弹性杆热过屈曲精确模型及其打靶法

An exact model of thermal post buckling of elastic bars and shooting method for its solution

基于轴线可伸长杆大变形几何理论，建立了两端不可移简支均匀加热直杆过屈曲行为的精确数学模型，把挠曲线弧长ｓ（ｘ）和纵向位移ｕ（ｘ）也作为基本未知量，采用打靶法和解析延拓法直接用数值求解，获得了非线性边值问题数值意义上的精确解，并给出了相应的数表和特性曲线．

Based on the geometric deformation theory of bars with large deflections and axial elongation, an exact mathematical model of post buckling behavior of uniformly heated straight bars with immovable and simply supported ends are developed, in which the arc length s(x) and the longitudinal displacement u(x) are taken as the basic unknown functions. By using shooting method and analytical continuation, the nonlinear ordinary differential equations with boundary values at two points are numerically solved. An exact solution of the problem (in the meaning of numerical computation) is obtained and corresponding data table and characteristic curves are also given.