变截面压杆临界载荷的迭代算法

针对变截面压杆临界载荷问题,基于一阶临界载荷作用下结构稳定平衡条件,进行杆件的离散化.以杆件各离散点的未知挠度和压杆临界力为未知量,以每个离散点的挠度与临界力所满足的差分方程,构建求解临界力非线性方程组.应用数值分析迭代理论,提出了临界力求解的直接迭代新方法.并编制计算程序.通过算例分析验证了该算法具有程序设计简单,收敛快和计算精度高等优点,为工程应用提供良好条件.

Iterative algorithm of the critical load about variable cross-section bar

In view of the problem of critical load of variable cross-section bar,based on stable equilibrium condition under first order critical load,bar structure is discretized.Making the unknown deflection of discrete points and critical force as unknown variables,relation of the deflection of each discrete point and the critical force is used to construct group of nonlinear equations.Iteration theory about numerical analysis is applied,and a new algorithm about of direct iteration of the critical force is proposed.By computing practical examples,it is proved that the algorithm is simple in program design,high in precise and fast in Convergence.The method can be well applied in engineering.