2019
Том 71
№ 11

All Issues

Lozhkin V. N.

Articles: 2
Brief Communications (Russian)

Conditions of existence of univalently stressed contours in the first main problem of the theory of elasticity for a plane with cut

Lozhkin V. N.

↓ Abstract   |   Full text (.pdf)

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.

Article (Russian)

Limiting equilibrium of a plane with a circular hole

Lozhkin V. N.

↓ Abstract   |   Full text (.pdf)

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.