Resumen:
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The nonlinear bending problem of a constant cross-section simply supported beam pinned at both ends
and subject to a uniformly distributed load qðxÞ is analyzed in detail. The numerical integration of the
two-point ...[+]
The nonlinear bending problem of a constant cross-section simply supported beam pinned at both ends
and subject to a uniformly distributed load qðxÞ is analyzed in detail. The numerical integration of the
two-point boundary value problem (BVP) derived for the nonlinear Timoshenko beam is tackled through
two different linearization schemes, the multi-step transversal linearization (MTrL) and the multi-step
tangential linearization (MTnL), proposed by Viswanath and Roy (2007). The fundamentals of these linearization
techniques are to replace the nonlinear part of the governing ODEs through a set of conditionally
linearized ODE systems at the nodal grid points along the neutral axis, ensuring the intersection
between the solution manifolds (transversally in the MTrL and tangentially in the MTnL). In this paper,
the solution values are determined at grid points by means of a centered finite differences method with
multipoint linear constraints (Keller, 1969), and a simple iterative strategy. The analytical solution for this
kind of bending problem, including the extensional effects, can be worked out by integration of the governing
two-point BVP equations (Monleón et al., 2008). Finally, the comparison of analytical and numerical
results shows the better ability of MTnL with the proposed iterative strategy to reproduce the
theoretical behavior of the beam for each load step, because the restraint of equating derivatives in MTnL
leads to further closeness between solution paths of the governing ODEs and the linearized ones, in comparison
with MTrL. This result is opposed to the conclusion reached in Viswanath and Roy (2007), where
the relative errors produced by MTrL are said to be smaller than the MTnL ones for the simply supported
beam and the tip-loaded cantilever beam problems.
2009 Elsevier Ltd. All rights reserved.
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