Closed-form solution of large deflection of a spring-hinged beam subjected to non-conservative force and tip end moment

• Nonlinear cantilever spring-hinged beam with nonconservative loads is investigated.
• An exact closed form solution under tip moment and end follower force is obtained.
• The springs at the hinged support were considered to be either linear or nonlinear.
• Results obtained by this analytical method are in good agreement with literature.
• The applied analytical method is more efficient than other numerical techniques.

The thrust of this paper is to present a novel approach to obtain the closed-form solutions of large deflection of beams subjected to inclined non-conservative load and tip-end moment. The beams are free at one end and spring-hinged at the other end, the spring at the hinged support is assumed to be nonlinear. The mathematical formulation based on Euler–Bernoulli nonlinear beam theory is presented, and the governing differential equation for the problem is established. The nonlinear governing differential equation was solved using the elliptic integral approach. The results were extensively analyzed and compared with existing solutions based on various numerical methods in the literature. The analytical solution presented shows very good agreements with those from literature with more adequateness, efficiency, and less time effort.