Abstract
The formulations of unilateral contact problems are considered that are based on the application of the method of nonlinear boundary integral equations (BIE). Such formulations of problems, the modern methods of the nonlinear analysis and theory of operator equations allow in the rather general cases (e.g. in the cases of unconnected and multiple-connected contact areas, multibody contact) to investigate the existence and uniqueness of their solutions, as well as some their properties. Besides, the possibility arises to apply the methods of solution equations which do not use the optimization algorithms and which can use a well-developed general purpose software. The theoretical basis and ideas of the method of BIE discussed here are described on the examples of contact problems which, we believe, sufficiently fully reflect the general nature of this method and variety of possibilities for the investigation of BIE. The theory is illustrated by the numerical examples for some engineering applications. Some unsolved problems are indicated.
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