Cutout Reinforcement of Stiffened Cylindrical Shells

Abstract

A study was carried out to determine the optimum placement and volume of a reinforcing frame around a cutout in an axially loaded stringer and ring and stringer stiffened cylindrical shell. The problem was analyzed using the linear bifurcation portion of STAGS (Structural Analysis of General Shells). Four parameters were varied; stringers vs rings and stringers, cutout size, ratio of frame volume to cutout volume, and frame position. It appeared that the frame's position next to the cutout edge was the most effective, which is simply a con- firmation of a well-known fact concerning reinforcement of shell cutouts. However, there was a relative maximum in the frame distance vs critical load curves for a frame positioned away from the cutout edge at a low ratio of frame to cutout volume. Nomenclature Asf,bsf,hsf =area, width, and depth of reinforcing frame a = hole radius or half-width of space cutout d = distance of frame from the centerline of the cutout E = modulus of elasticity G = shear modulus h = shell thickness Ixory Iz = moment of inertia of reinforcing frame L = length of the shell Previous research into the presence of cutouts in cylindrical shell structures can be traced to work performed by Starnes,' who investigated the buckling of a thin unstiffened cylindrical shell with a single cutout, both experimentally and theoretically. He conducted two series of experiments, one on shells made of Dupont's Mylar with a lap seam; and the other series of tests on seamless electroformed copper shells. The parameters ranged between 400 <R/h< 960 and 0<#//?<0.5; where a was the hole radius. The experimental buckling loads, displacements, and the stress distribution applied at the end of the shell were correlated with a theoretical parametric study performed by means of a Rayleigh-Ritz-type approximation . The results of these ex- periments led to the conclusion that the governing parameter of the problem was related to a2/Rh. It has been shown in Ref. 1 that the parameter mu=1/2(12(l-v2)} l/4 (a2/Rh) l/2 (D governs the prebuckling stress distribution and displacements for a circular cylinder with a circular hole in its side. It should be noted that the effect of the hole is very localized in nature. Both membrane and bending stress increments occur; but the bending stress increment is always much less than the membrane stress increment. It should be appreciated that the maximum membrane stress will rise significantly above the stress value obtained for a hole in a flat plate. Work related to stiffened cylindrical shells without cutouts is discussed by Singer2 and will not be presented herein. Palazotto3 explored the validity of using linear bifurcation theory for the buckling analysis of stringer and ring stringer stiffened cylindrical shells with rectangular cutouts employing clamped boundary conditions. The analysis was performed using the STAGS (Structural Analysis of General Shells)4 computer program. This program incorporates linear bifurcation theory, nonlinear collapse analysis, discrete stiffening, and smeared stiffening theory. The buckling loads of stringer and ring and stringer cylindrical shells were computed using both the linear bifurcation analysis and the nonlinear collapse analysis capability of STAGS. When the results for the linear and nonlinear analyses compared within a few percent, Palazotto concluded that linear bifurcation theory adequately predicted the buckling load of a stiffened cylindrical shell with cutouts. The importance of this fact is that a nonlinear collapse analysis is much more expensive than a linear bifurcation analysis in terms of computer time.