英汉双语材料力学11.ppt

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1、CHAPTER11ENERGYMETHODS1材料力学第十一章能量方法2CHAPTER11ENERGYMETHOD§11–1GENERALEXPRESSIONSOFTHESTRAINENERGY§11–2MOHR’STHEOREM(METHODOFUNITFORCE)§11–3CATIGLIANO’STHEOREM3第十一章能量方法§11–1变形能的普遍表达式§11–2莫尔定理(单位力法)§11–3卡氏定理4§11–1GENERALEXPRESSIONSOFTHESTRAINENERGY1、Principleofenergy：2、Calcul

2、ationofthestrainenergyofrods：1).Calculationofthestrainenergyofrodsintensionorcompression：Strainenergystoredintheelasticbodyisequaltotheworkdonebyexternalforces，thatis:Methodtoanalyzeandcalculatedisplacements、deformationsandinternalforcesofdeformablebodiesbythiskindofrelatio

3、niscalledenergymethod.ENERGYMETHODorDensityofthestrainenergy:5§11–1变形能的普遍表达式一、能量原理：二、杆件变形能的计算：1.轴向拉压杆的变形能计算：能量方法弹性体内部所贮存的变形能，在数值上等于外力所作的功，即利用这种功能关系分析计算可变形固体的位移、变形和内力的方法称为能量方法。62.Calculationofthestrainenergyofrodsintorsion：3.Calculationofstrainenergyofrodsinbending：ENERGYMET

4、HODorDensityofthestrainenergy: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，thestrainenergyduetoshe

5、aringforcesmaybeneglected.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）①DetermineinternalforcesAENERGYMETHODBendingmoment:Torque:Example1Asem

6、icirclerodasshowninthefigureislieinhorizontalplane.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APROQMTAAPNBjTO12③Workdonebyexternalforcesisequaltothes

7、trainenergy②Strainenergy：ENERGYMETHODLetthen13③外力功等于应变能②变形能：能量方法14Example2DeterminethedeflectionofpointCbytheenergymethod,wherethebeamisofequalsectionandstraight.Solution：WorkdonebyexternalforcesisequaltothestrainenergyByusingsymmetryweget：Thinking：Forthedistributedload,can

8、wedeterminethedisplacementofpointCbythismethod？qCaaAPBfENERGYMETHODLet15[例2]用能量法求C