We study the stress-strain state and limiting equilibrium of a thin cracked plate reinforced by intact and broken riveted stringers and consider two types of loading of the stringers: their ends either are loaded by forces acting at infinity or free of loads. The boundary-value problem is reduced to a system of singular integral and integral-algebraic equations whose numerical solution is obtained by the method of mechanical quadratures for a series of geometric and physical parameters of the plate, crack, stringers, and rivets. It is shown that, as rule, broken stringers weaken the reinforced cracked plate and that the effect of breaks in the stringers on the stress intensity factors in the plate and the ultimate load is significant.To reinforce thin-walled structural elements both in the stage of their manufacturing and in service, it is customary to use stiffening ribs, stringers, and wide patches, The same reinforcing elements may have different effect on the stress-strain state of structures, especially if the structures have holes or crack-like defects. Depending on the loading mode and the location of the reinforcing elements (relative to cracks and holes), the latter may strengthen a load-bearing structure or additionally weaken it. This problem is closely connected with the problems of the influence of breaks in the stringers in the vicinity of defects.For rectilinear cracks perpendicular to a set of parallel stringers connected with the plate by perfect discrete joints, the analysis of the effect of broken stringers on the stress-strain state of a thin cracked plate was performed in [1,2]. In the present work, on the basis of the results obtained in [3][4][5], we study the influence of breaks in riveted stringers on the elastic and limiting equilibrium of the reinforced plate containing an arbitrarily located curvilinear crack (taking into account the compliance of riveted joints).
Mathematical Model of a Plate with Curvilinear Crack Reinforced by Broken StringersAn infinite thin plate containing a curvilinear crack L is reinforced by Nx horizontal and Ny vertical riveted stringers. The stringers have the form of narrow thin (as compared with the crack length) elastic rods with constant cross sections attached to the plate by compliant rivets whose radius r is small as compared with the distances between them. All stringers work only in tension-compression (due to small cross sections of the stringers, we neglect bending forces both in the plane of the plate and in the perpendicular planes). The cracked plate is in the generalized plane stressed state. We introduce the principal xOy and local x 10 l Yl Cartesian coordinate systems related to the x-and y-stringers and the crack contour L, respectively (Fig. 1). In what follows, the superscripts x and y always mean that the quantities under consideration correspond to the x-and y-stringers, respectively.At infinity, the plate is loaded by mutually perpendicular stresses p and q. The stresses p are directed at an angle y to the x-axis. The crack lips are n...