Computerized buckling analysis of shells

438 Pages·1985·31.96 MB·English

by  D. Bushnell (auth.)

Computerized buckling analysis of shells
MECHANICS OF ELASTIC STABILITY
Editors: H.H.E. Leipholz and G.lE. Oravas
H.H.E. Leipholz, Theory of elasticity. 1974.
ISBN 90-286-0193-7
L. Librescu, Elastostatics and kinetics of anisotropic and heterogeneous
shell-type structures. 1975.
ISBN 90-286-0035-3
C.L. Dym, Stability theory and its application to structural mechanics.
1974.
ISBN 90-286-0094-9
K. Huseyin, Nonlinear theory of elastic stability. 1975.
ISBN 90-286-0344-1
H.H.E. Leipholz, Direct variational methods and eigenvalue problems in
engineering. 1977.
ISBN 90-286-0106-6
K. Huseyin, Vibrations and stability of multiple parameter systems. 1978.
ISBN 90-286-0136-8
H.H.E. Leipholz, Stability of elastic systems. 1980.
ISBN 90-286-0050-7
V.V. Bolotin, Random vibrations of elastic systems. 1984.
ISBN 90-247-2981-5
D. Bushnell, Computerized buckling analysis of shells. 1985.
ISBN 90-247-3099-6
Computerized buckling analysis
of shells
by
D. Bushnell
Lockheed Palo Alto Research Laboratory
3251 Hannover St.
Palo Alto, California 94304
USA
KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON
Library of Congress Cataloging in Publication Data
Bushnell, D, (David), 1938-
Computerized buckling analysis of shells.
(Mechanics of elastic stability ; 9)
Bibliography: p.
1. Shells (Engineering)--Data processing. 2. Buckling
(Mechanics)--Data processing. I. Title. II. Series.
TA660.S5B87 1985 624.1'7762 84-27376
ISBN 90-247-3099-6 (this volume)
ISBN 90-247-2743-X (series)
Published by Kluwer Academic Publishers,
P.O. Box 17, 3300 AA Dordrecht, The Netherlands.
Kluwer Academic Publishers incorporates
the publishing programmes of
D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press.
Sold and distributed in the U.S.A. and Canada
by Kluwer Academic Publishers,
101 Philip Drive, Norwell, MA 02061, U.S.A.
In all other countries, sold and distributed
by Kluwer Academic Publishers Group,
P.O. Box 322, 3300 AH Dordrecht, The Netherlands.
ISBN-13:978-94-010-8741-4 e-ISBN-13:978-94-009-5063-4
DOl: 10.1007/978-94-009-5063-4
Reprinted 1989
All Rights Reserved
© 1989 by Kluwer Academic Publishers
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner.
To my wife, Kay
Contents
Page
Foreword xiii
1. Descriptions of types of instability and classical buckling problems 1
Introduction 1
Summary of the volume 1
Purpose 7
Why do shells buckle? 7
What is buckling? 8
Various types of bifurcation buckling 10
Capsule of recent progress in buckling analysis 12
Asymptotic analysis 12
General nonlinear analysis 12
Axisymmetric structures 13
Simple examples to illustrate various types of buckling 13
Column buckling 13
Pre buckling solution or fundamental equilibrium path 15
Bifurcation buckling 15
Post-bifurcation stability 17
Loss of stability and imperfections 18
Buckling of plates 18
"Classical" buckling of cylindrical and spherical shells 20
Cylindrical shells under axial compression 20
A caution for novice users of computer programs for buckling 23
Stiffened cylinders under axial compression 24
Cylinders under uniform external pressure or torsion 26
Spherical shells under uniform external pressure 27
Spherical caps 28
2. Nonlinear collapse 30
Summary 30
Elastic-plastic-creep collapse of axially compressed monocoque cylinders 30
No-creep 30
Creep included 33
Creep collapse of ring-stiffened cylinder under external hydrostatic pressure 34
Snap-through of very shallow spherical caps 36
vi
Straight and curved tubes under bending and external pressure 38
Introduction 38
Long tubes and elbows: A survey of work done 39
Elastic models 39
Bending tests on long elastic-plastic straight pipes and elbows 40
Elastic-plastic piping analysis 40
Axisymmetric model of long pipe or elbow-bending problem 42
Simulation of the pipe-bending problem by thermal loading of a torus 42
Collapse and bifurcation buckling moment of a long straight pipe 43
Collapse of a 90° elastic plastic elbow 45
Collapse and bifurcation buckling due to bending of straight elastic pipes of
fmite length 47
Collapse of cylindrical panels and shells with concentrated loads and cutouts 49
Introduction 49
Cylindrical panels and shells with concentrated nOTmalloads 50
Panels 51
Complete cylindrical shells 51
Collapse of axially compressed cylindrical shells with cutouts 53
Rectangular cutouts 53
Circular cutouts 55
Collapse of axially compressed non circular cylinders 57
Axially compressed elliptical cylinder 57
Axially compressed "Pear-shaped" cylinder 59
Axially compressed cylindrical shell with local load path eccentricity 62
3. Bifurcation buckling in which nonuniformity or nonlinearity of the prebuckling state
is important 64
Introduction 64
Summary 64
Bifurcation buckling due to edge effects and localized circumferential compression 66
Bifurcation buckling due to edge effects 66
Cylindrical shell under axial compression 66
Externally pressurized spherical caps with edge rings 67
Buckling of shallow and deep spherical caps 71
Buckling due to localized hoop compression 73
Thermal buckling of cylindrical shells 74
Introduction 74
Buckling of cylinder heated halfway along length 75
Buckling of axisymmetric ally heated clamped cylinder 78
Buckling of an internally pressurized rocket fuel tank 83
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 86
Axial load applied uniformly over latitude with finite radius r I 86
Axial load applied at a point 90
Buckling of internally pressurized vessel heads 92
Introduction 92
Cause and characteristics of nonsymmetric bifurcation buckling 94
Difference in elastic behavior of ellipsoidal and tori spherical heads 95
Elastic bifurcation buckling 96
Elastic-plastic bifurcation buckling 99
Conclusions about bifurcation buckling of internally pressurized heads 107
Bifurcation buckling near the axisymmetric collapse load 109
A summary of examples already described 109
Failure of a water tank 110
vii
An attempt to predict elastic-plastic buckling of the large steel water tower
including fabrication effects 114
Tank configuration and discretized model 114
Welding 115
Mismatch 119
Cold bending 119
Conclusions 121
4. Effect of boundary conditions and eccentric loading 123
Introduction 123
Summary 126
Effect of boundary conditions on buckling of monocoque shells 127
Cylinders subjected to uniform external hydrostatic pressure 127
Cylinders subjected to uniform axial compression 130
Inextensional buckling 131
Simulation of effects of local plastic flow by appropriate constraint conditions 134
Effect of boundary conditions and loading eccentricity on buckling of axially com-
pressed stiffened cylindrical shells 13 8
Boundary conditions 138
Load eccentricity 146
5. Instability of shells of revolution subjected to combined loads and nonsymmetric loads 151
Summary 151
Combined loading 151
Nonsymmetric loading 152
Monocoque cylindrical shells under combined loading 152
Axial compression or bending and internal pressure 152
Torsion and internal pressure 154
Stiffened cylindrical shells under combined loading 157
Buckling of composite cylindrical shells under combined loading 159
Definitions 159
Previous work done 160
Buckling under combined loads 163
Buckling of nonaxisymmetrically loaded shells of revolution 166
Modeling considerations 166
Examples of buckling of nonsymmetrically loaded shells of revolution 167
Thermal buckling of nonsymmetrically heated shells 168
Introduction 168
Anderson and Card tests 170
Simply-supported cylinder heated on an axial strip 173
Parameter study - cylinders heated on axial strips 175
Buckling of conical shells heated on axial strips 176
Conclusions 177
Buckling of nuclear reactor containment vessel due to ground motion during an
earthquake 180
6. Buckling of ring-stiffened shells of revolution 182
Introduction 182
Summary 183
Elastic buckling of ring-stiffened cylinders under external hydrostatic pressure 184
Elastic-plastic buckling of ring-stiffened cylinders under external hydrostatic
pressure 188
Effects of residual stresses and deformations on plastic buckling of ring-stiffened
shells of revolution 192
Review of previous work 192
viii
Cold bending 192
Welding 193
Bending and welding 193
Effect of welding on the plastic buckling pressure of an ellipsoid ring-stiffened shell 194
Residual deformations from welding internal v. external rings 196
Effect of cold bending and welding on buckling of ring-stiffened cylinders 198
Cold bending of a flat sheet into a cylindrical shell of infinite length 199
Initial elastic loading 200
Elastic-plastic loading 201
Relaxation 201
Obtaining a value of Ro 202
Simulation of cold bending in BOSOR5 203
Procedure for using BOSOR5 to calculate buckling loads including residual
effects due to cold bending and welding 203
Comparisons with tests on cold-bent sheet 204
Buckling of cold bent and welded ring-stiffened cylinder: comparison of
test and theory 205
Possible causes of the remaining discrepancy between test and theory 207
Effect on buckling of deformations of the ring cross sections 208
General and local instability 208
Modal interaction 209
Comparisons with tests in which local ring deformations are important 215
Crippling of ring web 215
Wide column ring web "buckling" 215
General instability of ring-stiffened shallow conical shell 219
7. Buckling of prismatic shells and panels 220
Summary 220
Use of a computer code for shells of revolution to predict buckling loads of pris-
matic structures 220
Introduction 220
Analysis technique 223
Convergence studies 226
Numerical results 228
Nonuniformly loaded circular cylindrical shells 229
Stress and buckling of elliptic cylinders 229
Cylinders of noncircular cross section under axial compression 232
Bifurcation buckling of axially compressed panels 235
Introduction 235
Numerical results 239
Buckling of axially compressed corrugated and beaded panels 239
Effect of manufacturing method on general and local buckling of a semi-
sandwich corrugated panel 242
Modal interaction and imperfection sensitivity of axially compressed prismatic
structures 245
Introduction 245
Two types of modal interaction 245
Previous work done 246
Summary of this section 249
Modal interaction in an axially compressed two-flange column 250
The perfect column 250
Buckling with imperfect flanges but straight column.axis 253
Stability of eqUilibrium at the bifurcation load, K b 254
Buckling of columns with imperfect flanges and imperfect axes 256
Modal interaction in axially compressed, eccentrically stiffened panels 256
ix
Optimization of imperfect columns and panels in which modal interaction occurs 259
Columns 259
Panels 262
Axially stiffened cylindrical shells 265
Transverse shear deformation effects 270
Laminated composite materials 270
8. Imperfection sensitivity 272
Introduction 272
Summary 272
Asymptotic post-buckling theory - a summary 273
Elastic post-bifurcation analysis 274
Elastic-plastic post-bifurcation analysis 276
Perfect elastic-plastic structures 277
Imperfect elastic-plastic structures 277
Qualitative guidelines for imperfection sensitivity 280
Axially compressed cylindrical shells and panels 282
Brief survey of work done 282
Nonlinear post-buckling behavior of perfect shells 283
Various boundary conditions and nonuniform or nonlinear pre-buckling
effects 283
Empirically derived design formulas for monocoque cylinders 284
Design rules for stiffened cylinders 284
Effect of geometric imperfections 285
Governing equations for asymptotic post-buckling approach 287
Karman-Donnell equations 287
Prebuckling analysis 287
Asymptotic analysis 289
Initial post-bifurcation load-deflection curve 291
Imperfection sensitivity 291
Numerical methods used to solve the various boundary-value problems and
evaluate b, 5, and ex 292
Governing equations for the nonlinear approach 292
Hutchinson's formulation [340] 293
Arbocz and Babcock's formulation [341] 294
Behavior of perfect cylinders 295
Behavior of imperfect cylinders 296
Axially compressed monocoque cylindrical shells: numerical results 297
Cylinders with sinusoidal axisymmetric imperfections 297
Cylinders with localized imperfections 299
Cylinders with random imperfections (axial compression or external pressure) 300
Cylinders with internal pressure 301
Axially compressed cylindrical panels 304
Axially compressed oval cylinders 306
Axially compressed stiffened and composite cylindrical shells: numerical results 307
Asymptotic post-buckling analysis of axially stiffened cylinders 307
Laminated cylindrical shells made of composite material 314
Calculation of load-carrying capability based on measurements of imperfections 318
Design method for axially compressed cylinders 319
Critical load from wide-column theory 321
Critical load from extended version of Koiter's special theory 321
Design philosophy 322
Numerical results 322
Conclusions 323
Imperfection sensitivity of cylinders under uniform hydrostatic pressure and torsion 326