最新英汉双语材料力学11ppt课件.ppt

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1、英汉双语材料力学11材料力学第十一章能量方法2CHAPTER11ENERGYMETHOD§11–1GENERALEXPRESSIONSOFTHESTRAINENERGY§11–2MOHR’STHEOREM(METHODOFUNITFORCE)§11–3CATIGLIANO’STHEOREM32.Calculationofthestrainenergyofrodsintorsion：3.Calculationofstrainenergyofrodsinbending：ENERGYMETHODorDensityo

2、fthestrainenergy:orDensityofthestrainenergy:72.扭转杆的变形能计算：3.弯曲杆的变形能计算：能量方法83、Generalexpressionsofthestrainenergy：Strainenergyisindependentoftheorderofloading.Deformationsduetomutuallyindependentloadmaybesummedupeachother.Forslendercolumns，thestrainenergyduet

3、oshearingforcesmaybeneglected.ENERGYMETHODDeflectionfactorofshear9三、变形能的普遍表达式：变形能与加载次序无关；相互独立的力（矢）引起的变形能可以相互叠加。细长杆，剪力引起的变形能可忽略不计。能量方法10Solution：Inenergymethod（workdonebyexternalforcesisequaltothestrainenergy）①DetermineinternalforcesAENERGYMETHODBendingmomen

4、t:Torque:Example1Asemicirclerodasshowninthefigureislieinhorizontalplane.AverticalforcePactatitspointA.DeterminethedisplacementofpointAinverticaldirection.PROQMNMTAAPNBjTO11MN[例1]图示半圆形等截面曲杆位于水平面内，在A点受铅垂力P的作用，求A点的垂直位移。解：用能量法（外力功等于应变能）①求内力能量方法APROQMTAAPNBjTO12

5、③Workdonebyexternalforcesisequaltothestrainenergy②Strainenergy：ENERGYMETHODLetthen13③外力功等于应变能②变形能：能量方法14Example2DeterminethedeflectionofpointCbytheenergymethod,wherethebeamisofequalsectionandstraight.Solution：Workdonebyexternalforcesisequaltothestrainenergy

6、Byusingsymmetryweget：Thinking：Forthedistributedload,canwedeterminethedisplacementofpointCbythismethod？qCaaAPBfENERGYMETHODLet15[例2]用能量法求C点的挠度。梁为等截面直梁。解：外力功等于应变能应用对称性，得：思考：分布荷载时，可否用此法求C点位移？能量方法qCaaAPBf16§11–2MOHR’STHEOREM(METHODOFUNITFORCE)Determinethedispla

7、cementfAofanarbitrarypointA.1、Provementofthetheorem：aAFigfAq(x)FigcA0P=1q(x)fAFigbA=1P0ENERGYMETHOD17§11–2莫尔定理(单位力法)求任意点A的位移fA。一、定理的证明：能量方法aA图fAq(x)图cA0P=1q(x)fA图bA=1P018Mohr’stheorem(methodofunitforce)2、GeneralformofMohr’stheoremENERGYMETHOD19莫尔定理(单位力法)二、普

8、遍形式的莫尔定理能量方法203、WhatwemustpayattentiontoasweapplyMohr’stheorem：④CoordinateofM0(x)mustbecoincidewiththatofM(x).Foreachsegmentthecoordinatemaybesetupfreely.⑤Mohr’sintegrationmustbethroughthewholestructur