On the contact problem for a half-plane with finite elastic reinforcement

The Contact Problems of the Mathematical Theory of Elasticity for Plates with an Elastic Inclusion

“…where (s) and (s) are Fourier's transformations for functions ϕ 0 (ξ ) = ξ −∞ e ζ ϕ(e ζ )dζ and ψ 0 (ξ ) = ψ(e ξ ), respectively, while F 1 (s) and F 2 (s)-for functions f 1 (e ξ ) and f 2 (e ξ ), k = −1/(h 0 A (2) 2 ) > 0. From the last system, relative to function (s), there is received the boundary condition of Karleman type problem for strip…”

“…β (2) ij -the elastic coefficients of plates material. Due to the contact condition of the inclusion with orthotropic plate du (1) …”

“…Besides, it is known that the derivations of displacements on the border of anisotropic, unorthotropic semiplane, dependent on outer load, acting on semi axis, has the form du (2) …”

“…where u (2) (x) and v (2) (x) are the boundary values of horizontal and vertical displacements on the semi axes; τ (2) (x), q (2) (x)-the boundary values of tangential and normal strains, respectively. When a body is orthotropic and the axes of anisotropy are parallel to coordinate axes, the characteristic equation is biquadrate and its roots are purely imaginary [23] …”

“…It was shown that the contact stresses near the ends of the stiffening member have square-root singularities. The behavior of the tangential contact stress is the same when the cross section of the stiffener is elliptic [2]. For an elastic isotropic wedge stiffened over a finite area with a rod whose crosssectional area varies linearly, the solution was constructed in [3].…”