This report describes the work performed by Lockheed Palo Alto Research Labora- tory, Palo Alto, California 94304. The work was sponsored by Air Force Office of Scientific Research, Bolling AFB, Washington, D. C. under Grant F49620-77-C-0l22 and by the Flight Dynamics Laboratory, Air Force Wright Aeronautical Laboratories, Wright-Patterson AFB, Ohio under Contract F3361S-76-C-31OS. The work was completed under Task 2307Nl, "Basic Research in Behavior of Metallic and Composite Components of Airframe Structures". The work was admini- stered by Lt. Col. J. D. Morgan (AFOSR) and Dr. N. S. Khot (AFWAL/FIBRA). The contract work was performed between October 1977 and December 1980. The technical report was released by the Author in December 1981. Preface Many structures are assembled from parts which are thin. For example, a stiffened plate or cylindrical panel is composed of a sheet the thickness of which is small com- pared to its length, breadth, and stiffener- spacing, and stiffeners the thickness of which is small compared to their _ heights and lengths.
These assembled structures, loaded in compression, can buckle overall, that is sheet and stiffeners can collapse together in a general instability mode; the sheet can buckle locally between stiffeners; the stiffeners can cripple; and a variety of complex buckling interactions can occur involving local and overall deformations of both sheet and stiffeners. More complex, built-up structures can buckle in more complex and subtle ways.
`The book is a valuable contribution for engineers in government, industry, and universities who have complex shell buckling problems to solve and who have available to them computer programs for the buckling analysis of shells.' Applied Mechanics Review, 38:8 (1986) `What makes this book unique is that the author has succeeded in providing a `feel' for shell buckling based on careful mixture of theoretical, analytical, and numerical procedures. Many of the richly illustrated examples are written in a tutorial form, a guide-by-example for the modeling and solving of complex of nonlinear problems. It shows convincingly that the modern structural engineer must have a very thorough understanding of how structures behave if he is to use the advanced computational tools successfully. This book is a must for all those who work in the field of shell stability.' Journal of Applied Mechanics, 53 (1986)
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 .- Arbocz and Babcock's formulation .- 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 .- 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.