Z is the Batdorf parameter:
Z = L*2(1 - nu*2)*(1/2)/(rt)
S.B. Batdorf, “A simplified method of elastic-stability analysis for thin cylindrical shells I - Donnell’s equation”, NACA Technical Note 1341, June 1947
SUMMARY: The equation for the equilibrium of cylindrcal shells introduced by Donnell in NACA Report No. 479 to find the critical stresses of cylinders in torsion is applied to find critical stresses for cylinders with simply supported edges under other loading conditions. It is shown that by this method solutions may be obtained very easily and the results in each case may be expressed in terms of two nondimensional parameters, one dependent on the critical stress and the other essentially determined by the geometry of the cylinder. The influence of boundary conditons related to edge displacements in the shell median surface is discussed. The accuracy of the solutions found is established by comparing them with previous theoretical solutions and with test results. The solutions to a number of problems concerned with buckling of cylinders with simply suppo9rted edges on the basis of a unified viewpoint are presented in a convenient form for practical use.
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