计算固体力学Chapter04 FEM for Trusses.pptx

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计算固体力学Chapter04 FEM for Trusses.pptx

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Chapter4

FEMforTrusses

桁架的有限元方法

Chapter4FEMforTrussesContents4.1Introduction4.2FEMEquations4.3WorkedExamples4.4HigherOrderOne-DimensionalElement

4.1Introduction

Chapter4FEMforTrussesFEMAnalysisAtrussisoneofthesimplestandmostwidelyusedstructuralmembersIntrusses,thetrussorbarmembersarejoinedtogetherbypinsorhinges(notbywelding),sothatthereareonlyaxialforces(notmoments)transmittedbetweenthebars

Chapter4FEMforTrussesThestraightbartakesonlyaxialforces,anddeformsonlyinitsaxialdirectionTheelementdevelopedfortrussiscommonlyknownasthetrusselementorbarelementplanartrussesspacetrussesInplanartrusses,therearetwocomponentsinthexandydirectionsforthedisplacementaswellasforcesatanodeForspacetrusses,therewillbethreecomponentsinthex,yandzdirectionsforbothdisplacementandforcesatanodeItisassumedthattheelementhasauniformcross-section

4.2FEMEquations

Chapter4FEMforTrussesShapeFunctionConstructionConsideratrusselement(barelement)ofuniformcross-sectionandlengthlewithnodes1and2ateachendoftheelement(nd=2)Thelocalx-axisistakenintheaxialdirectionoftheelementwiththeoriginatnode1Inthelocalcoordinatesystem,thereisonlyoneDOFateachnodeoftheelement(theaxialdisplacementu1andu2)

Chapter4FEMforTrussesAssumethattheaxialdisplacementinthetrusselementinthelocalcoordinatesystemcanbegiveninageneralformInderivingtheshapefunction,usethefactthatItgives

Chapter4FEMforTrussesThesolutionisTheapproximatedisplacementisThematrixofshapefunctionsiswhere

Chapter4FEMforTrussesTherefore,andi.e.,

Chapter4FEMforTrussesElementMatricesintheLocalSystemElementstiffnessandmassmatrixare

Chapter4FEMforTrussesSupposetheelementisloadedbyandistributedforcefxalongthex-axis,andtwoconcentratedforcesfs1andfs2,