The adhesive contact problem for a piecewise-homogeneous orthotropic plate with an elastic patch

Abstract

A piecewise-homogeneous elastic orthotropic plate, reinforced with a finite patch of the wedge-shaped, which meets the interface at a right angle and is loaded with tangential and normal forces is considered. Using methods of the theory of analytic functions, the problem is reduced to the system of singular integro-differential equations (SIDE) with fixed singularity. Under tension-compression of patch using an integral transformation a Riemann problem is obtained, the solution of which is presented in explicit form. The tangential contact stresses along the contact line are determined and their asymptotic behavior in the neighborhood of singular points is established.

Some effective solutions for Prandtl's type integro‐differential equation

“…Exact and approximate solutions of static contact problems for different domains, reinforced with elastic thin inclusions and patches of variable stiffness, were obtained, and the behavior of the contact stresses at the ends of the contact line has been investigated as a function of the law of variation of the geometrical and physical parameters of these elements [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. As is known, stringers and inclusions, such as rigid punch and cuts, represent the stress concentrates.…”

Exact solutions of some singular integro-differential equations related to adhesive contact problems of elasticity theory

“…Exact or approximate solutions of static contact problems for different domains, reinforced by elastic thin inclusions and patches of variable stiffness were obtained and the behavior of the contact stresses at the ends of the contact line has been investigated as a function of the geometrical and physical parameters of these elements [1,2,3,4,5,6,7,14,15,16,17,20,18,19,21,22,23,24]. One model assumes continuous interaction, while the other assumes the adhesive contact of thin-shared elements (stringers or inclusions) with massive deformable bodies.…”