Non-stationary Contact Problems for Thin Shells and Solids

A spatial non-stationary contact problem with moving boundaries of the interaction region for a thin elastic cylindrical shell and an absolutely rigid indenter bounded by a smooth convex surface is considered. A closed mathematical formulation is given and a system of resolving equations is constructed. The system of resolving equations is based on the spatial-temporal integral equation resulting from the principle of superposition and contact conditions. The core of this equation is the transient function for the cylindrical shell. To a closed system of resolving equations, it is supplemented by a kinematic relation for determining the moving boundary of the contact area and the equation of motion of the indenter as an absolutely rigid body. An algorithm for solving the spatial non-stationary contact problem for an infinitely long cylindrical shell and absolutely rigid indenter in the case of a normal impact on the side surface of the shell is constructed and implemented. Examples of calculations are given.