Stress distributions in orthotropic solids with blunt notches under in-plane shear loadings

The present work is devoted to the analysis of the stress distributions in orthotropic solids weakened by blunt notches and loaded under in-plane shear. In particular, using Lekhnitskii's approach, new closed form equations are derived for the stress components, explicitly accounting for the notch geometrical features, namely the notch radius and the opening angle, in conjunction with the elastic material properties. Three main geometries are considered, described using proper conformal mappings: lateral symmetric hyperbolic notches, parabolic notches and hyperbola-like notches in plates loaded under in-plane shear. Appropriate complex potential functions are introduced in the analytical formulation and analytical expressions for the whole stress fields are derived, taking advantage of free-of-stress boundary conditions along the notch edge. Eventually, the very good accuracy of the new solutions is proved against numerical results, as obtained from a number of two-dimensional finite element analyses carried out on plates with rounded notches under shear, also discussing the main features of the mode II stress fields in notched plates.