UNSTEADY CONTACT PROBLEM OF THE INDENTATION OF A RIGID PUNCH INTO AN ELASTIC HALF-PLANE

A classical contact problem of the impact of a rigid punch against an elastic half-plane is considered. The problem is reduced to the solution of the integral convolution equation of the first kind for the Laplace transform of the contact pressure distribution function. For large values of the Laplace parameter, the asymptotic solution is constructed on the basis of a special approximation of the kernel symbol of the integral equation in the complex plane. The solution of the contact problem for a flat punch is obtained in the form of simple quadratures. The analysis of the wave field of stresses in the elastic medium is presented. This problem was previously considered in [1-4] and other works.