框架分析的点元迭代法及矩阵级数法

Point Element Iteration Method and Matrix Series Method for Frame Analysis

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。

Based on the Cross and Kani methods as well as on the author's θi iteration method, the point element iteration method for analysis of frames is presented in this paper.In the paper, the concept of point element is first introduced and the Cross and Kani's indirect approaching distribution factors and carry-over factors are drawn from the equations of the θi iteration method. From then the carry-over factors of point element and the mathematical and mechanical parameters of the total propagating matrix of point element are developed. Taking the total propagating matrix as a series matrix, it is found that this matrix is a convergent one, so that it is easy to find its sum and the internal forces of the frame.Numerical examples are given for illustrating the application of the suggested method.