Abolfathi, A., Brennan, M.J. and Waters, T.P.
Large deflection of a simply supported beam. Southampton, GB, University of Southampton, 28pp.
(ISVR Technical Memorandum, 988).
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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