非保守力作用下可伸长简支梁的过屈曲

Post-buckling of a simply supported extensible elastic be am under a non-conservative distributed load

基于可伸长梁 (杆 )的大变形理论 ,建立了受沿轴线分布切向非保守力作用的可伸长简支梁的弹性过屈曲控制方程 .这是一个强非线性常微分方程边值问题 ,其中将变形后的轴线弧长作为基本未知量之一 ,使得求解区间仍然为梁的原长 .采用打靶法求解该边值问题 ,获得了数值意义上的精确解 ,给出了梁的过屈曲平衡路径及平衡构形 .结果表明 ,过屈曲平衡路径不是载荷的单调函数和单值函数 .对于机械载荷作用的细长梁 ,轴向伸长可以忽略 .

Based on the large deformation theory of ex te nsible elastic beams, governing equations of post buckling of a simply supporte d elastic beam subjected to a non conservative distributed tangential load alon g the central axis are established. They consist of a boundary value problem of ordinary differential equations with a strong non linearity, in which the arc length of the deformed axis is considered as the one of the basic unknown functi ons in this problem. By using shooting method, the obtained boundary value prob lem is numerically solved and the equilibrium paths as well as the post buckled configurations of the deformed beam are given.It can be seen from the results t hat the post buckling equilibrium path is not a monotonic and a single valued function of the load. For a slender beam subjected to mechanical loads, the axia l extension can be neglected.