Semi-exact solutions for large deflections of cantilever beams of non-linear elastic behaviour

The problem of large deflections of cantilever beams made of materials obeying a Ludwick type stress-strain law under the combined action of one vertical concentrated force at the free end and a uniformly distributed load were investigated in the so-called bending moment formulation. A corrected bending moment is introduced and it is shown that the resulting governing differential equation for the slopes can be solved semi-analytically for some few selected cases of interest in which materials like acetal plastic and glass fibre enter. A discovered coupling between the material and geometrical non-linearities involved in the problem divides the general solution into two regions separated by one in which there is no coupling at all and where it is expected to exist an elastic critical behaviour.