Plane problem for an orthotropic body with a crack whose lower side is reinforced by an elastic membrane

We study the stress state of an orthotropic plane with one linear defect whose lower side is reinforced by an elastic membrane. The Lekhnitskii potentials are constructed as solutions of the Riemann two-dimensional boundary-value problem. They are obtained in closed form. It is shown that the asymptotic behavior of stresses at the tips of the defect can have a singularity of any order from -1 to 0, depending on the stiffness of the membrane. The cases of low and high stiffness are considered separately.