Equilibrium of an elastic layer weakened by plane cracks

The spatial problem of the elastic equilibrium of a layer in whose middle plane there is a system of cracks is considered. The cracks are maintained open under the action of a normal load applied to their edges. The layer faces are compressed between two rigid smooth foundations. The problem is reduced to solving an integral equation of the first kind. The asymptotic methods of “large and small λ” /1/ as well as the method of successive approximations and a variational method are used to construct the solutions of this equation for elliptically and rectangularly shaped cracks in different ranges of variation of the geomtrical parameters.