Abstract:
A nonlinear mathematical model of the equilibrium of a plate contacting with two obstacles is investigated. The first non-deformable obstacle is defined by inclined generatrices, and the second one restricts the plate displacements on the side face. In this case, the plate can contact both along the side edge and at the points of the curve corresponding to the intersection of the front surface of the plate and the side cylindrical surface of the plate. These circumstances lead to the fact that boundary conditions are imposed in the form of three inequalities fulfilled on the same curve. Along with the model of a homogeneous plate, the case of a nonhomogeneous plate in which a rigid inclusion is located near the contact boundary is also considered. The unique solvability of the problems for both models is proven. Under the condition of additional smoothness of the solutions to these problems, optimality conditions are found in the form of boundary conditions, as well as the corresponding equivalent differential formulations.
Keywords:variational problem, inclined obstacle, plate, non-penetration condition, contact problem
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