MODELING OF CONTACT INTERACTION OF THE EDGES OF THE INTERFACIAL SECTION ALONG THE ARC OF THE CIRCLE BETWEEN THE ORTHOTROPIC PLATE AND THE CLOSED ELASTIC RIB

Abstract

Under the conditions of the generalized plane stress state it is researched a mixed contact problem for an infinite orthotropic plate with a circular hole, the contour of which is reinforced by a closed elastic rib. The line connecting the plate and the elastic rib contains a symmetrical interfacial section, the edges of which are in smooth contact during the deformation process.

The components of the deformation tensor (relative elongation, angle of rotation of the normal and curvature) at the points of the contour of the hole of the plate are represented with integral dependences on the contact forces. The authors choose a closed elastic rod of large curvature with a constant rectangular cross section as a model of the reinforcing element.

Using the basic equations of the linear theory of closed rods of large curvature, the mathematical model of the problem is constructed in the form of a system of three singular integral equations with Hilbert kernel in order to find the contact forces between the plate and the rib. The approximate solution of the issue is found with the help of the combined method of mechanical quadrature and collocation. This method investigates the influence of the material orthotropy on the stress state of the plate and the reinforcing rib and on the size of the smooth contact area.