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三维有限元任意截面剖分和插值计算方法.docx

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三维有限元任意截面剖分和插值计算方法 Abstract Inengineeringcalculationsusingfiniteelementmethods,itisoftennecessarytodividethecross-sectionofthestructureintosmallelementsasaccuratelyaspossiblesothatitcanbesolvedmoreaccurately.Inthispaper,wepresentamethodofarbitrarycross-sectionsubdivisionandinterpolationcalculationbasedonthree-dimensionalfiniteelementanalysis.First,thecross-sectionisdividedintosmallpiecesandlabeled.Then,thenodalcoordinatesanddegreesoffreedomofthesesmallpiecesareobtained,andtheshapefunctionisderived.Finally,thenodaldisplacementinterpolationequationisobtainedbyusingtheshapefunction.Themethodpresentedinthispapernotonlysimplifiesthesubdivisionprocess,butalsoimprovestheaccuracyofthecalculationinthefiniteelementanalysisofthestructure. Introduction Instructuralmechanics,thefiniteelementmethod(FEM)iswidelyusedtosolvevariousstructuralproblems.Infiniteelementanalysis,thecross-sectionofthestructureisoftendividedintosmallelementsforaccuratecalculation.Themoreaccuratethesubdivision,themoreaccuratethefinalcalculationwillbe.However,inpracticalengineeringcalculations,thegeometryofthestructureiscomplex,andthecross-sectionmaynotberegular.Therefore,thesubdivisionofthecross-sectionismoredifficultandcomplex. Inthispaper,weproposeanarbitrarycross-sectionsubdivisionmethodbasedonthree-dimensionalfiniteelementanalysis.Themethodisusedtodivideandinterpolatethecross-sectionofastructure,andcanbeappliedtovariouscomplexcross-sectionshapes. Methodology -Thecross-sectionisdividedintosmallpieces:Inthismethod,thefirststepistodividethecross-sectionofthestructureintosmallpiecesbydrawinglinesorcreatinggridsthatintersectthecross-section.Thesmallpiecesshouldbenumberedtoformaconnectionsequence. -Obtainthenodalcoordinatesanddegreesoffreedomofeachsmallpiece:Inthisstep,eachsmallpieceisassignednodalcoordinatesanddegreesoffreedom.Thenodalcoordinatesrepresentthelocationofeachnodeinthestructure,andthedegreesoffreedomrepresentthedisplacementalongeachaxis. -Derivetheshapefunction:Theshapefunctionisusedtocalculatethe