math - functional and structural tensor analysis for engineers - brannon

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1、UNMBOOKDRAFTSeptember4,20035:21pmFunctionalandStructuredTensorAnalysisforEngineersAcasual(intuition-based)introductiontovectorandtensoranalysiswithreviewsofpopularnotationsusedincontemporarymaterialsmodelingR.M.BrannonUniversityofNewMexico,AlbuquerqueCopyri

2、ghtisreserved.Individualcopiesmaybemadeforpersonaluse.Nopartofthisdocumentmaybereproducedforprofit.Contactauthoratrmbrann@sandia.govNOTE:WhenusingAdobe’s“acrobatreader”toviewthisdocument,thepagenumbersinacrobatwillnotcoincidewiththepagenumbersshownatthebott

3、omofeachpageofthisdocument.Notetodraftreaders:Themostusefultextbooksaretheoneswithfantasticindexes.Thebook’sindexisrathernewandstillunderconstruction.Itwouldreallyhelpifyouallcouldsendmeanotewheneveryoudiscoverthatanimportantentryismiss-ingfromthisindex.I’l

4、lbesuretoaddit.Thisworkisacommunityeffort.Let’strytomakethisdocumenthelpfultoothers.FUNCTIONALANDSTRUCTUREDTENSORANALYSISFORENGINEERSAcasual(intuition-based)introductiontovectorandtensoranalysiswithreviewsofpopularnotationsusedincontemporarymaterialsmodelin

5、gRebeccaM.Brannon††UniversityofNewMexicoAdjunctprofessorrmbrann@sandia.govAbstractElementaryvectorandtensoranalysisconceptsarereviewedinamannerthatprovesusefulforhigher-ordertensoranalysisofanisotropicmedia.Inadditiontoreviewingbasicmatrixandvectoranalysis,

6、theconceptofatensoriscov-eredbyreviewingandcontrastingnumerousdifferentdefinitiononemightseeintheliteraturefortheterm“tensor.”Basicvectorandtensoroperationsareprovided,aswellassomelesser-knownoperationsthatareusefulinmaterialsmodeling.Considerablespaceisdev

7、otedto“philosophical”discussionsaboutrelativemeritsofthemany(oftenconflicting)tensornotationsystemsinpopu-laruse.iiAcknowledgmentsAnindeterminatelylarge(but,ofcourse,countable)setofpeoplewhohaveofferedadvice,encouragement,andfantasticsuggestionsthroughoutth

8、eyearsthatI’vespentwritingthisdocument.Isayyearsbecausetheseedsforthisdocumentweresownbackin1986,whenIwasaco-opstudentatLosAlamosNationalLaboratories,andImadethemistakeofaskingmysupervisor,NormJohnson,