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From:
Michael P. Nemeth (NASA Langley Research Center, Hampton, Virginia, USA), “Buckling analysis for stiffened anisotropic circular cylinders based on Sanders’ nonlinear shell theory”, NASA/TM-2014-218176, March 2014
SUMMARY: Nonlinear and linear-bifurcation buckling equations for elastic, geometrically perfect, right- circular cylindrical shells subjected to combined loads is presented. The loads include compression, shear, and uniform external and hydrostatic pressure. The analysis includes constitutive equations that are applicable to stiffened or unstiffened cylinders made from isotropic or laminated-composite materials. Complete sets of equations are presented for the nonlinear boundary-value problem of shell buckling and the corresponding prebuckling and linear- bifurcation buckling problems that are based on Sanders’ shell theory for "small" strains and "moderately small" rotations. Based on these equations, a three-parameter approximate Rayleigh-Ritz solution and a classical solution to the buckling problem are presented for cylinders with simply supported edges. Extensive comparisons of results obtained from these solutions with published results are also presented for a wide range of cylinder constructions. These comparisons include laminated- composite cylinders with a wide variety of shell-wall orthotropies and anisotropies. Numerous results are also given that show the discepancies between the results obtained by using Donnell’s equations and variants of Sanders’ equations. For some cases, nondimensional parameters are identified and "master" curves are presented that facilitate the concise representation of results.
This is Fig. 6 in the 2014 NASA report.
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