横向随动分布载荷作用下悬臂梁的非线性弯曲

基于可伸长梁的大变形理论,建立了悬臂梁受垂直轴线均匀分布非保守载荷作用下的几何非线性静平衡控制方程.这是一个包含7个未知函数的强非线性常微分两点边值问题,其中将变形后的轴线弧长也作为基本未知量之一.采用打靶法和解析延拓法数值求解所得非线性边值问题,获得了数值意义上的精确解,给出了梁的非线性弯曲特征曲线.结果表明,非保守载荷作用下,载荷与各相关物理量呈现明显的非线性性,非保守载荷作用下的载荷变化范围比保守载荷作用下的要大得多.

Nonlinear Bending of a Cantilever Beam Subjected to a Conservative Force

Based on the large deformation theory for the extensible beams,the governing equations for axially extensible cantilever elastic beam subjected to a distributed conservative force along the central axis are established.They consist of a boundary value problem of ordinary differential equations with strong non-linearity,in which seven unknown functions are included and the arc length of the deformed axis is considered as one of the basic unknown functions. By using the shooting method and analytical continuation,the nonlinear boundary-value problem is numerically solved,and a non-linear bending curve of the deformed beam is obtained. The results show that the features of the equilibrium paths of the cantilever beam are evidently in non-linearity.The changes of non-conservative loads of loads are much greater in scope than the conservative loads.