Effect of a riveted wide patch on stresses in a cracked plate

Abstract

We study the stress-strain state and limiting equilibrium of a thin plate with curvilinear cracks reinforced by a wide patch. The patch is arbitrarily located relative to the cracks and attached to the plate with elastic rivets. The boundary-value problem is reduced to a system of singular integral and integro-algebraic equations and this system is solved by the method of mechanical quadratures. Numerical analysis is performed for the case of a plate with one curvilinear or rectilinear crack reinforced by an elliptic patch. The stress intensity factors formed in this reinforced cracked plate and ultimate loads are determined for various geometric and physical parameters of the plate, crack, patch, and rivets.For the reinforcement of load-carrying thin-walled structural elements, it is customary to use strengthening patches of various types. They are very often fastened to cracked elements by using riveted joints. At the same time, thin cracked plates reinforced by riveted wide patches are studied much less satisfactorily [ 1-3] than plates reinforced by stringers, stiffening ribs, or various types of crack arresters [4]. Thus, some problems for plates with rectilinear cracks reinforced by riveted wide patches were solved under the conditions of geometric symmetry and symmetry of forces. In [2,3], plates subjected to uniaxial tension were studied by using simplified models of wide patches regarded as a system of independent parallel stringers working only in tension and compression. The indicated problems were solved by the methods of finite elements [ 1], bulk forces [2], and complex potentials and Green's functions [3].In the present work, on the basis of our results obtained in [4-8], we develop a general approach to the solution of the problems of reinforcement of cracked plates by riveted wide patches with regard for the compliance of the riveted joints posed as problems of linear fracture mechanics. We construct a complete algorithm of their numerical solution and analyze the accumulated numerical data. Statement of the ProblemConsider a stress-strain state of an infinite thin plate (of constant thickness h) weakened by cracks with smooth contours Ln (n = 1, N t ) and reinforced by a finite two-dimensional patch of constant thickness h s (a thin simply connected plate S with smooth contour F). The patch is riveted to the plate by Nz rivets whose radius r is small as compared with the distances between the rivets and the sizes of the patch and cracks. The cracks are located arbitrarily and the patch may either completely or partially cover them or lie outside the region occupied by the cracks. We introduce a Cartesian coordinate system xOy and relate the crack contours Ln ( n = 1, N t ) and the patch F to this system (Fig. 1). We assume that the crack lips do not contact and are loaded by self-balanced forceswhere N(t) and T(t) are the normal and tangential components of stresses on the crack contours, respectively, and the superscript "+" ("-") denotes the limiting value of the corresponding quantity if we a...

Effect of breaks in riveted stringers on the elastic and limiting equilibrium of a cracked plate

“…Here, T = texp (ict) + z0 is a point on the crack contour represented in the principal coordinate system xOy and z is a point By constructing a Lagrange interpolating polynomial at the Chebyshev nodes of the function u (~), we find the values of this function at the points ~ = _+ 1 and use these values to determine the relative stress intensity factors (SIF) [3,6,8]:…”

“…where N~ are the numbers of rivets in the n th x-stringer and ruth y-stringer, respectively (the rivets and elements of the stringers are numbered along the axes of the principal coordinate system), and c x (c y ) is the relative compliance of the riveted joint in the n(m)th x(y)-stringer given by the formula [1,5,6] s _ 5Eh…”