The Approximate Solutions of Large Deflection of a Cantilever Beam under a Point Load

Abstract

By integrating the physical and time domains with the Galerkin method and adopting approximate solutions satisfying the boundary conditions, a set of algebraic equations of nonlinear nature is obtained from the nonlinear differential equation of an elastic beam for the undetermined coefficients of solutions of the deflection. These coefficients are to be used with the approximate basis functions for the asymptotic and explicit solutions of the nonlinear differential equation of flexure of a beam widely known as an elastica. Taking advantage of powerful tools for the symbolic manipulation of algebraic equations, such a novel method and procedure offer a new and efficient approach and option with known linear solutions in dealing with increasingly complex nonlinear problems in practical applications of both static and dynamic nature.