The plane self-similar anisotropic and angularly inhomogeneous wedge under power law tractions and the asymptotic analysis of the stress field

Abstract

In this study the generally anisotropic and angularly inhomogeneous wedge, under power law tractions of order n of the radial coordinate r at its external faces is considered. At first, using variable separable relations in the equilibrium equations, the strain–stress relations and the strain compatibility equation, a differential system of equations is constructed and investigated. Decoupling this system, an ordinary differential equation is derived and the stress and displacement fields may be determined. The proposed procedure is also applied to the elastostatic problem of an isotropic and angularly inhomogeneous wedge. In the sequel William's asymptotic analysis in the case of angular inhomogeneity is examined. Finally, applications for the case of an angularly inhomogeneous wedge-shape dam and for the asymptotic procedure in an isotropic wedge with angularly varying shear modulus, are made.