Zhupans'ka O. Compression of spherical and cylindrical elastic bodies in assumption of non-hertzian contact

Elastic sphere, half-space, cylinder. To obtain solutions of contact compression problems of spherical and cylindrical bodies taking into account the real curvature of bodies' surfaces and the friction in contact zone. Research methods include the paired series-equations method, the integral Fourier and Mehler-Fok transforms, Wiener-Hopf technique. Solutions are obtained for problem of contact pressing of elastic spheres by concentrated forces applied in their centers, problems of frictional contact of a rigid cylinder with an elastic half-space and a rigid sphere with an elastic half-space. The non-uniqueness of the solutions under the Spence's hypothesis of self-similarity is determined. A difference between the relative sizes of zones for the planar and axisymmetric problems is pointed out