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Unilateral elastic subsoil of Winkler's type: Semi-coercive beam problem

Stanislav Sysala (2008)

Applications of Mathematics

The mathematical model of a beam on a unilateral elastic subsoil of Winkler's type and with free ends is considered. Such a problem is non-linear and semi-coercive. The additional assumptions on the beam load ensuring the problem solvability are formulated and the existence, the uniqueness of the solution and the continuous dependence on the data are proved. The cases for which the solutions need not be stable with respect to the small changes of the load are described. The problem is approximated...

Vibrations of a beam between obstacles. Convergence of a fully discretized approximation

Yves Dumont, Laetitia Paoli (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider mathematical models describing dynamics of an elastic beam which is clamped at its left end to a vibrating support and which can move freely at its right end between two rigid obstacles. We model the contact with Signorini's complementary conditions between the displacement and the shear stress. For this infinite dimensional contact problem, we propose a family of fully discretized approximations and their convergence is proved. Moreover some examples of implementation are presented....

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