Title: Bending of a nonlinear beam reposing on an unilateral foundation
Authors: Machalová, Jitka
Netuka, Horymír
Citation: Applied and Computational Mechanics. 2011, vol. 5, no. 1, p. 45-54.
Issue Date: 2011
Publisher: University of West Bohemia
Document type: článek
URI: http://www.kme.zcu.cz/acm/index.php/acm/article/view/111/92
ISSN: 1802-680X (Print)
2336-1182 (Online)
Keywords: nosníky;namáhání těles;Lagrangeův formalismus;metoda konečných prvků
Keywords in different language: beams;load of bodies;Lagrange formalism;finite element method
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.
Rights: © 2011 - University of West Bohemia. All rights reserved.
Appears in Collections:Volume 5, number 1 (2011)
Volume 5, number 1 (2011)

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