Exact Solutions to a Problem in Terms of Stresses for Incompressible Elastic Conical Bodies / D. V. Georgievskii. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2017. № 4. P. 69-71 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 101-102].

Exact solutions to the elasticity theory problem in terms of stresses for an incompressible conical body of arbitrary shape under the action of a given concentrated force applied at its vertex are given and analyzed. A solution in terms of stresses with a singularity whose order is higher by one than that in the classical solution is discussed. The surface load at the boundary of the conical body corresponding to such a solution is obtained.

Key words: conical solid, incompressible elastic material, point force, stress, Beltrami compatibility equations, singularity, surface load.

№ 4/2017