三维线弹性力学修正的功的互等定理及其应用

该研究发现，三维线弹性力学Betti(贝蒂)功的互等定理命题中的两个主要前提，“一个弹性体”和“两组力的作用”是相互矛盾的，因为两组力的任意一组力都可能改变已知的弹性体为另外一个弹性体.这一矛盾导致Betti功的互等定理是一个具有逻辑错误的定理.基于对这一矛盾的分析，提出了修正的功的互等定理，在这一定理中，给出了功的互等定理的正确命题.此外，该修正的功的互等定理为功的互等法提供理论基础，该法是结构分析的一个新颖的和强有力的方法.

Corrected Reciprocal Theorem for 3D Linear Elasticity and Its Application

It was discovered that the 2 main premises in the proposition of Betti’s reciprocal theorem for 3D linear elasticity, i.e. “1 elastic body” and “action of 2 sets of forces”, were contradictory to each other because either of the 2 sets of forces may change the given elastic body to another one. This contradiction leads to the result that Betti’s reciprocal theorem is one with error in logic. On the basis of the analysis of contradiction, the corrected reciprocal theorem was proposed, in which the correct proposition of the reciprocal theorem was given. In addition, the corrected reciprocal theorem provides a theoretical basis for the reciprocal method of works, which makes a novel and powerful way to the analysis of elastic bodies and structures.