Computer analysis of various shells of revolution.

Abstract

A computer program for the buckling of shells of revolution under axisymmetrical loading has been applied in an extensive numerical analysis. The axisymmetric collapse and the nonsymmetric bifurcation buckling behavior are studied for axially compressed cylinders, cones, and spherical and toroidal segments. Comparisons are made with a large number of experimental results. A parameter study is performed in which particular emphasis is placed on the effects of eccentricity in load application and on the influence of elastic end rings. Nomenclature Cn = value of JVi due to unit axial strain E . = Young's modulus for ring G = shear modulus for ring H = see Fig. 9 Ix = moment of inertia of ring around axis perpendicular to shell axis / = torsional constant for ring Kp = ring resistance against prebuckling deformations Kb = ring resistance against buckling deformations Mi = meridional moment resultant Ni — meridional stress resultant n — number of circumferential waves in buckling pattern P = total axial load applied to shell, positive compression r = horizontal radius from axis of rotation to reference surface tr = length of side of square end ring UH = horizontal displacement uy = vertical displacement v = circumferential displacement w = normal displacement, positive outward B = meridional rotation Subscripts ( )Cr = critical = prebuckling quantity 0