Equilibrium Configurations of Cantilever under Terminal Loads

Abstract

The paper provides an exact analytical solution for equilibrium configurations of cantilever rod subject to inclined force and torque acting on its free end. The solution is given in terms of Jacobi elliptical functions and illustrated by several numerical examples and several graphical presentations of shapes of deformed cantilever. Possible forms of cantilever underlying elastica are discussed in details and various simple formulas are given for calculation of characteristic dimensions of elastica. For the case when cantilever is subject only to applied force four load conditions are discussed: follower load problem, load determination problem, conservative load problem and rotational load problem. For all the cases the formulas or effective procedure for solution is given.