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1、UNMBOOKDRAFTSeptember4,20035:21pmFunctionalandStructuredTensorAnalysisforEngineersAcasual(intuition-based)introductiontovectorandtensoranalysiswithreviewsofpopularnotationsusedincontemporarymaterialsmodelingR.M.BrannonUniversityofNewMexico,AlbuquerqueCopyrightisreserved.Individualcop
2、iesmaybemadeforpersonaluse.Nopartofthisdocumentmaybereproducedforprofit.Contactauthoratrmbrann@sandia.govNOTE:WhenusingAdobe’s“acrobatreader”toviewthisdocument,thepagenumbersinacrobatwillnotcoincidewiththepagenumbersshownatthebottomofeachpageofthisdocument.Notetodraftreaders:Themostu
3、sefultextbooksaretheoneswithfantasticindexes.Thebook’sindexisrathernewandstillunderconstruction.Itwouldreallyhelpifyouallcouldsendmeanotewheneveryoudiscoverthatanimportantentryismiss-ingfromthisindex.I’llbesuretoaddit.Thisworkisacommunityeffort.Let’strytomakethisdocumenthelpfultoothe
4、rs.FUNCTIONALANDSTRUCTUREDTENSORANALYSISFORENGINEERSAcasual(intuition-based)introductiontovectorandtensoranalysiswithreviewsofpopularnotationsusedincontemporarymaterialsmodelingRebeccaM.Brannon??UniversityofNewMexicoAdjunctprofessorrmbrann@sandia.govAbstractElementaryvectorandtensora
5、nalysisconceptsarereviewedinamannerthatprovesusefulforhigher-ordertensoranalysisofanisotropicmedia.Inadditiontoreviewingbasicmatrixandvectoranalysis,theconceptofatensoriscov-eredbyreviewingandcontrastingnumerousdifferentdefinitiononemightseeintheliteraturefortheterm“tensor.”Basicvect
6、orandtensoroperationsareprovided,aswellassomelesser-knownoperationsthatareusefulinmaterialsmodeling.Considerablespaceisdevotedto“philosophical”discussionsaboutrelativemeritsofthemany(oftenconflicting)tensornotationsystemsinpopu-laruse.iiAcknowledgmentsAnindeterminatelylarge(but,ofcou
7、rse,countable)setofpeoplewhohaveofferedadvice,encouragement,andfantasticsuggestionsthroughouttheyearsthatI’vespentwritingthisdocument.Isayyearsbecausetheseedsforthisdocumentweresownbackin1986,whenIwasaco-opstudentatLosAlamosNationalLaboratories,andImadethemistakeofaskingmysupervisor,
8、NormJohnson,
