Large deflection of a simply supported beam
Large deflection of a simply supported beam
The large deflection of a simply-supported beam loaded in the middle is a classic problem in
mechanics which has been studied by many people who have implemented different
methods to determine the solution, such as analytical exact solutions and the finite element
method. The problem is investigated again here but the Galerkin method is used to obtain
an approximate force-deflection characteristic of the beam. It is shown that the beam can be
modelled with a Duffing-type stiffness with hardening nonlinearity. The exact solution and
that from the finite element method are used to validate the results. The accuracy of the
results and the suitability of the Sine function to model the deflected shape of the beam in
the Galerkin method are investigated.
The large deflection of a simply-supported beam due to a pure bending moment is also
investigated. The exact solution is obtained and the results are used to describe the
behaviour of the beam.
University of Southampton
Abolfathi, A.
5992bc45-5bfd-42ba-9b7e-39c4b9789bca
Brennan, M.J.
87c7bca3-a9e5-46aa-9153-34c712355a13
Waters, T.P.
348d22f5-dba1-4384-87ac-04fe5d603c2f
August 2010
Abolfathi, A.
5992bc45-5bfd-42ba-9b7e-39c4b9789bca
Brennan, M.J.
87c7bca3-a9e5-46aa-9153-34c712355a13
Waters, T.P.
348d22f5-dba1-4384-87ac-04fe5d603c2f
Abolfathi, A., Brennan, M.J. and Waters, T.P.
(2010)
Large deflection of a simply supported beam
(ISVR Technical Memorandum, 988)
Southampton, GB.
University of Southampton
28pp.
Record type:
Monograph
(Project Report)
Abstract
The large deflection of a simply-supported beam loaded in the middle is a classic problem in
mechanics which has been studied by many people who have implemented different
methods to determine the solution, such as analytical exact solutions and the finite element
method. The problem is investigated again here but the Galerkin method is used to obtain
an approximate force-deflection characteristic of the beam. It is shown that the beam can be
modelled with a Duffing-type stiffness with hardening nonlinearity. The exact solution and
that from the finite element method are used to validate the results. The accuracy of the
results and the suitability of the Sine function to model the deflected shape of the beam in
the Galerkin method are investigated.
The large deflection of a simply-supported beam due to a pure bending moment is also
investigated. The exact solution is obtained and the results are used to describe the
behaviour of the beam.
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Published date: August 2010
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Local EPrints ID: 167815
URI: http://eprints.soton.ac.uk/id/eprint/167815
PURE UUID: a48fb9c7-5606-4356-a783-b2c9229ae1b5
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Date deposited: 18 Nov 2010 12:10
Last modified: 14 Mar 2024 02:16
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Author:
A. Abolfathi
Author:
M.J. Brennan
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