Intuitive analytical solution for the uniformly loaded elastica using elliptic integrals.

In this work, an approximate analytical solution was given for the large deformation of a cantilever beam subjected to a uniformly distributed load using elliptic integrals and Jacobi elliptic functions. The formulation is based on reducing the differential equation of the problem to the same one that describes the classical, force-loaded elastica by introducing a modified arc length parameter. A new, intuitive formula was given for the relation between the deflection angle and the non-dimensional load. The results were validated by the nonlinear shooting method with the Matlab program. The method can be used only in the case of one inflection point, but gives accurate results even for extremely large deflections. [ABSTRACT FROM AUTHOR]