对能量法及其计算杆系结构位移的探讨

摘要

The Clapeyron's theorem is proved with the mathematical induction.The Castigliano's theorem can directly be obtained with the Clapeyron's theorem while the strain energy of elastic body is expressed as a general form of the quadratic homogeneous function of load.The displacement calculation of linear elastic bar structure with Castigliano's theorem and the unit load method is the same,but the unit load method based on the principle of virtual work is more universal and more simple,and it's physical meaning is more explicit.%用数学归纳法证明了克拉贝依隆原理.将弹性体的应变能表达为荷载的二次齐次函数的一般形式,并用克拉贝依隆原理直接得到了卡氏第二定理.指出了卡氏第二定理与单位荷载法计算线弹性杆系结构位移的方法其本质是相同的,而基于虚功原理的单位荷载法则具有广泛的适应性,方法更简单,物理意义更明确.