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桥墩是变断面、抗挠、抗压杆件,自重在負荷中所占的比值很大。将这个力学問題翻譯成数学問題,即得到一个三阶变系数,非齐次线性常微分方程,求它在特定的边值条件的解释表达式是很困难的,故拟用有限差分法求其近似解,而后并用插值法,求出一条近似形变曲綫,以資分析內力。一、微分方程的推导桥墩受力图式如下(图一):
Bridge pier is a variable cross-section, anti-scratch, anti-pressure bar, weight in the load share in a large ratio. To translate this mechanical problem into a mathematical problem, that is, to obtain a third-order variable coefficient, inhomogeneous linear ordinary differential equation, it is very difficult to find an explanation expression for a particular boundary value condition. Therefore, the finite difference method Approximate solution, and then use the interpolation method, find an approximate deformation curve for the analysis of internal forces. First, the derivation of differential equations Pier stress pattern is as follows (Figure 1):