非对称支承弹性杆的热过屈曲

本文基于轴线可伸长细杆的几何非线性理论,建立了一端固定夹紧另一端固定简支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,获得了杆的热过屈曲状态解,给出了具有不同长细比杆的热过屈曲平衡路径。

THERMAL POST-BUCKLING OF ASYMMETRICALLY SUPPORTED ELASTIC RODS

In this paper, based on the non-linearly geometric theory for extensible elastic rods, an exact mathematical model of thermal post-buckling behavior of uniformly heated elastic rods with clamped-simply supported ends is derived. This is a two-end point boundary value problem of first-order ordinary differential equations with strong non-linearity and multiple unknown functions, in which the arc length s(x) as one of the unknown functions is involved. By using shooting method and analytical continuation, the non-linear boundary value problem is numerically solved and the thermal post-buckled states of the rods are obtained. The equilibrium paths of thermal post-buckled rods for a variety of the slenderness are given.