变截面弹性杆的热过屈曲分析

Thermal post buckling of rods with variable c ross sections

基于 Kirchhoff假设和轴向可伸长杆几何非线性理论 ,建立了受均匀静态升温场作用的两端不可移简支—夹紧变截面杆热弹性过屈曲控制方程 .采用打靶法和解析延拓法数值求解所得强非线性常微分方程边值问题 ,获得了相应的过屈曲响应 .以横截面宽度不变 ,高度沿轴向线性变化的变截面杆为例 。

On the basis of Kirchhofff′s assumption and nonlinearly geometrical th eory for axially extensible rods, the governing equation for the post buckling o f immovably hinged clamped elastic rods with variable cross sections and subject ed to a static temperature rise is developed. By using the shooting method and i n conjunction with the concept of analytical continuation, a computational analy sis of the obtained nonlinear boundary value problem is achieved. For some speci fied variations of the cross sections, the thermal post buckled configurations c orresponding to some specific values of buck1ed temperature are presented and th e curves of secondary equilibrium paths for various values of the slenderness ra tio are given .