Large deflections of a cantilever beam subjected to a rotational distributed loading

Abstract

Large deflection problems of a uniform cantilever beam under a rotational distributed loading are formulated by means of a second order nonlinear integro-differential equation. The problem is numerically solved by considering a uniform rotational distributed load and a linearly varying rotational distributed load along the span of the beam. The details of load deflection curves are presented. Assuming Dirac delta function as a load distribution function along the span of the beam, the present general formulation yields the solution for the problem of a uniform cantilever beam with end rotational concentrated load. The numerical results for this case are found to be in good agreement with existing closed form solutions. As the formulation is general, the problem with nonuniform rotational distributed load of any complexity can be solved following the present numerical procedure which is quite simple, accurate and involves less computational time.