In earlier works of the authors related to the investigation of the properties of hidden defects in materials with coverings, a number of features was established for defects and coverings, differently bonded to the substructure or substrate. In particular, it should be pointed out that on a number of occasions a contact of covering with the substrate can be rigid, though the nature of the loading of the covering is such that some components of contact straining in the interaction zone of the covering with the substructure can be neglected. So, if the covering is loaded, as a rule, by forces normal to the covering standards, then in the area of the contact of the covering with the substrate, tangential straining, very accurately, can be neglected. Then you can take into consideration the boundary problem in simplified position the contact of the covering with the substrate without friction. If the covering is thin enough in thickness, then if there are significant tangential effects and in the absence of normal forces, we can consider the boundary problem under the assumption of flexible contact, that is, with neglect of normal components. The mentioned types of the boundary problems were studied in many works of authors. At the same time, in connection with the complexity, the tridimensional boundary problem for the object with rigid bonded covering has not studied before. In this setting, in the contact area of the covering with the substrate all three components of the contact straining arise, none of which can be neglected. The covering experiences a general type of the impact, as normal, and tangent. It is this type of formulation of the boundary problem for an object with covering that is considered in this article.

В более ранних работах авторов, связанных с исследованием свойств скрытых дефектов в материалах с покрытиями, был установлен ряд особенностей для дефектов и покрытий, по-разному скрепленных с основанием или подложкой. В частности, следует заметить, что в ряде случаев контакт покрытия с подложкой может быть жестким, однако характер нагружения покрытия такой, что некоторыми компонентами контактных напряжений в зоне взаимодействия покрытия с основанием можно пренебречь. Так, если покрытие нагружается в основном усилиями, нормальными к границе покрытия, то в зоне контакта покрытия с основанием касательными напряжениями с высокой степенью точности можно пренебрегать. Однако это дает неточное решение. В настоящей работе предпринята попытка исследования проблемы в точной постановке. Получен новый результат о поведении контактных напряжений на границах зон контакта.