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| This contribution will deal with the issue related to contact problems. We want to formulate, analyze and numerically solve a contact of a large deformed beam with an elastic obstacle. The beam model is governed by a nonlinear fourth-order differential equation developed by D.Y. Gao, while the obstacle is considered as the elastic foundation of the Winkler's type in some distance under the beam. The contact is static and modeled by using the contact conditions with normal compliance and without a friction. In contrast to usual formulations based on variational inequalities we can infer for our problem a nonlinear variational equation. The problem under consideration is then reformulated as an optimal control problem what is useful both for theoretical aspects as well as 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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