Variational problem for a shallow shell with a vertical crack
In this paper the problem of an elastic shell equilibrium with a vertical through-crack in the Kirchhoff-Love model is investigated. The conditions of non-penetration are given at the crack which have a form of the inequalities. We believe that in the rigid state of the shell, the negative edges of the crack bulge above the positive bank for a certain distance. The problem is formulated as a variation. Differential problem statement equivalent to a variational problem is obtained assuming sufficient smoothness of the solution.