Judging the relative qualities and merits of Galerkin's approximate solutions to a dynamically loaded beam system

Abstract

Galerkin's method is applied to a beam structure that is forced to nonlinear behavior by a dynamic load. Nonlinearities in the system include a nonlinear stress-strain relation and consideration of geometry changes due to large deflections. Several trial deflection shapes are assumed as approximate solutions of the problem and these trial shapes are combined in various manners in an effort to produce a better quality solution. All resulting solutions are studied in the light of three criteria that are postulated in an attempt to define the relative merits and qualities of approximate solutions. It is concluded that although the criteria are good guidelines to finding reasonable solutions, they are not strict in defining a good quality solution.