A model of deformations of a rod – console with a displacement limiter

In the present paper a model of deformations of a singular rod – console under the influence of an external force is studied. We assume that one of the ends of the rod is hinged, and the displacement of the free end of the console is restricted by a limiter. Depended on the applied external force this end of the console either remains the internal point of the limiter or touches the boundary of the limiter. The corresponding model is implemented in the form of a boundary value problem for an integro-differential equation with the Stieltjes integral and a nonlinear boundary condition. A variational justification of the model is carried out; the necessary and sufficient conditions for the minimum of the corresponding potential energy functional are established; theorems of existence and uniqueness of the solution to the model are proved; a formula for representing of the solution is written out explicitly; the solution dependence on the size of the limiter is studied. Acknowledgements The work is supported by the Russian Science Foundation (project number 22-71-10008).