Non-symmetrical plane contact of a wedge indenter

Asymmetric contact problem of an elastic wedge and an elastic half-plane has been considered. Contact pressure distributions as well as the lengths of the contact zones are extracted analytically. The results have been compared with the results of the symmetric problem and also the FE modelling of the problem which show excellent agreement. The method of approach is a completely analytical method based on the singular integral equations. In this method, the boundary conditions of the problem are stated as some singular integrals and distribution of the contact pressure is determined. Then, with the aid of the equilibrium equations and the consistency conditions of the singular integral solution, the lengths of the contact zones are extracted. Finally, using the Muskhelishvili potential function and Legendre polynomials, a new method for calculating stress field has been established. It is shown that application of Legendre polynomials is simpler than Chebyshev polynomials which have been used widely in the previous researches.