiedinoneframe,thecomponentsofthatforcerelativetoanyotherframecanbefoundthroughtheuseofappropriatetransformationrules.Butvectorquantitiesalonedonotsufficeforthedescriptionofcon-tinuummedia.Thestressandstrainatapointinsideabodyarealsoobjectivequantities;