诸能量原理的统一性

The Unification of the Energy Principles

多数弹性力学中的能量方法都是从П=U-W 及П~*=U-W~*出发,通过变分得到最小势能原理δП=0及最小余能原理δП~*=0.实际上,最小势能原理、最小余能原理只不过是虚位移原理及虚力原理的特殊情况,而虚位移原理是人为的用能量表示的平衡条件,虚力原理是人为的用能量表示的连续性条件.因此不需要讨论П及П~*的物理含义.本文把理论力学的虚位移原理,分析力学的哈密顿原理,弹性力学的最小势能原理都统一到虚位移原理,把材料力学的卡氏定理、莫尔定理,弹性力学的最小余能原理都统—到虚力原理。

Energy methods from ()=U-W as well ()=U-W^()bring about the Minimum Poten- tial Energy Principle δ()=0 and the Minimum Complementary Energy Principle δ()=0 by way of a variation.Rather than a natural law,these principles are a special case of the Virtual Displace ment and Force Principles.The former is a man-made condition in equilibrium expressed by energy while the latter is a man-made contiunous condition expressed by energy.Therefore,discussing their physical implication of () as well as () is unnecessary. This paper attempts to unite the Virtual Displacement Principle in theoretical mechanics,the Hamilton's principle in analytical mechanics,and the Minimum Potential Energy in elastic mechanics to the Virtual Displacement Principles.And it unites the Castigliano's Second Theorem Principle and Mohr's Theorem in strength of materials,and the Minimum Complementary Energy Principle in elas tic mechanics to the Virtual Force Principle.