On the determination of stresses in the case of a plastic problem with an ellipsoidal cavity

The material of the work is an integral element of the problem of determining the stress-strain state of various types of arrays, including various forms of recess. In the current problem, the stress state is determined in the plastic zone near an ellipsoidal recess for a compressible mass. There is no pressure inside the recess, and at a considerable distance there is compression by mutually perpendicular forces. A solution is obtained for the case of the first approximation by the small parameter method. The results can be applied in the field of structural mechanics, mining business, and other related fields.