СALCULATION OF STRESS INTENSITY COEFFICIENTS FOR THE ISOTROPIC PLATE WITH A SOLDERED CIRCULAR ELASTIC DISK

Abstract

Improving the reliability of machine parts designed in the form of piecewise homogeneous plates is one of the important problems of mechanical engineering. Their durability largely depends on the presence on the line of demarcation of materials defects such as cuts or cracks that may occur during manufacture, and during operation significantly reduce the allowable external load on the part.

By the action of concentrated power load applied at the center of the elastic disk, the banks cut lamellar structure partially in contact. We consider that the area of contact plate and drive no friction. Solution of this problem involves identifying the components of stress state on the contour of the hole of the plate, calculation of stress intensity coefficients and set the size and position of the contact zone. Boundary conditions of the problem in the area smooth frictionless contact elected as equality normal displacement of the plate and disk, as in the area of junction in the form of equal displacement of contour points.

Dependencies between the components of the displacement vector contour points of the plate and the elastic disk and contact stresses recorded in the form of integral relations with logarithmic kernels. By substituting these expressions into the boundary conditions, obtained a system of four singular integral equations for determining the functions, which an expressed through the normal and tangent force on the contact area and the junction.

For approximate solution of this problem the structure of the desired functions in the vicinity of the ends of sections of smooth frictionless contact zone and junction. Approximate solution of the problem is realized mechanical quadrature and collocation. The numerical example is considered. The calculation of normal and tangent force and calculation of stress intensity coefficients is conducted. The resulting table shows the values of the stress intensity coefficients around the vertices of the section and the values of the contact zones.