Transient Contact Interaction of Solid Bodies and Thin Shells

Abstract

A spatial transient contact problem with moving boundaries for a thin elastic cylindrical shell and a 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 main integral equation follows 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 region and the equation of motion of the indenter as a rigid body. An algorithm for solving the spatial non-stationary contact problem for an infinitely long cylindrical shell and 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.