弹性力学-第一章1

弹性力学第一章1弹性力学及有限元ElasticityandFiniteElementMethod1ThelectureswillbegivenbothinEnglishandChinese采用中英文双语讲授弹性力学第一章2GivemeafishandIwilleattoday,TeachmetofishandIwilleatforalifetime.授人以鱼，不如授人以渔。弹性力学第一章3Textbook:AppliedElasticity徐芝纶中文教材：弹性力学简明教程徐芝纶弹性力学第一章4Chapter1.Introduction第一章绪论弹性力学第一章51.1ContentsofTheoryofElasticity1.1弹性力学的内容•NAMETheoryofelasticityisoftencalledelasticityforshort.Itisthebranchofsolidmechanics.弹性力学的理论简称为弹性理论或弹性力学.它是固体力学的一个分枝弹性力学第一章6Threebranchesofsolidmechanics固体力学的三个分枝•Mechanicsofmaterials材料力学,StructuralMechanics结构力学Elasticity弹性力学弹性力学第一章7•WhatdoestheElasticitydealwith?Itdealswiththestresses,deformationsanddisplacementsinelasticsolidsproducedbyexternalforcesorchangesintemperature.研究弹性体由于外力和温度改变而引起的应力，形变和位移。•Itanalyzesthestresses,deformationsanddisplacementsofstructuralelementswithintheelasticrangeandtherebytocheckthesufficiencyoftheirstrength,stiffnessandstability.分析结构的应力，形变和位移，检查是否满足强度，刚度和稳定性条件。弹性力学第一章8Comparisonamongthethreecoursesinsolidmechanics固体力学三门学科的比较•Threebrancheshavethesamepurposeanddodifferfromoneanotherbothinobjectsstudiedandthemethodsofanalysisused.•1.Objectsstudied研究对象2.Methodsofanalysis研究方法弹性力学第一章9todealwiththeelasticsolids都是研究弹性体1.objectsstudied:--研究对象:(1)Similarity---------相同点弹性力学第一章10(2)objectsstudied--difference研究对象--不同点Mechanicsofmaterials:barelement材料力学单根杆件Structuralbarsystems:--Mechanics:truss,rigidframe结构力学杆件系统：桁架，刚架。Elasticity:1.platesandshells板，壳弹性力学2.blocks:块体e.g.dams,foundations坝，基础3.analyzebarelementprecisely对杆件作精确分析弹性力学第一章11•Mechanicsofmaterialsdealsessentiallywiththestressesanddisplacementsofstructuralelementintheshapeofabar,straightorcurved,whichissubjectedtotension,compression,shear,bending,ortorsion.材料力学研究受到拉、压、剪、弯或扭的直杆或曲杆的应力和位移。弹性力学第一章12•StructuralMechanicsdealswiththestressesanddisplacementsofastructuralintheformofabarsystem,suchasatrussorarigidframe.•结构力学研究杆件系统（例：桁架或刚架）的应力和位移弹性力学第一章13•Elasticitydealswiththestressesanddisplacementsofthestructuralelementssuchasblocks,platesandshells,whicharenotintheformofabar.•弹性力学研究块体、板和壳体的应力和位移。•Elasticityalsoanalyzeabarelementthoroughlyandprecisely.•弹性力学对杆件作更精确分析弹性力学第一章142.methodsofanalysis:研究方法(1)Similarity---相同点:equilibriumaspects静力学方面geometricalaspects几何学方面physicalaspects物理学方面弹性力学第一章15•equilibriumaspects--equilibriumofforcesofanisolatedbody静力学方面--脱离体力的平衡•geometricalaspects--therelationsbetweendisplacementsandstrains.几何学方面--位移和应变的关系•physicalaspects----therelationsbetweenstressesandstrains物理学方面--应力和应变的关系弹性力学第一章16(2)methodsofanalysis:------difference研究方法--------不同点:Mechanicsofmaterials:someassumptionsonthestrainconditionorthestressconditionaremade材料力学：对应变或应力情况作某些假定Elasticity：noassumptionsonthestrainconditionorthestressconditionaremade.弹性力学:对应变或应力情况不作假定弹性力学第一章17Mechanicsofmaterials:someassumptionsonthestrainconditionorthestressconditionaremadeTheassumptionssimplifythemathematicalderivationtoacertainextent.Theassumptionsinevitablyreducethedegreeofaccuracyoftheresultsobtained..弹性力学第一章18Elasticity：noassumptionsonthestrainconditionorthestressconditionaremade.TheresultsobtainedinelasticityaremoreaccurateandmaybeusedtochecktheapproximateresultsobtainedinMechanicsofmaterials.弹性力学第一章19•Theproblemofbendingofastraightbeamundertransverseloads.•Itisassumedinmechanicsofmaterialsthataplanesectionofthebeamremainsplaneafterbending,whichleadstothelineardistributionofbendingstresses.•Noassumption,thataplanesectionofthebeamremainsplaneafterbending,ismadeinElasticity.弹性力学第一章20•Aprismaticaltensionmemberwithasmallhole•Itisassumedinmechanicsofmaterialsthatthetensilestressesareuniformlydistributedacrossthenetsectionofthemember.•Theanalysisinelasticityshowsthatthestressesarebynomeansuniform,butareconcentratednearthehole.弹性力学第一章211.2someimportantconceptsintheoryofelasticity1.2弹性力学中的几个重要概念A.ExternalForces外力B.Stress应力C.Deformation(Strain)形变(应变)D.Displacement位移弹性力学第一章22A.externalforces外力1.Bodyforces体积力，体力2.Surfaceforces表面力，面力弹性力学第一章231.Bodyforces体力。Externalforcesortheloads,distributedoverthevolumeofthebody,arecalledbodyforces.分布在物体体内的外力叫体力E.g.gravitationalforces,orinertiaforcesinthecaseofabodyinmotion.例如：重力，惯性力弹性力学第一章24BodyforceFig.体力定义图。弹性力学第一章25F=limQ/Vv0F--bodyforcevectoratp,ThevectorquantityFistheintensityofbodyforceatPF--P点的体力矢量V--anelementaryvolumeofthebodyaroundpointpV--包含P点的小体积Q--bodyforceactingonVQ--作用在V上的体力的合力弹性力学第一章26Bodyforcecomponents体力分量•F=Xi+Yj+Zk=(X,Y,Z)•TheprojectionsofFonthex,y,andzaxesarecalledthebodyforcecomponentsatP.体力在坐标轴上的投影叫体力分量。•ThebodyforcecomponentswillbedenotedbyX,YandZ体力分量用X,Y,Z表示弹性力学第一章27SignConventions,dimension正负约定，因次•Itisconsideredpositive(negative)whenitactsinthepositive(negative)directionofthecorrespondingcoordinate.与坐标轴正向一致为正。•Itsdimensionis[force]/[length]3因次：力/长度3•forexample:弹性力学第一章282.Surfaceforces面力•Definition:externalforces,ortheloads,distributedoverthesurfaceofabody,arecalledsurfaceforces.分布在物体表面的外力叫面力•e.g.hydrostaticpressure,thepressureofonebodyonanother例：水压力，接触力弹性力学第一章29SurfaceforceFig.面力定义图。弹性力学第一章30•F=limQ/S•F---surfaceforcevectoratP.thevectorquantityistheintensityofsurfaceforceatP.F---P点的面力矢量。•S