M. Barboteu, M. Sofonea and D. Tiba The control variational method for beams in contact with deformable obstacles ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 92
The authors consider a mathematical model which describes the equilibrium of an elastic beam in contact with two obstacles. The contact is modeled with a normal compliance type condition in such a way that the penetration is allowed but is limited. They state the variational formulation of the problem and prove an existence and uniqueness result for the weak solution. Then, they provide an alternative approach to the model, based on the control variational method. Necessary and sufficient optimality conditions are derived, together with an approximation property. They also adapt your results to some versions of the model which describe the contact with a single obstacle. For this type of problems they present two methods of numerical approach, based on the iterative control variational method and the Newton method, respectively, and provide numerical simulations for the two algorithms.
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