Computerized buckling analysis of shells

1. Descriptions of types of instability and classical buckling problems.- Summary of the volume.- Purpose.- Why do shells buckle?.- What is buckling?.- Various types of bifurcation buckling.- Capsule of recent progress in buckling analysis.- Asymptotic analysis.- General nonlinear analysis.- Axisymmetric structures.- Simple examples to illustrate various types of buckling.- Column buckling.- Prebuckling solution or fundamental equilibrium path.- Bifurcation buckling.- Post-bifurcation stability.- Loss of stability and imperfections.- Buckling of plates.- "Classical" buckling of cylindrical and spherical shells.- Cylindrical shells under axial compression.- A caution for novice users of computer programs for buckling.- Stiffened cylinders under axial compression.- Cylinders under uniform external pressure or torsion.- Spherical shells under uniform external pressure.- Spherical caps.- 2. Nonlinear collapse.- Summary.- Elastic-plastic-creep collapse of axially compressed monocoque cylinders.- No-creep.- Creep included.- Creep collapse of ring-stiffened cylinder under external hydrostatic pressure.- Snap-through of very shallow spherical caps.- Straight and curved tubes under bending and external pressure.- Long tubes and elbows: A survey of work done.- Elastic models.- Bending tests on long elastic-plastic straight pipes and elbows.- Elastic-plastic piping analysis.- Axisymmetric model of long pipe or elbow-bending problem.- Simulation of the pipe-bending problem by thermal loading of a torus.- Collapse and bifurcation buckling moment of a long straight pipe.- Collapse of a 90 elastic plastic elbow 45 Collapse and bifurcation buckling due to bending of straight elastic pipes of finite length.- Collapse of cylindrical panels and shells with concentrated loads and cutouts.- Cylindrical panels and shells with concentrated normal loads.- Panels.- Complete cylindrical shells.- Collapse of axially compressed cylindrical shells with cutouts.- Rectangular cutouts.- Circular cutouts.- Collapse of axially compressed noncircular cylinders.- Axially compressed elliptical cylinder.- Axially compressed "Pear-shaped" cylinder.- Axially compressed cylindrical shell with local load path eccentricity.- 3. Bifurcation buckling in which nonuniformity or nonlinearity of the prebuckling state is important.- Summary.- Bifurcation buckling due to edge effects and localized circumferential compression.- Bifurcation buckling due to edge effects.- Cylindrical shell under axial compression.- Externally pressurized spherical caps with edge rings.- Buckling of shallow and deep spherical caps.- Buckling due to localized hoop compression.- Thermal buckling of cylindrical shells.- Buckling of cylinder heated halfway along length.- Buckling of axisymmetrically heated clamped cylinder.- Buckling of an internally pressurized rocket fuel tank.- Local buckling at a field joint in a large rocket payload shroud 84 Bifurcation buckling of spherical shells under meridional tension combined with hoop compression.- Axial load applied uniformly over latitude with finite radius r1.- Axial load applied at a point.- Buckling of internally pressurized vessel heads.- Cause and characteristics of nonsymmetric bifurcation buckling.- Difference in elastic behavior of ellipsoidal and torispherical heads.- Elastic bifurcation buckling.- Elastic-plastic bifurcation buckling.- Conclusions about bifurcation buckling of internally pressurized heads.- Bifurcation buckling near the axisymmetric collapse load.- A summary of examples already described.- Failure of a water tank.- An attempt to predict elastic-plastic buckling of the large steel water tower including fabrication effects.- Tank configuration and discretized model.- Welding.- Mismatch.- Cold bending.- Conclusions.- 4. Effect of boundary conditions and eccentric loading.- Summary.- Effect of boundary conditions on buckling of monocoque shells.- Cylinders subjected to uniform external hydrostatic pressure.- Cylinders subjected to uniform axial compression.- Inextensional buckling.- Simulation of effects of local plastic flow by appropriate constraint conditions.- Effect of boundary conditions and loading eccentricity on buckling of axially compressed stiffened cylindrical shells.- Boundary conditions.- Load eccentricity.- 5. Instability of shells of revolution subjected to combined loads and nonsymmetric loads.- Summary.- Combined loading.- Nonsymmetric loading.- Monocoque cylindrical shells under combined loading.- Axial compression or bending and internal pressure.- Torsion and internal pressure.- Stiffened cylindrical shells under combined loading.- Buckling of composite cylindrical shells under combined loading.- Definitions.- Previous work done.- Buckling under combined loads.- Buckling of nonaxisymmetrically loaded shells of revolution.- Modeling considerations.- Examples of buckling of nonsymmetrically loaded shells of revolution.- Thermal buckling of nonsymmetrically heated shells.- Anderson and Card tests.- Simply-supported cylinder heated on an axial strip.- Parameter study - cylinders heated on axial strips.- Buckling of conical shells heated on axial strips.- Conclusions.- Buckling of nuclear reactor containment vessel due to ground motion during an earthquake.- 6. Buckling of ring-stiffened shells of revolution.- Summary.- Elastic buckling of ring-stiffened cylinders under external hydrostatic pressure.- Elastic-plastic buckling of ring-stiffened cylinders under external hydrostatic pressure.- Effects of residual stresses and deformations on plastic buckling of ring-stiffened shells of revolution.- Review of previous work.- Cold bending.- Welding.- Bending and welding.- Effect of welding on the plastic buckling pressure of an ellipsoid ring-stiffened shell.- Residual deformations from welding internal v. external rings.- Effect of cold bending and welding on buckling of ring-stiffened cylinders.- Cold bending of a flat sheet into a cylindrical shell of infinite length.- Initial elastic loading.- Elastic-plastic loading.- Relaxation.- Obtaining a value ofR0.- Simulation of cold bending in BOSOR5.- Procedure for using BOSOR5 to calculate buckling loads including residual effects due to cold bending and welding.- Comparisons with tests on cold-bent sheet 204 Buckling of cold bent and welded ring-stiffened cylinder: comparison of test and theory.- Possible causes of the remaining discrepancy between test and theory.- Effect on buckling of deformations of the ring cross sections.- General and local instability.- Modal interaction.- Comparisons with tests in which local ring deformations are important.- Crippling of ring web.- Wide column ring web "buckling".- General instability of ring-stiffened shallow conical shell.- 7. Buckling of prismatic shells and panels.- Summary.- Use of a computer code for shells of revolution to predict buckling loads of prismatic structures.- Analysis technique.- Convergence studies.- Numerical results.- Nonuniformly loaded circular cylindrical shells.- Stress and buckling of elliptic cylinders.- Cylinders of noncircular cross section under axial compression.- Bifurcation buckling of axially compressed panels.- Numerical results.- Buckling of axially compressed corrugated and beaded panels.- Effect of manufacturing method on general and local buckling of a semi-sandwich corrugated panel.- Modal interaction and imperfection sensitivity of axially compressed prismatic structures.- Two types of modal interaction.- Previous work done.- Summary of this section.- Modal interaction in an axially compressed two-flange column.- The perfect column.- Buckling with imperfect flanges but straight column axis.- Stability of equilibrium at the bifurcation load, Kb.- Buckling of columns with imperfect flanges and imperfect axes.- Modal interaction in axially compressed, eccentrically stiffened panels.- Optimization of imperfect columns and panels in which modal interaction occurs.- Columns.- Panels.- Axially stiffened cylindrical shells.- Transverse shear deformation effects.- Laminated composite materials.- 8. Imperfection sensitivity.- Summary.- Asymptotic post-buckling theory - a summary.- Elastic post-bifurcation analysis.- Elastic-plastic post-bifurcation analysis.- Perfect elastic-plastic structures.- Imperfect elastic-plastic structures.- Qualitative guidelines for imperfection sensitivity.- Axially compressed cylindrical shells and panels.- Brief survey of work done.- Nonlinear post-buckling behavior of perfect shells.- Various boundary conditions and nonuniform or nonlinear pre-buckling effects.- Empirically derived design formulas for monocoque cylinders.- Design rules for stiffened cylinders.- Effect of geometric imperfections.- Governing equations for asymptotic post-buckling approach.- Karman-Donnell equations.- Prebuckling analysis.- Asymptotic analysis.- Initial post-bifurcation load-deflection curve.- Imperfection sensitivity.- Numerical methods used to solve the various boundary-value problems and evaluate b, b, and ?.- Governing equations for the nonlinear approach.- Hutchinson's formulation [340].- Arbocz and Babcock's formulation [341].- Behavior of perfect cylinders.- Behavior of imperfect cylinders.- Axially compressed monocoque cylindrical shells: numerical results.- Cylinders with sinusoidal axisymmetric imperfections.- Cylinders with localized imperfections 299 Cylinders with random imperfections (axial compression or external pressure).- Cylinders with internal pressure.- Axially compressed cylindrical panels.- Axially compressed oval cylinders.- Axially compressed stiffened and composite cylindrical shells: numerical results.- Asymptotic post-buckling analysis of axially stiffened cylinders.- Laminated cylindrical shells made of composite material.- Calculation of load-carrying capability based on measurements of imperfections.- Design method for axially compressed cylinders.- Critical load from wide-column theory.- Critical load from extended version of Koiter's special theory.- Design philosophy.- Numerical results.- Conclusions 323 Imperfection sensitivity of cylinders under uniform hydrostatic pressure and torsion.- Uniform hydrostatic pressure.- Monocoque cylinders.- Axially-stiffened cylinders.- Ring-stiffened cylinders.- General conclusions.- Cylinders under torsion.- Imperfection sensitivity of spherical shells.- Governing equations for the asymptotic post-buckling analysis.- Application to a shallow spherical segment.- Classical buckling analysis.- Post-buckling equilibrium paths.- Special theory vs. general theory.- Difficulties encountered in the asymptotic analysis of complete spherical shells.- Nonlinear numerical studies 339 Other asymptotic imperfection sensitivity analyses for doubly-curved shells of revolution.- Spherical caps with axisymmetric loading over part of the surface.- Results of Fitch and Budiansky [391].- Questions raised by the results shown in Fig. 304.- Nonsymmetrically loaded spherical shell.- Initial post-buckling behavior of toroidal segments.- Limitations of asymptotic imperfection sensitivity theory.- Bifurcation buckling with stable post-buckling behavior.- Spherical shell with an inward-directed point load.- Stable post-buckling shearing deformations.- Wagner beam.- Computerized analysis of a complex stiffened curved panel under shear.- Wrinkling of an antenna membrane 355 The Southwell method for determination of buckling loads from non-destructive tests.- Definition of the method.- Examples of application of the Southwell method.- Limitations of the Southwell method.- 9. Buckling of hybrid bodies of revolution.- Summary.- Ring-stiffened cylindrical shells under uniform hydrostatic pressure.- Spherical shells embedded in structural foam.- Elastic-plastic instability of axially compressed shells of revolution with axisymmetric frangible joints.- Comparison of test and theory for a frangible joint embedded in a simple cylindrical shell.- Test configuration and BOSOR6 model.- Discretization.- Pads.- Material properties.- Junction and contact conditions between the primacord tube and the cavity provided for it.- Numerical results.- Frangible joint embedded in a complex shell structure.- Structural configuration and segmented model.- Substitution of uniform axial compression for the actual loads.- Axisymmetric collapse of the rocket interstage.- Effect of a minor design change.- Effect of a steel primacord tube.- References.- Author index.