UNILATERAL CONTACT OF AN ORTHOTROPIC PLATE WITH A CIRCULAR HOLE AND AN ELASTIC DISK

Abstract

The reliability of machine parts and structural elements designed in the form of piecewise homogeneous plates is one
of the important problems of engineering mechanics. Their functionality and durability largely depend on the presence of
defects such as cuts or cracks on the material boundary line, which can occur at the manufacturing stage and significantly
reduce the permissible external load on the part during operation.
A solution to the problem is proposed for an infinite orthotropic plate with a circular hole and an elastic isotropic disk,
which are welded together on one part of the common contour, and on the rest of the contour there is a symmetrical circular
cut between them. The plate structure is in conditions of a uniform generalized plane stress state at infinity. Under the action
of uniformly distributed forces directed along the coordinate axes, the edges of the cut of the plate structure are in contact
partially or along the entire length. Friction forces in the contact zone of the plate and disk are absent. The solution to this
problem involves determining the components of the stress state at the interface between the materials of an orthotropic plate
and an elastic disk, and establishing the dimensions and position of the boundary contact zone.
The boundary conditions of the problem in the smooth contact area are chosen as the equality of the normal
displacements of the contour points of the plate and the disk, and in the joint area as the equality of their displacements. The
dependencies between the components of the displacement vector of the contour points of the orthotropic plate and the elastic
disk and the contact stresses are written as integral relations 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 in the contact and joint areas are expressed. In addition to the obtained system of equations,
the conditions of force equilibrium of the disk must be fulfilled. The approximate solution of the problem is implemented by the
method of mechanical quadratures and collocation. The size and position of the contact zone are determined by the method of
dichotomy.
For a piecewise-homogeneous orthotropic plate with a symmetric circular section, the edges of which are in contact
partially or along the entire length, the influence of the material orthotropy on the distribution of contact and annular stresses
is investigated. The value of the limiting angle of the section zone for which the complete contact is broken at its end points is
established. The results of numerical calculations are shown in two figures and a table.