math - functional and structural tensor analysis for engineers - brannon

《math - functional and structural tensor analysis for engineers - brannon》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

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,