Shyshkanova G. Three-dimensional contact problem solving for unknown doubly-connected contact domains

Three-dimensional contact interaction of elastic bodies is researched at the present work. The problem determined by double integral equations containing integrals of simple fiber potential type. Analytic and numerical-analytic methods for solution of the problem with unknown contact domain are developed. The methods are based on small parameter expansion of simple fiber potential distributed along doubly-connected and different from circular ring domain. Expansion of simple fiber potential is obtained when density has no circular symmetry. Coefficient of roughness deformation could be used as a parameter of regularization. There are investigated next cases: non-plane elliptical ring punch; contact of two bodies initially touched in a point; punch in shape of revolution accounting binomial friction law; plane punches with base of arbitrary shape taking into account various laws of roughness, friction. Shape and sizes of contact domain, normal pressure distribution, embedding and inclination angles areobtained. Influence of punch shape, roughness and friction coefficients values is analyzed. Application is in industry, building