THE CONTACT PROBLEM FOR A SHALLOW SHELL WITH A CRACK

The contact problem for a shallow shell containing a vertical crack is considered. The solution of the problem satisfies two inequality rest rictions describing the mutual non-interpenetration of the shell and a punch, and the condition of non-interpenetration for the crack faces. The purpose of this paper is to investigate a control problem using e xternal loading with an objective functional describing the crack open ing. The regularity of the solution is investigated near the tips of t he crack. In particular, for a crack with zero opening the solution is shown to below to the class C-infinity. The convergence of the soluti ons of the optimal control problems when the parameters are perturbed is analysed.