Existence of generalized solutions of contact problems for a nonlinear shallow shell with a rigid obstacle is demonstrated. A mathematical model accounting for the presence of an obstacle is proposed. The solution is a minimizer of the total energy functional on the set of admissible displacements. The problem reduces to the solution of a variational inequality in a cone of the energy space.
Khludnev, A. M.Variational approach to a contact problem of a shallow shell and a rigid body [in Russian] . Differential Equations in Partial Derivatives, 2, 109-114 (1981).
2.
Kikuchi, N. and Oden, J. T.Contact Problems in Elasticity: a Study of Variational Inequalities and Finite Elements, SIAM, Philadelphia, PA , 1988.
3.
Bernadou, M. and Oden, J. T.An existence theorem for a class of nonlinear shallow shell problems , Journal de Mathématiques Pures et Appliquées, 60, 285-308 (1981).
4.
Vorovich, I. I.Nonlinear Theory of Shallow Shells, Springer, New York , 1999.
5.
Vorovich, I. I. and Lebedev, L. P. : On the finite element method in the nonlinear shallow shell theory . Russian Journal of Computational Mechanics, 1, 85-106 (1993).
6.
Lebedev, L.P. and Vorovich, I.I.Functional analysis in mechanics, Springer, New York , 2002.
7.
Koiter, W. T.On the nonlinear theory of thin elastic shells, I, II, III . Nederlandse Akademie van Wetenschappen Proceedings, B69, 1-54 (1966).
8.
Neymark, A. B. and Lebedev, L. P.Equilibrium of an arch with an obstacle [in Russian] . Izvestiya Vuzov. Severo-Kavkazskiy Region. Estestvennie Nauki, 4, 67-71 (2001).
9.
Lions, J.-L. and Magenes, E.Problemes aux Limites non Homogènes et Applications: V, Vol. 1, Dunod, Paris , 1968.
10.
Bernadou M. , Ciarlet P. G. , and Miara B.Existence theorems for two-dimensional linear shell theories . Journal of Elasticity, 34, 111-138 (1994).
