跨内支撑杆及阶梯杆屈曲的一种解析法分析

Buckling Analysis of Bars with Internal Bracings and Stepped Bars Based on an Analytical Method

针对跨内含支撑的杆和变截面阶梯杆的弹性屈曲问题,提出一种分段作屈曲分析再叠加重组的分析方法.首先在杆两端引入横向和旋转弹簧,用以模拟弹性边界条件.其次建立两端弹性约束杆屈曲方程的通用形式,并通过屈曲方程求得几种边界约束杆端部弹性刚度因子的解析表达式.最后,建立拆分杆段连接处的平衡方程和协调条件,综合杆段的屈曲方程和节点的补充刚度条件得到整个杆件的屈曲方程,从而求得临界力.本文还提出一种基于泰勒展开求解屈曲特征方程近似根的方法.算例中将本方法所得结果与既有文献和有限元软件计算结果对比,验证本方法的适用性和准确度.所提方法属于解析方法,得到简洁、严密和易用的解析公式,可为多跨结构和变截面杆件的屈曲分析提供新参考.

To solve the elastic buckling problem of stepped bars and bars with internal bracings,a new method of subsection buckling analysis followed by superposition reorganization is proposed.Firstly,transverse and rotational springs are introduced at both ends of the rod to simulate any elastic boundary condition.Secondly,the general form of the buckling equation considering elastic boundary conditions at the ends is established,and analytic expressions for the end elastic stiffness factors under different boundary conditions are obtained through the buckling equation.Lastly,the equilibrium equation and compatibility conditions at the connection of bar segments are established,and the buckling equation of the whole bar is obtained by combining the buckling equations of the bar segments and the supplementary stiffness condition at the nodes,leading to the solution of the critical force.We also present a method for finding the approximate solution of the buckling characteristic equation based on Taylor expansion.The applicability and accuracy of the proposed method are verified by comparing the obtained results with those from the existing literature and numerical simulations using finite element software.The presented method is an analytical method with brief form,rigorousness,and convenience of application.It can provide new reference for the buckling analysis of multi-span structures and variable cross-section bars.