Indentation of the Regular System of Punches into the Foundation with Routh Coating

Abstract

We study plane contact problem for ageing viscoelastic bases with regular finite systems of rigid punches. The case in which the punch and the coating surfaces are conformal (mutually repeating) is under consideration. Such problems can arise, for example, when the punch immerses into a solidifying coating before its complete solidification, e.g. into some sort of glue or new concrete. The shape of thin coating as well as the shapes of the punches bases can be described by rapidly changing functions. These problems arises when designing of machines and mechanisms, when dealing with erection of structure complexes on bases and foundations, when determining the admissible tilt angle of objects erected in close proximity to each other, or when reinforcing engineering or civil engineering structures, when designing and assembling structures that are in close vicinity to each other, etc. We obtain the system of basic integral equations with the system of additional conditions, convert it into one operator equation with two additional vector conditions, and construct its analytical solution by using a generalized projection method.