R. Bantsuri and N. Shavlakadze

A. Razmadze Mathematical Institute, Georgian Academy of Sciences Tbilisi, Georgia

THE CONTACT PROBLEM FOR AN ANISOTROPIC WEDGE-SHAPED PLATE WITH AN ELASTIC STRENGTHENING OF VARIABLE RIGIDITY

We consider plane-strassed state of an infinite elastic anisotropic wedge, strengthened over one boundary by an elastic bar whose rigidity varies by the law: x^{α} (x is the distance from the wedge vertex, α is any real number). Tangential load of intensity τ_{0}(x) is applied along the bar.

The problem is reduced to the Carleman type problem for a strip with the boundary condition

G(t)Ψ(t) − HΨ(t − i(α − 1)) = F (t), −∞ < t < ∞,

where G(t) and F (t) are the given meramorphic functions and H is a constant.

The problem is solved in a closed form, the contact stress along the line of strengthening in the vicinity of the angle vertex admits the estimate

τ(x) − τ_{0}(x) = \begin{cases}O(x^{α−2}), & α > 2, \\ O(x^{τ_{0}−1}), & 1 < α ≤ 2, \\ O(x^{τ_{1}−1}), & α ≤ 1, \end{cases}

where τ_{0} = Im z_{0} and τ_{1} = Im z_{1}, z_{0} is the nearest to the real axis pole of the function G(z) in the lower half-plane, z_{1} is the nearest to the real axis zero of the function G(z) (for α = 1, of the function G(z) − H) in the lower half-plane.