第十三章能量法 Chapter13 Energy Method
r (Energy Method) 第十三章能量法( Energy Methods) D§13-1概述( Introduction) D§13-2杆件变形能的计算( Calculation of strain energy for various types of loading D§13-3互等定理( Reciprocal theorems) §13-4单位荷载法·莫尔定理(Unit-oad method mohr's theorem) D§13-5卡氏定理( Castigliano’ s Theorem) D§13-6计算莫尔积分的图乘法( The meth. od of moment areas for mohr's integration)
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r (Energy Method) §13-1概述( Introduction) 、能量方法( Energy methods) 利用功能原理V=W来求解可变形固体的位移变形和内力 等的方法 二、外力功( Work of the external force) 固体在外力作用下变形,引起力作用点沿力作用方向位移, 外力因此而做功,则成为外力功 、变形能( Strain energy) 在弹性范围内弹性体在外力作用下发生变形而在体内积蓄 的能量称为弹性变形能简称变形能
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能量滤( Energy Method) 四、功能原理(Work- energy principle) 可变形固体在受外力作用而变形时,外力和内力均将作功对 于弹性体不考虑其他能量的损失外力在相应位移上作的功在数 值上就等于积蓄在物体内的应变能 The formula: V=w(Work-Energy Principle We will not consider other forms of energy such as thermal energy, chemical energy, and electromagnetic energy. Therefore, if the stresses in a body do not exceed the elastic limit, all of work done on a body by external forces is stored in the body as elastic strain energy. 用
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r (Energy Method) §13-2杆件变形能的计算 Calculation of strain energy for various types of loading 杆件变形能的计算( Calculation of strain energy for various types of loading) 1.轴向拉压的变形能( Strain energy for axial loads) 当拉力为F1时杆件的伸长为△1 当再增加一个dF1时,相应的变形增量为d(△M1) 此外力功的增量为: dw=fd(al) d(Al)=dFL :EA
5 d d(Δ ) 1 1 W F l EAF l l 1 1 d d(Δ )