Matuzko Y. Spatial contact problems for the elastic multilayer foundation with smooth border

The multilayer foundation is a package which includes the finite number of the weightless isotropic plane-parallel layers. The package is situated in the semispace (rigid or elastic). The neighbor layers can be either coupled or they can slip without delay. The contact types of the layers may alternate arbitrarily. The space contact problem connected with determination of the normal stresses under die, unknown beforehand domain of the contact and stresses and displacements in the foundation. This problem has been reduced to the solution of two-dimensional nonlinear integral equation by Hankel integral transformation and method of functions of pliability. The circuit of discretization of a obtained integral equation is offered. The rectangular do-main of the foundation surface which exceeds the domain of contact is subdivided into rectangular elements. Nonlinear system of equations with respect to unknown normal stresses is solved by Zendel method. The designed method allows to decide spatial contact problems for the multilayer foundation with any finite number layers for a die with arbitrary not necessarily convex form of a trough. With the help of this method it is possible to determine not only unknown domain of a contact and contact pressures in her, but also stresses and displacements in an arbitrary point inside the multilayer foundation. On examples of the solution of a series of new contact problems the capability of a phenomenon of backlog of a trough of a flat die from the foundation is established.