Summary: 1028-3358/05/5010- $26.00 © 2005 Pleiades Publishing, Inc.0524
Doklady Physics, Vol. 50, No. 10, 2005, pp. 524528. Translated from Doklady Akademii Nauk, Vol. 404, No. 5, 2005, pp. 618621.
Original Russian Text Copyright © 2005 by Argatov.
The nonclassical contact problem for an elastic
layer is analyzed under the assumption that the thick-
ness of the layer is small as compared to the a priori
unknown contact area. The asymptotic behavior is
found for the internal stressed state. Explicit expres-
sions are derived for the boundary layer and variation of
the elliptic contact domain. The asymptotic behavior is
found for the contact pressure and its resultant.
FORMULATION OF THE PROBLEM
Let us constructively consider the nonlinear prob-
lem concerning the pressure of an elliptic-paraboloidal
die on an elastic layer with thickness H:
The displacement vector u is determined as the solu-
tion of the Lamé system that satisfies the condition of
the absence of friction and the Signorini boundary con-
dition (see, e.g., [1, 2]):