Large deflections of cantilever beams of nonlinear materials

Abstract

This paper deals with the large deflections (finite) of thin cantilever beams of nonlinear materials, subjected to a concentrated load at the free end. The stress-strain relationships of the materials are represented by the Ludwick relation. Because of the large deflections, geometrical nonlinearity arises and, therefore, the analysis is formulated according to the nonlinear bending theory. Consequently, the exact expression of the curvature is used in the moment-curvature relationship. The resulting second-order nonlinear differential equation is solved numerically using fourth-order Runge-Kutta method. For comparison purposes, the differential equation is solved for linear material and the results are compared to the exact solution which uses elliptic integrals. Deflections and rotations along the central axis of beams of nonlinear materials are obtained. The numerical algorithm was performed on the UNIVAC 1110.