Large deflections of cantilever beams of non-linear materials of the Ludwick type subjected to an end moment

Abstract

This paper deals with the large deflections (finite) of thin cantilever beams of non-linear materials of the Ludwick type. The beam is subjected to an end constant moment. Large deflections of beams induce geometrical non-linearity. Therefore, in formulating the analysis, the exact expression of the curvature is used in the Euler-Bernoulli law. A closed-form solution is presented for the resulting second-order non-linear differential equation. This solution is compared to previous results assuming linear elastic materials. Deflections at the free end of beams of aluminum alloy and annealed copper are obtained.