Bending of a nonlinear beam reposing on an unilateral foundation
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Date issued
2011
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Publisher
University of West Bohemia
Abstract
This article is going to deal with bending of a nonlinear beam whose mathematical model was proposed by
D. Y. Gao in (Gao, D. Y., Nonlinear elastic beam theory with application in contact problems and variational
approaches,Mech. Research Communication, 23 (1) 1996). The model is based on the Euler-Bernoulli hypothesis
and under assumption of nonzero lateral stress component enables moderately large deflections but with small
strains. This is here extended by the unilateralWinkler foundation. The attribution unilateral means that the foundation
is not connected with the beam. For this problem we demonstrate a mathematical formulation resulting
from its natural decomposition which leads to a saddle-point problem with a proper Lagrangian. Next we are concerned
with methods of solution for our problem by means of the finite element method as the paper (Gao, D. Y.,
Nonlinear elastic beam theory with application in contact problems and variational approaches, Mech. Research
Communication, 23 (1) 1996) has no mention of it. The main alternatives are here the solution of a system of
nonlinear nondifferentiable equations or finding of a saddle point through the use of the augmented Lagrangian
method. This is illustrated by an example in the final part of the article.
Description
Subject(s)
nosníky, namáhání těles, Lagrangeův formalismus, metoda konečných prvků
Citation
Applied and Computational Mechanics. 2011, vol. 5, no. 1, p. 45-54.