Bifurcation Buckling of Shells of Revolution including Large Deflections, Plasticity and Creep

A summary is first presented of the conceptual difficulties and paradoxes surrounding plastic bifurcation buckling analysis. Briefly discussed are nonconservativeness, loading rate during buckling, and the discrepancy of buckling predictions with use of .I2 flow theory vs JZ deformation theory. The axisymmetric prebuckling analysis, including large deflections, elastic-plastic material behavior and creep is summarized. Details are given on the analysis of nonsymmetric bifurcation from the deformed axisymmetric state. Both JZ flow theory and JZ deformation theory are described. The treatment, based on the finite-difference energy method, applies to layered segmented and branched shells of arbitrary meridional shape composed of a number of different elastic-plastic materials. Numerical results generated with a computer program based on the analysis are presented for an externally pressurized cylinder with conical heads. NOMENCLATURE Plastic loading matrix, equation (6) elastic constants defined in equations (7) and (17) total strain anywhere in the shell wall elastic modulus shear modulus = E/[2(1 + v)] identity matrix integrated constitutive IawAquations (23) and (24) stress, moment resultants or number of degrees-of-freedom in prebuckling, stability problems number of full circumferential waves normal pressure, Fig. I dependent variables-displacements and Lagrange multipliers infinitesimal change in 4 radius of parallel circle, Fig. 1 radius of curvature, Fig. 1 arc length along meridian or stress deviator, depending on context work done by external forces distance from reference surface, Fig. 1 reference surface strain reference surface change in curvature Poisson’s ratio stress effective stress, G = (ol* + uZz ~~0,)~ circumferential coordinate energy gradient or shell wall rotation component, depending on context meridional rotation Superscripts i.; , =d( )/ds =d( )/de (l), (2) =first, second order terms in 6q T thermal, or transpose of matrix i Staff Scientist.