On the determination of displacements in the Galin problem

Elastoplastic problem of an extended cylindrical working

“…The elastoplastic problem of bilateral tension (compression) of a plane with a circular hole was solved in [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The elastoplastic problem of bilateral tension (compression) of a plane with a circular hole was solved in [2][3][4][5][6][7][8][9][10][11][12][13][14][15].…”

“…

From a math~me~tical viewpoint, the given problem is equivalent to the problem of bilateral compression of a plane with a circular hole. In [2][3][4][5][6][7][8][9][10][11][12][13], the case of a plane-deformed state was investigated, and in [14, 15] the case of a plane-stressed state. In [2][3][4][5][6][7][8][9][10][11][12][13], the case of a plane-deformed state was investigated, and in [14, 15] the case of a plane-stressed state.

…”

“…It is assumed that a state of plane deformation is realized in its vicinity, the plastic state of the rock mass is determined by the Coulomb~ohr condition, and that the relation of [1] holds. In [2][3][4][5][6][7][8][9], the case of complete coverage of the hole periphery by the elastoplastic boundary was investigated, and the elastoplastic boundary was determined, together with the stresses and displacements in the elastic region of deformation. A step-by-step method of solution is proposed for the elastoplastic problem.…”

“…In [3,7,9], the problem of determining the displacements in the plastic region of deformation was solved; the relations of deformational theory of plasticity were used. The case of incomplete coverage of the periphery of the circular hole by the elastoplastic boundary was investigated in [4,5,[10][11][12], where the Tresk condition was taken as the plasticity condition.…”

Use of elastoplastic analysis in the relief method

“…1). Furthermore, the problem of determination of displacements in the plastic region, and therefore at the periphery (since it is postulated that the plastic zone completely encompasses the hole), has been solved in completed form only in the Galin problem [11][12][13]. Furthermore, the problem of determination of displacements in the plastic region, and therefore at the periphery (since it is postulated that the plastic zone completely encompasses the hole), has been solved in completed form only in the Galin problem [11][12][13].…”