Solution of a Plane Contact Problem of the Theory of Elasticity on the Basis of an Elastic Half-Space Model

A theoretical solution of a plane contact problem of the theory of elasticity based on a method of determination of the convergence of elastic bodies using an elastic half-space model is presented, and the contact deformation (diameter change) of circular cylinders with parallel axes is determined on its basis. The possibility of obtaining a precise solution for the problem, using an elastic half-space model based on the Hertz theory, is demonstrated for the first time. It is shown that the known Kovalskii solution for contact deformation of circular cylinders with parallel axes is a rough approximation of a more precise solution of the problem. It is found that the obtained result agrees well with the Dinnik's experimental data.