Non-prismatic Non-linearly Elastic Cantilever Beams Subjected to an End Moment

Abstract

This paper analyzes large deflection profiles of slender, inextensible cantilever beams of prismatic and non-prismatic longitudinal shapes with rectangular cross-sections subjected to a concentrated moment at the free end. The stress—strain relationship of the material is represented by the Ludwick constitutive law. Different non-linear stress—strain relations in tensile and compressive domain are considered. The main purpose of this paper is to investigate the influence of geometrical and material non-linearities on the shape of the deflection curve. The solution of a strongly non-linear set of equations is obtained numerically. In the case when non-linear stress—strain relationship in tensile and compressive domain is identical, an analytical solution is given in terms of infinite series. Several examples for a variety of different shapes of beams are presented considering both linearly and non-linearly elastic materials in the elastic domain.