On the state of stress of an orthotropic elastic plane region in the neighborhood of a corner point

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By using the solutions of certain special boundary value problems, the nature of the stress field features at a corner point is investigated. The asymptotic of the stress field is determined to constant accuracy in the neighborhood of the corner point, in particular, in the neighborhood of the terminus of a crack, a corner point of a reentrant point type. As an example, there is considered the deformation of a half-plane with an oblique crack on the boundary. The features of stress fields at smooth points at which external loads have singularities, or the nature of the boundary conditions changes, are also determined. The problem of corner points for an elliptic system of equations to which the system of statics equations of linear elasticity theory also belongs, was investigated in /1–3/, but re-entrant points were not considered. Results referring intrinsically to the system of elasticity theory equations for an isotropic body were published in /4/. The results of this paper follow directly from the solutions of certain special problems /5/.