广义力法公式及其证明

Demonstration of the Generalized Force Formula

在传统的力法分析中,无论是力法基本方程的建立还是方程中系数和自由项的求解,都要求在同一基本结构上进行,而在广义力法中,可以同时基于两个不同的基本结构求解超静定问题.对n次超静定结构,本文以引理形式给出了广义的力法方程和叠加公式并给出了证明,当选取的两个基本结构完全一致时,给出的广义力法公式退化为传统的力法方程和叠加公式.本文工作有助于人们对力法的进一步认识.

In the traditional analysis of redundant structures by the force method, a suitable simple structure is needed in order to obtain the canonical equations and to find the coefficients in the equations. It is shown in this paper that there is a generalized formula which is established based at the same time on two simple structures. The generalized canonical equations and the new superposition formula are introduced and verified. The traditional expressions are the special cases considered in present paper. It is helpful for us to understand the theory of the force method.