双层梁在均匀升温场内的几何非线性问题

基于精确的几何非线性理论,建立了轴线可伸长双层梁在温度载荷作用下的非线性弯曲控制方程。其中包含了由于材料在横向非均匀分布而导致的拉-弯耦合项。应用打靶法数值求解相应的非线性边值问题,得到了均匀加热下两端不可移简支双层梁的热弯曲数值解。作为算例,给出了由铜和钢组成的双金属梁的平衡构形和平衡路径,分析和讨论了几何和物理参数对梁变形的影响。

GEOMETRICALLY NONLINEAR PROBLEM OF A TWO-LAYER BEAM SUBJECTED TO UNIFORM TEMPERATURE RISE

Based on an accurate geometrically nonlinear theory, governing equations for nonlinear thermal bending and buckling of axially extensible two-layer beam subjected to a temperature rise are derived, in which the stretching-bending coupling terms produced by the non-homogenous distribution of the material properties are included. By using the shooting method to solve the corresponding nonlinear boundary value problem, numerical solutions for thermal bending of a tow-layer beam with its both ends immovably simply supported under uniform temperature rise are obtained. As an example, equilibrium paths and configurations for a beam laminated by brass and steel are presented. The effects of the geometric and physical parameters on the deformation of the beam are also examined.