The plane elasticity problem of an isotropic wedge under normal and shear distributed loading––application in the case of a multi-material problem

The anisotropic and angularly inhomogeneous elastic wedge under a monomial load distribution

“…Then relations for g θθ , g rθ and g rr derived from (23), (15) and (16), respectively, coincide with the corresponding relations for g θθ , g rθ and g rr given in [23]. The multi-material isotropic wedge, consisted of isotropic sub-wedges loaded by monomial distributed loads of order n (n = 0, 1, 2, ±3, ±4, ...), at its free faces θ 0 = α and θ = β, is considered as a special case of the isotropic and angularly inhomogeneous wedge.…”

“…The isotropic and angularly inhomogeneous wedge, the isotropic multi-material wedge [23] and finally the isotropic and homogeneous wedge are proved in our analysis to be special cases of the proposed general procedure. In our study, we do not investigate the region in the neighbourhood of the singular point (apex) of the wedge.…”

“…For the determination of the stress field (4), g θθ is derived from (17), g rr and g rθ are derived from (15) and (16), whereas the unknown coefficients of the functions g ij (θ ) (i, j = r, θ ), are derived from the boundary conditions (6) and the equilibrium of forces and moments [23].…”

“…In [23], the multi-material wedge problem was confronted and was proved to be self-similar in linear elasticity, considering isotropy and monomial-type distributed loading at its external faces. In the present work, the generally anisotropic and angularly inhomogeneous wedge with distributed loading of the order n(n = 0, ±1, ±2, ...) of the radial coordinate r at its external faces is studied under the validity of the self-similarity property.…”

“…From the equilibrium of forces at the sector (s, θ) [23], r 1 = 1 ≤ s ≤ r and α ≤ θ ≤ β (Fig. 2), one obtains h rr (r) = r n .…”