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2015 Solution of Contact Problems for Nonlinear Gao Beam and Obstacle
J. Machalová, H. Netuka
J. Appl. Math. 2015: 1-12 (2015). DOI: 10.1155/2015/420649

Abstract

Contact problem for a large deformed beam with an elastic obstacle is formulated, analyzed, and numerically solved. The beam model is governed by a nonlinear fourth-order differential equation developed by Gao, while the obstacle is considered as the elastic foundation of Winkler’s type in some distance under the beam. The problem is static without a friction and modeled either using Signorini conditions or by means of normal compliance contact conditions. The problems are then reformulated as optimal control problems which is useful both for theoretical aspects and for solution methods. Discretization is based on using the mixed finite element method with independent discretization and interpolations for foundation and beam elements. Numerical examples demonstrate usefulness of the presented solution method. Results for the nonlinear Gao beam are compared with results for the classical Euler-Bernoulli beam model.

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J. Machalová. H. Netuka. "Solution of Contact Problems for Nonlinear Gao Beam and Obstacle." J. Appl. Math. 2015 1 - 12, 2015. https://doi.org/10.1155/2015/420649

Information

Published: 2015
First available in Project Euclid: 13 October 2015

zbMATH: 07132064
MathSciNet: MR3399550
Digital Object Identifier: 10.1155/2015/420649

Rights: Copyright © 2015 Hindawi

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