Partially closure of rectilinear crack emanating from contour of circular hole in stringer plate

The technical holes existing in plates create an increased concentration of stress in the plate. In present article, a thin plate with a circular hole from which a rectilinear crack emanates is studied. The plate is reinforced by stringers. The model of crack with interfacial bonds in end zone is used. The plate and reinforcing ribs are made of different elastic and isotropic materials. It is assumed that the stringers are not bending and their thickness does not change during deformation. The plate is assumed to be unbounded and subjected to stretching at infinity. The case of partial crack closure is considered. The action of the stringers is replaced by unknown equivalent concentrated forces applied at the points of connection of the ribs and the plate. To solve the problem under consideration, the method of solution of the elastic problem and the method of construction in explicit form of the Kolosov - Muskhelishvili potentials corresponding to unknown normal displacements along a rectilinear crack are combined. To determine the parameters that characterize the crack closure, a singular integral equation is obtained and converted to a finite nonlinear algebraic system. To determine the unknown equivalent concentrated forces, Hooke's law is used. Solution of the algebraic system was obtained using the method of successive approximations. Directly from the solution of the obtained algebraic systems the cohesive forces in the bonds, contact stresses and size of the crack contact zone were found. Using the obtained relations it is possible to solve the inverse problem, i.e. to determine the characteristics and stress state of the stringer-reinforced thin plate with a circular hole at which the predetermined contact area of the faces of the rectilinear crack emanating from the hole is reached.