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本文是在克劳斯(Cross)的弯矩分配法、卡尼(Kani)的迭代法以及点元θ_1迭代法基础上,经过进一步的力学分析和数学论证而提出的。文中先介绍“点有限元”概念,再从θ_1迭代法公式中,引出克劳斯及卡尼的间接渐近的分配与传递系数,并由此建立了点元传递系数,点元总分传矩阵等数学力学参量,又从卡尼法及θ_1迭代法模型中,视总分传矩阵为一个矩阵级数,通过数学论证,可以发现它是一个收敛的矩阵级数(数列),于是,解算框架内力成为易事,文中并举例以阐明之。
This paper is based on Cross’s bending moment distribution method, Kani’s iteration method and point element θ_1 iterative method, after further analysis of mechanics and mathematical arguments put forward. In this paper, the concept of “point finite element” is first introduced. From the θ_1 iteration formula, the indirect asymptotic distribution and transfer coefficients of Claus and Carney are derived, and the point transfer coefficients are established. Matrices and other mathematical mechanics parameters, from Carney’s and θ_1 iterative method models, regard the total distribution matrix as a matrix series. Through mathematical argumentation, it can be found that it is a convergent matrix series (a sequence of numbers). Thus, the solution It is easy to calculate the internal force of the framework, and examples are given in the article.