Periodic System of Closely Located Holes in an Elastic Plane Under the Conditions of Antiplane Deformation

Abstract

We construct a singular integral equation of an antiplane periodic problem of the theory of elasticity for an isotropic plane weakened by smooth curvilinear holes. A numerical solution of the problem is obtained in the case of closely located holes with rounded V-shaped vertices made in the elastic plane under the conditions of uniform shear at infinity. On this basis, we determine the stress concentration factors at the rounded vertices of a bilateral V-shaped semiinfinite notch. By using the well-known relation between the stress intensity and stress concentration factors for sharp and rounded V-shaped notches, we perform the limit transition to a bilateral sharp V-shaped notch. The dependence of the stress intensity factor at the sharp vertices of a bilateral V-notch on its apex angle is determined.