弹性欧拉梁大变形分析的椭圆积分统一形式

一端固支、一端受集中载荷的欧拉梁受载问题是一种基础的力学模型，具有重要的理论研究意义。针对传统的线性求解方法在大变形分析中不适用及无法计算中心定向受压杆在载荷系数超过临界值后屈曲变形的问题，提出一种非线性精确解来进行受集中载荷梁的大变形计算方法。通过椭圆积分形式来推导受集中载荷梁的变形表达，考虑在固支梁自由端加载任意角度下的定向载荷及随动载荷，给出形式统一的梁大变形方程，求解一定载荷因子系数及载荷方位角组合下的变形结果；同时利用此形式对定向受压杆的平衡分支解问题进行了分析。所提方法计算结果准确，可以应用于弹性欧拉梁受定向及随动载荷的大变形分析。 

Unified form of large deflection analysis of elastic Euler beam based on elliptic integral

The loading problem of Euler beam with one end clamped and one end having concentrated load is a basic mechanical model, which has important theoretical significance. In order to solve the problem that the traditional linear method is not applicable to large deflection analysis and cannot calculate the post buckling deflection of the central direction compressed column when the load coefficient exceeds the critical value, a nonlinear exact solution is proposed to calculate the large deformation of the beam under concentrated load. In this paper, the elliptic integral form is used to derive the deflection expression of the beam under concentrated load. Considering the dead force and follower force at any angle on the free end of the fixed-supported beam, a large deflection equation of the beam in a unified form is given. The deflection results under the combination of load factor and load angle are calculated. At the same time, the balance branch solution of the compressed column with dead force is analyzed using this form. The calculation results of this method are accurate and can be applied to the large deflection analysis of elastic beam under dead force and follower force.