MIXED CONTACT PROBLEM FOR THE ORTHOTROPIC PLATE WITH CIRCULAR HOLE AND ELASTIC DISK

Abstract

The enhancement of the reliability of machine components designed as piecewise-homogeneous plates is one of the
critical issues in modern engineering mechanics. Their durability largely depends on the presence of defects, such as cuts or
cracks, at the material interface, which may arise during the manufacturing process and significantly reduce the permissible
external load on the component during operation.
A solution is proposed for the contact problem of an infinite orthotropic plate with a circular hole and a flexible isotropic
disk, which are bonded together along one part of their common boundary, while a symmetric crack exists along the rest of the
contour between them. Under the action of a concentrated force applied at the center of the disk, the edges of the crack in the
plate-like structure make partial or full contact along the entire length. Frictional forces in the contact area between the plate
and the disk are absent.
The solution to this problem involves determining the components of the stress state at the interface between the
materials of the plate and the disk, as well as establishing the dimensions and position of the contact zone.
The boundary conditions of the problem on the smooth contact region are chosen as the equality of normal
displacements at the contour points of the plate and the disk, while on the bonding region, the boundary conditions are defined
by the equality of displacements. The relationships between the components of the displacement vector at the contour points of
the orthotropic plate and the elastic disk, and the contact stresses, are expressed as integral equations with logarithmic kernels.
By substituting these expressions into the boundary conditions of the problem, a system of four singular integral equations is
constructed to determine the functions through which the contact forces on the contact and bonding regions are expressed. In
addition to the derived system of equations, the condition of force equilibrium of the disk must be satisfied. An approximate
solution to the problem is implemented using the method of mechanical quadratures and collocation. The dichotomy method
determines the size and position of the contact zone.
For a homogeneous orthotropic plate with a symmetric circular crack, whose edges make partial or full contact under
the action of a force load, the influence of material orthotropy on the distribution of contact and hoop stresses has been studied.
The value of the critical angle of the crack zone at which the complete contact separation occurs at its endpoints has been
determined. The results of numerical calculations are presented in two figures and a table.