加热弹性杆的热过屈曲分析

Analysis of Thermal Post-Buckling of Heated Elastic Rods

基于轴线可伸长细杆的过屈曲变形几何理论,建立了两端轴向不可移的均匀加热直杆热弹性过屈曲行为的精确数学模型· 这是一个包含杆轴线弧长在内的多未知函数的强非线性一阶常微分方程两点边值问题· 采用打靶法和解析延拓法直接数值求解上述非线性边值问题,分别获得了两端横向简支和夹紧杆的热过屈曲状态解。

Based on the non_linear geometric theory of extensible rods, an exact mathematical model of thermal post_buckling behavior of uniformly heated elastic rods with axially immovable ends is developed, in which the arc length s(x) of axial line and the longitudinal displacement u(x) are taken as the basic unknown functions. This is a two point boundary value problem of first order ordinary differential equations with strong non_linearity. By using shooting method and analytical continuation, the nonlinear boundary value problems are numerically solved. The thermal post_buckled states of the rods with transversely simply supported and clamped ends are obtained respectively and the corresponding numerical data tables and characteristic curves are also given.