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首页> 外文期刊>International journal of non-linear mechanics >Elastica of a variable-arc-length circular curved beam subjected to an end follower force
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Elastica of a variable-arc-length circular curved beam subjected to an end follower force

机译：弧长可变的圆弧形梁在末端跟随力的作用下

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摘要

This paper presents postbuckling behaviors of a variable-arc-length (VAL) circular curved beam subjected to an end follower force. One end of the VAL circular curved beam is hinged while the other end is supported by a frictionless slot, which is fixed horizontally and vertically but is allowed to rotate corresponding to loading direction. When the VAL circular curved beam is deformed, the total arc-length of the circular curved beam varies. Two approaches have been applied for the solution of this problem. The first approach is an elliptic integrals method based on elastica theory, which yields the exact closed-form solution in terms of the first and second kinds of elliptic integrals. For validation of the results, the shooting method is employed for a numerical solution by developing the set of nonlinear governing differential equations together with boundary conditions, and then integrating them by using the fourth-order Runge-Kutta algorithm. The results from both approaches are in very good agreement. From the results, it is found that the VAL circular curved beam subjected to an end follower force can be deformed in many mode shapes. For the first and third modes, the beam exhibits both stable and unstable configurations, whereas for the second mode only an unstable configuration exists. The influences of initial curvature on the critical load and the deformed configurations are highlighted.
机译：本文介绍了可变弧长（VAL）圆弧形弯曲梁在末端跟随力作用下的后屈曲特性。 VAL圆形弯曲梁的一端是铰接的，而另一端则由无摩擦的槽支撑，该槽在水平和垂直方向上固定，但可以根据加载方向旋转。当VAL圆形弯曲光束变形时，圆形弯曲光束的总弧长会发生变化。解决此问题的方法有两种。第一种方法是基于弹性理论的椭圆积分方法，它根据第一类和第二类椭圆积分产生精确的闭合形式解。为了验证结果，采用射击方法进行数值解，方法是将非线性控制微分方程组与边界条件一起开发，然后使用四阶Runge-Kutta算法对其进行积分。两种方法的结果非常吻合。从结果发现，受到末端跟随力的VAL圆形弯曲梁可以以多种模式形状变形。对于第一和第三模式，光束表现出稳定和不稳定的配置，而对于第二模式，仅存在不稳定的配置。突出了初始曲率对临界载荷和变形构型的影响。

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