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本文利用结构力学中的力法原理,以及数值积分和曲线拟合等方法,完成了无铰拱影响线在PC—1500(或PC—1501)计算机上的绘制。与常规的手算算法、弹性中心法、近似算法、有限元法相比,具有简便、实用的优点。本文所述的程序逼真地描绘了拱轴线及其任一截面内力影响线的图形,可直接用于工程实践中。一、数学方法简述 1.最小二乘法曲线拟合假设有一批数据(x_0,y_0)、(x_1,y_1)……(x_n,y_n)。它的对应图形如图1。用最小二乘法求一条曲线(或直线),使它的某一点与求出的曲线(或直线)对应点的差值的平方和为最小。
In this paper, the principle of force method in structural mechanics, and numerical integration and curve fitting methods are used to complete the drawing of PC-1500 (or PC-1501) computer. Compared with the conventional hand arithmetic, elastic center method, approximate algorithm and finite element method, it has the advantages of simplicity and practicality. The program described in this paper can vividly depict the arch of the arch axis and the influence line of internal force of any section, which can be directly used in engineering practice. First, a brief mathematical method 1. Least-squares curve fitting Assume a group of data (x_0, y_0), (x_1, y_1) ... (x_n, y_n). Its corresponding graphics as shown in Figure 1. Find a curve (or straight line) by the least square method and minimize the square of the difference between a point on the curve and the point on the curve (or line).