Analysis of Large Deflection in a Cantilever Beam with Low Support Stiffness.

Abstract

A cantilever beam subjected to a tip load is widely used in machine elements, for example, the boom of a jib crane, an arm of an industrial robot, and an aircraft wing. In such elastic elements, a large deflection characteristic is observed without exceeding the elastic limit of the materials. This property is of both analytical and technological interest. It is necessary to analyze the large deflection behavior to achieve high reliability of the structural components. In this report, an elastica problem of a spring-hinged cantilever beam with an inclined concentrated load applied at free end is examined. Several analytical formulae are derived in terms of elliptic integrals for arc length, vertical and horizontal displacements, bending moment, curvature and bending stress. Moreover, a large flexural-bending test is performed on a thin PVC plate in order to assess the applicability of the theoretical solutions. Experimental data agree very well with the result of the large-deflection theory.