圆拱稳定的变分分析

根据势能原理,建立以位移为基本未知量的圆拱总势能,采用变分分析,推导出圆拱在弯曲平面内的平衡微分方程,应用能量法,可直接近似计算在均布压力作用下不同支承的变截面圆拱,以及在非均布压力作用下等截面圆拱屈曲的临界荷载,算例表明,能量法计算圆拱稳定问题十分简便,适合于工程应用。

Variation Analysis of the Stability of Circular Arch

The general potential energy of circular arch with displacement as fundamental unknown quantity is established according to principle of potential energy; the equilibrium differential equation of circular arch at a bending plane is derived by adopting variation analysis. By applying energy method, an approximate computation can be directly conducted on nonprismatic circular arch with different bearing under the action of uniformly distributed pressure and also on the critical load of prismatic circular arch in buckling under the action of non uniformly dcstributed pressure. As indicated by example of computation, energy method is very simple and convenient for computing the stability of circular arch, it is suitable for engineering application.