An asymptotic method of solving transient dynamic contact problems

Abstract

Using a special approximation in the complex plane of the symbol of the kernel of the contact-problem integral equation, an asymptotic form of its solution is constructed which is the fundamental solution of the transient dynamic plane contact problem of the impact of a rigid punch with an elastic half-plane for short interaction times. The proposed approximation of the kernel symbol enables it to be approximated in the complex plane with any previously specified accuracy. Unlike existing approaches [1, 2, etc.], the approximation of the kernel symbol of the integral equation employed here enables the solution of this problem to be obtained in the form of simple formulae not containing singular quadratures.