Analytical Solution for Large Deflections of a Cantilever Beam under Nonconservative Load

In this paper large deflection and rotation of a nonlinear beam subjected to a co-planar follower static loading is studied. It is assumed that the angle of inclination of the force with respect to the deformed axis of the beam remains unchanged during deformation. Governing equation of thisproblem is solved analytically for the first time using a new kind of analytic technique for nonlinear problems namely the Homotopy Analysis Method (HAM). The present solution can be used in wide range of load and length for beams under large deformations. The results obtained fromHAM are compared with those results obtained by fourth order Range Kutta method. Finally, the load–displacement characteristics of a uniformcantilever under a follower force normal to the deformed beam axis are presented.

کلیدواژه ها:

Nonconservative load ، Large deformation ، Homotopy analysis method ، Nonlinear ordinary differential equation ،