Convergence of Boobnov-Galerkin method exemplified

Abstract

In this Note, Boobnov–Galerkin’s method is proved to converge to an exact solution for an applied mechanics problem. We address in detail the interrelation of Boobnov–Galerkin method and the exact solution in the beam deflection problems. Namely, we show the coincidence of these two methods for clamped–clamped boundary conditions, using an alternative set of functions proposed by Filonenko-Borodich.12 Received 25 February 2003; accepted for publication 13 March 2004. Copyright c 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0001-1452/04 $10.00 in correspondence with the CCC. ∗J. M. Rubin Distinguished Professor, Department of Mechanical Engineering, 777 Glades Road. †Researcher, Dipartimento di Ingegneria Strutturale e Geotecnica, Viale delle Scienze. We consider a particular case of transverse concentrated load. The series is summed up and shown to coincide with well-known closed-form solutions.