弹性曲梁在机械和热载荷共同作用下的几何非线性模型及其数值解

基于Euler-Bernoulli梁的几何非线性理论,建立了弹性曲梁在任意分布机械载荷和热载荷共同作用下的几何非线性静平衡控制方程。该模型不仅计及了轴线伸长,同时也精确地考虑了梁的初始曲率对变形的影响以及轴向变形与弯曲变形之间的相互耦合效应。应用打靶法数值求解了半圆形曲梁在横向均匀升温作用下的非线性弯曲问题,数值比较了轴向伸长对曲梁变形的影响。

Geometrically nonlinear model and numerical simulation of elastic curved beams subjected to mechanical and thermal loads

Based on an exact geometrically nonlinear theory of Euler-Bernoulli beams,geometrically nonlinear static equilibrium governing equations of the large deformation of elastic curved beams under mechanical and thermal loads are derived.The equations contain seven independent unknown functions such as the arc length,the displacements of the central line,the rotational angle and the resultant internal forces at a cross section.By introducing the deformed arc length as one of the unknown functions,it makes the range of the spatial variables of the problem still within the undeformed length of the beam.In the mathematical model,the effects of the axial elongation,the initial curvature,and the stretching-bending coupling on the beam deformation are accurately taken into account.As a numerical example,nonlinear bending of a semicircle beam subjected to transversely uniform temperature rise is studied by shooting method.The influence of axial extension on the deformation of curved beam is compared with that being neglected through numerical results.