摘要
基于可伸长梁的大变形理论,建立了受沿轴线分布切向随动载荷作用简支梁的弹性过屈曲控制方程。这是一个包含七个未知函数的强非线性常微分方程两点边值问题,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,获得了梁的过屈曲平衡路径和平衡构形。结果表明,非保守载荷作用梁的平衡路径与保守载荷作用梁的平衡路径有着明显不同。
Based on the large deformation theory for the extensible elastic beams, the governing equations of post-buckling of a simply supported elastic beam subjected to a distributed tangential follower 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 the one of the basic unknown functions. By using shooting method and analytical continuation, the nonlinear boundary-value problem is numerically solved and the equilibrium paths as well as the post-buckling configurations of the deformed beam are obtained. The results show that the features of the equilibrium paths of the beam subjected to a non-conservative load are evidently different from those to a conservative one.
出处
《工程力学》
EI
CSCD
北大核心
2003年第3期94-97,共4页
Engineering Mechanics
基金
甘肃工业大学学术梯队及特色研究方向重点资助计划基金
国家杰出青年科学基金(1005200)资助项目
关键词
非保守力
可伸长梁
打靶法
过屈曲
平衡路径
nonconservative load
extensible beam
shooting method
post-buckling
equilibrium path
