On dynamic contact problems for an elastic half-plane with initial stresses in the case of a moving rigid punch

Abstract

Dynamic contact problems are investigated for an elastic half-plane with initial stresses with an absolutely rigid punch that moves along the boundary of the elastic half-plane. The investigation employs a version of linearized elasticity theory proposed in the author’s previous publications. The stresses and displacements of the linearized elasticity theory are represented by analytical functions of complex variables in the case of dynamic problems. An exact solution for dynamic contact problems for the general case of distinct roots of the main equation is presented in a very brief form. Exact solutions of contact problems for a particular case of distinct roots and a general case of equal roots were presented in the author’s previous publications in a very brief form as well. It should be noted that the above-mentioned results were obtained for compressible and incompressible bodies with an arbitrary elastic-potential structure.