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This and the next image are from:
D. Bushnell and W. D. Bushnell (Department 93-30, 255, Lockheed Palo Alto Research Laboratory, 3251 Hanover St, Palo Alto, CA 94394, U.S.A.), “Approximate method for the optimum design of ring and stringer stiffened cylindrical panels and shells with local, inter-ring, and general buckling modal imperfections”, Computers & Structures, Vol. 59, No. 3, May 1996, pp. 489-527, doi:10.1016/0045-7949(95)00264-2
ABSTRACT: The PANDA2 computer program for minimum-weight design of stiffened composite panels is expanded to handle optimization of ring and stringer stiffened cylindrical panels and shells with three types of initial imperfections in the form of buckling modes, any combination of which may be present: local (buckling between adjacent stringers and rings), inter-ring (buckling between rings with stringers bending with the panel skin), and general (buckling in which both stringers and rings bend with the panel skin). Stresses and buckling load factors of the imperfect panels are computed with use of the assumption that the amplitudes of the buckling modal imperfections grow hyperbolically with increasing load factor according to the formula AMP(i) = EIG(i)/(EIG(i) - 1), in which AMP(i) is a factor to be multiplied by the initial buckling modal imperfection and EIG(i) represents the critical load factor for the ith type of buckling mode (i = 1 = local buckling, i = 2 = inter-ring buckling, i = 3 = general buckling). Buckling load factors corresponding to local, inter-ring, and general buckling of the imperfect panel are computed with use of the maximum radius of curvature that develops in whatever portion of the panel (between stiffeners, inter-ring, overall) is being considered in the calculations and including redistribution of stress resultants over panel skin and stiffener cross-sections caused by prebuckling bending. Stress constraints in the optimization problem are computed including local, inter-ring, and general bending stresses generated by the growth of the initial local, interring, and general imperfections. These bending stresses are added to the stresses from other sources (thermal, in-plane loading, normal pressure, curing, redistribution of membrane stresses from overall prebuckling bending of the imperfect panel). Minimum-weight designs for various imperfect unstiffened and stiffened cylindrical shells derived by PANDA2 are evaluated with use of the STAGS general-purpose finite element code. The agreement of results from PANDA2 and STAGS appears to qualify PANDA2 for the preliminary design of imperfect, stiffened, composite cylindrical shells.
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