Large deflection of a cantilever beam with multiple geometric and/or material discontinuities under a concentrated end-point load

In this paper, large deflection problem of a discontinuous cantilever beam with multiple step changes in material and/or geometry is analyzed using elliptic integral method. The main objective is to solve the problem without using direct integration methods such as Runge-Kutta that is available to solve ordinary differential equations. The considered beam is assumed to be made of a linear elastic material with an external vertical load at the free end. At first, differential equations governing the behavior of a cantilever beam with one step change are presented. Then, considering the boundary conditions at the free end, the clamped point and the discontinuity point, two relations which represent the horizontal and vertical coordinates of any point along the neutral axis of the beam are obtained. The presented formulations are extended for the cantilever beams with arbitrary numbers of step changes in geometry and/or material. The accuracy of the obtained results for beams with one and two step changes in the material and geometry are verified using finite element results. The presented formulations can be used for modeling and optimization of structures that consist of step change beams.