弹性欧拉梁大变形分析的椭圆积分统一形式

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.