A plane periodic boundary-value problem of elasticity theory for a half-plane with curvilinear edge

We deduce a singular integral equation of a plane periodic problem of the theory of elasticity for a half plane with loaded curvilinear edge. The numerical solution of the integral equation is obtained by the method of quadratures for various configurations of the boundary of the half plane. The stress concentration factors are computed for a half plane with sinusoidal edge and for a periodic system of rounded V-shaped notches. On this basis, as a result of the limit transition, we get the stress intensity factors at the tips of sharp V-shaped notches and analyze their dependence on the opening angle of the notch.