Three-dimensional contact problems of an elastic wedge are considered for the case of an elliptic punch and an extra concentrated force acting outside the contact zone on the wedge edge. The other wedge face is stress-free or subject to sliding support. Regular asymptotic solutions are constructed for the case when the contact zone is given and the punch is relatively remote from the wedge edge. For the particular case when the wedge with one stress-free face transforms into a half-space, the solution obtained for a circular contact zone coincides with the well-known Galin exact solution expanded into a power series. For an elliptic punch situated relatively nearly to the wedge edge when the contact zone is unknown, numerical solutions are calculated using the method of nonlinear boundary integral equations (BEM). The problem of interaction of two punches on one wedge face is treated with the help of the asymptotic and of the numerical method. Using the asymptotic method, the contact problems for an elastic layer are investigated for the case of an extra concentrated force acted outside an elliptic contact zone. The other layer face is fixed or subject to sliding support. Using the nonlinear BEM, the contact problems are analyzed for two identical punches on a layer face.
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