Spatial Non-Stationary Contact Problem for a Cylindrical Shell And Absolutely Rigid Body

Abstract

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