Lozhkin V. N.
Conditions of existence of univalently stressed contours in the first main problem of the theory of elasticity for a plane with cut
Ukr. Mat. Zh. - 1995. - 47, № 2. - pp. 295–296
A definition of a univalently stressed contour in a compressible isotropic plane with a curvilinear cut is given, which extends the notion of an equiresistant contour. Conditions for elliptic and square contours to be univalently stressed are formulated and proved.
Limiting equilibrium of a plane with a circular hole
Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 980–981
The elastoplastic state of a compressible isotropic plane with a circular hole is studied by the method of a small parameter. An unknown boundary separating the domain of limiting equilibrium and the elastic domain is determined. We construct the complex Kolosov-Muskhelishvili functions that describe the elastic state of a plane and compare these with the solutions of Galin's problem.
