North holland series in applied mathematics and mechanics 27 elastic stability of circular cylindrical shells

N O R T H - H O L L A N D S E R I E S IN A P P L IE D M A T H E M A T IC S A N D M E C H A N IC S EDITORS: E B E C K E R Institutfür Mechanik Technische Hochschule, Darmstadt B B U D IA N S K Y Division of Applied Sciences Harvard University W T K O IT E R Laboratory of Applied Mechanics University of Technology, Delft H A L A U W E R IE R Institute of Applied Mathematics University of Amsterdam V O L U M E 27 N O R T H -H O L L A N D AM STERDAM · NEW YORK · OXFORD ELASTIC STABILITY OF CIRCULAR CYLINDRICAL SHELLS N Y A M A K I I n s t it u t e o f H ig h S p e e d M e c h a n ic s T o h o k u U n iv e r s ity S e n d a i, J a p a n 1984 N O R TH -H O LL A N D AM STERDAM · NEW YORK · OXFORD ® Elsevier Science Publishers Β V , 1984 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the copyright owner ISBN: 444 86857 Published by: ELSEVIER SCIENCE PUBLISHERS B.V P.O Box 1991 1000 BZ Amsterdam The Netherlands Sole distributors for the U.S.A and Canada: ELSEVIER SCIENCE PUBLISHING COMPANY, INC 52 Vanderbilt Avenue New York, N.Y 10017 U.S.A Library of Congress Cataloging in Publication Data Yamaki, N (Noboru), 1920Elastic stability of circular cylindrical shells (North-Holiand series in applied mathematics and mechanics ; v 27) Includes bibliographical references Shells (Engineering) Cylinders Buckling (Mechanics) I Title II Series -2 ^ TA660.S5Y36 1981* 62^.1*7762 ISBN O-Wt-86857-7 (U.S.) PRINTED IN THE NETHERLANDS INTRODUCTION Buck l i n g of pr oblems to e n g i n e e r i n g the problem thanks of most circu l a r ma y no w to the e f forts the present extensive cylindrical shells for man y years be has p o s e d ba f f l i n g In the e l a s t i c dom ain c o n s i d e r e d to be of n u m e r o u s autho rs so lv ed complet el y, inclu d i n g b o o k P r o f e s s o r Y a maki wh o has and accurate up to the p r e s e n t time for e l a s t i c stabi lit y, is o t r o p i c circular the o r e t i c a l His wor k will be buckling cyl i n d r i c a l the wri t e r c o n t r i b u t e d the and e x p e r i m e n t a l and p o s t - b u c k l i n g b e h a v i o u r shells for m a n y years of to come W.T v data the stan d a r d re fer ence Koit er PREFACE For the design of light-weight structures, it is of great technical importance to clarify the elastic stability of circu­ lar cylindrical shells under various loading conditions Hence, numerous researches have been made on this subject since the beginning of this century along with the development of air­ craft structures In the early stage of the relevant research­ es, only approximate solutions were obtained under special loading and boundary conditions, owing to the inherent mathe­ matical difficulty and physical complexity Experimental stud­ ies had also been conducted with thin-walled metal test cylin­ ders, but the results were not precise enough to examine and to improve the corresponding theoretical analyses, due to the de­ teriorating effect of both initial imperfections and plastic deformations With the advent of high-speed digital computers in the 1960s, it became possible to solve the buckling problem with suffi­ cient accuracy and effects of boundary conditions and further those of prebuckling edge rotations have been pursued under various loading conditions Experimental techniques have also made a great progress , and nearly perfect test cylinders as well as highly elastic cylinders sustainable fairly large de­ formations became available , leading to the verification of reasonable agreement between theory and experiment , not only for the buckling problem but also for the postbuckling behav­ iors This book presents a comprehensive treatise on the elastic stability of circular cylindrical shells, which represents the sum of the past 17 years of research conducted at the Institute of High Speed Mechanics, Tohoku University Only the static conservative problems are treated concerning the unstiffened cylinders made of homogeneous, isotropic elastic material with constant thickness Both theoretical and experimental studies were performed on the buckling, postbuckling and initial-postv ii PREFACE v iii b u c k l i n g pr o b l e m s under p a y i n g due a t t e n t i o n pha ses were exten s i v e results, the or combined give a of of to precise the o r e t i c a l data for cylindrical complete c l osely r e l a t e d both fun d a m e n t a l st ab i l i t y loadings, the ef fect of b o u n d a r y conditions presentations to p r o v i d e to to singl e p l a c e d on the a c c u r a t e an al yses, ela stic made typ ica l experimental the bas i c p r o b l e m s shells bibl iog rap hy, the sp eci fic an d Em­ tests an d bu t problems No atte m p t only the s t udied in on is pap e r s the b o o k are cited at a p p r o p r i a t e places In the first ch apter, cyl i n d r i c a l typi ca l n o n l i n e a r cal f o u n d ations of the ensu i n g analyses C h a p t e r deals equations, with the buckling the h o m o g e n e o u s derived are theories, w h i c h are a p p l i e d su b j e c t e d the torsional, sets of load an d to on boundary to the the and of of c i r c u l a r the shell ge ometry, for of compressive considered and for bas ic the e i g e n v a l u e nonlinear cylindrical three f u n d a m e n t a l are the relevant buckling axially condi t i o n s the book First, the c o r r e s p o n d i n g m o d e are c l a r i f i e d loads, i.e., loads the Eig h t cr it ical a w i d e nge of ta king the ef fect of p r e b u c k l i n g edge r o t a ­ tions into consider ati on Donn e l l the basis one of pressure th r o u g h o u t problem li ne ar e q u ations problem, shells theor ies shells are d e s c r i b e d w h i c h c o n s t i t u t e the t h e o r e t i ­ Mo s t of the anal y s e s equations , the v a l i d i t y of which is are b a s e d on the e x a m i n e d through a p p l i c a t i o n of the F l ü g g e equations Ch a p t e r isd e v o t e d to pletely clamped three cylindrical fun d a m e n t a l loads are first presente d, test cy linders, are gi ven , the postbuckling problems shells s u b j e c t e d In each case, to an d then by the com­ of the re sults six p o l y e s t e r c o r r e s p o n d i n g theore t i c a l res ults applying Do n nell n o n l i n e a r equations one experimental c a r e f u l l y c o n d u c t e d by u s i n g obtained of the Galerkin method to R e a s o n a b l e agr e e m e n t s b e t w e e n ory and e x p e r i m e n t are revealed Analyses the the­ for the initia l pos t- b u c k l i n g b e h a v i o r s an d i m p e r f e c t i o n s e n s i t i v i t i e s c o r r e s p o n d i n g to the same cases as in the for e g o i n g are p r e s e n t e d Und e r eac h by a p p l y i n g the line ar equat i o n s l o ading condit io n, the p r o b l e m is in Chapter first so lv ed G a l e r k i n p r o c e d u r e di r e c t l y to the Do n n e l l an d then asy m p t o t i c so lut ions are non­ obtained ix PREFACE thro u g h a p e r t u r b a t i o n pr ocedure, effect of m o d e as in itial well as imperfections the r ange of thus c l a r i f y i n g the d e g r a d i n g in the shape of applicability init ial p o s t b u c k l i n g th eory o r i g i n a t e d by the b u c k l i n g of the so-ca l l e d Koiter and d e v e l o p e d by Bud ian sky Buckling and postbuckling problems under combined loads are treated in Chapter 5, in which the combined actions of hydro­ static pressure together with the torsional, axial and trans­ verse edge loads, respectively, are considered Finally, effects of the contained liquid on the buckling and postbuckling of clamped cylindrical loads are tanks under each of examined in Chapter the three fundamental In each case above stated, the buckling problem is theoretically analysed and experimental results are presented for typical postbuckling behaviors check­ ing the accuracy of the critical load theoretically determined Both theoretical and experimental results are given for the postbuckling problems under the first two loading conditions in Chapter 5, demonstrating fairly good agreement between theory and experiment Thin-walled circular cylindrical m o r e e x t e n s i v e l y u s e d in m a n y as m o s t efficient sess of b e e n m o r e and an d the auth o r h opes to d eepen the b a s i c u n d e r s t a n d i n g stab i l i t y c h a r a c t e r i s t i c s the v a l i d i t y have d i f f e r e n t b r a n c h e s of e n g i n e e r i n g struc t u r a l m e mbers, b o o k to be b e n e f i c i a l complex shell s of this s t r ucture o ther n u m e r i c a l p r o c e d u r e s of and such this the to a s ­ as those u t i l i z i n g the f inite el e m e n t metho d T he aut h o r Professors Seri es Koiter and to a c k n o w l e d g e hi s tion to w r i t e at this He volume is also si nc ere gratitude to B u d i a n s k y , E d i t o r s of the N o r t h - H o l l a n d in A p p l i e d M a t h e m a t i c s manusc rip t Editor wishes an d an d for thankful North-Holland, Mecha n i c s , thei r to Drs for their kind re m a r k s Seve nst er, for his c o u r t e o u s and sugges­ on the Mathematical efficient c o l ­ laboration The auth o r stud ent s for is i n d e b t e d to all the ir contrib u t i o n s , d u ring the past of Drs J Tani, two decades of hi s as so ciates, cooperations He a p p r e c i a t e s S K o d a m a and H Doki, staffs and an d a s s i s t a n c e s the co l l a b o r a t i o n s in w r i t i n g the port i o n s X PREFACE o f th e book r e l a t e d and through to M e s s rs M r and H fo r 4 and , r e s p e c tiv e ly K Otomo and T K Asano M is s to s e c tio n s m aking Hoshi f o r S Kodama, K Otomo and S ato th e ty p in g T He i s fo r S ato th r o u g h e s p e c ia lly to Mrs m an u scrip ts fo r t h e i r h e lp and in th an kfu l p r e p a r in g th e draw ings, photographs, th e , to K T s u c h i y a to M e s s rs e d itin g th e f i n a l m an u s c rip t Noboru YAMAKI CHAPTER NONLINEAR THEORY OF CIRCULAR CYLINDRICAL SHELLS 1.1 I NTRODUCTI ON When an e l a s t i c body i s s u b je c te d to a sm all d e fo rm a tio n w h ic h d i s p l a c e m e n t s as are s m a ll, d efo rm atio n w ith s tra in s , -s tra in th a t we w i l l n e g le c tin g w e ll as d e riv a tiv e s and s tra in -s tre s s o f d i s p la c e m e n t s sm all r o t a t io n s have l i n e a r e x p r e s s i o n s re la tio n s rium c o n d itio n s tio n s is , re la tio n s and t h e e q u i l i b ­ th e e f f e c t o f d is p la c e m e n ts th e d efo rm atio n of th e b a s ic term s o f d i s p l a c e m e n t , re s u ltin g When t h e body i s s u b j e c t e d t o [1 ,2 ] in Thus, d e fo rm a tio n in which e i t h e r th e c l a s s i c a l th e r o t a t io n s n o t s m a l l enough i n c o m p a ris o n w i t h u n i t y , cease t o h o l d i n g e n e r a l and t h e l i n e a r In p a rtic u la r but la rg e ro ta tio n s , v a l i d b u t th e ered in fo r n o n lin e a r e ffe c t of ro ta tio n s s h o u ld be exam ined at c o n s id e rin g th e e f f e c t o f d is p la c e m e n ts e q u a t i o n s w i l l be n o n l i n e a r in th e cases under the o f s o l u t i o n as w e l l as lin e a r e q u ilib riu m c o n d itio n s , sm all In o th e r words, are in a d e ­ s tra in s re la tio n s r e m a in s h o u ld be c o n s i d ­ F u rth e r, th e th e e q u i­ d e fo rm ed s ta te The r e s u l t i n g b a s i c [3 ,4 ] e q u ilib riu m of le a d in g I n c o n t r a s t to th e o ry o f e l a s t i c i t y , th e s t a b i l i t y o f n o t be g e n e r a l l y a s s u r e d on t h e b a s i s of e la s t ic it y or s tra in s term s o f d i s p l a c e m e n t , to th e n o n l in e a r th e o ry o f e l a s t i c i t y th eo ry a la r g e or becomes w ith s tre s s -s tra in th e d is p la c e m e n t - s t r a i n r e l a t i o n s lib r iu m c o n d itio n s lin e a r in t h e above a s s e r t i o n s th e o ry d efo rm atio n th e l i n e a r equa­ t h e body become l i n e a r of e la s t ic ity quate and s m a l l f o r b o th d i s p l a c e m e n t can be d e r i v e d a t t h e o r i g i n a l un deform ed s t a t e governing fin ite in u n iq u en es s s ta te th e n o n lin e a r can th e o ry we may have s e v e r a l d i f f e r e n t c o n f i g u r a t i o n s u n d e r t h e same l o a d i n g and bo un d ary some o f w h i c h a r e s t a b l e and t h e o t h e r s u n s t a b l e CHAPTER Of cou rse only the sta ble e q u i l i b r i u m state can the phys i c a l world fication, definition [5 ,6 ,7 ] systems and and alth o u g h the m a t h e m a t i c a l theory of el astic its ex t e n s i o n system, i.e., pl i s h e d [8 ] r e a l i z e d in on the c l a s s i ­ c r i t e r i o n of the stabi l i t y of ela st ic sta bility has b e e n e s t a b l i s h e d by L i a p o u n o v system, be The r e hav e been lon g deba te s and generalization elast ic bodies, However, for does no t a to a load, continuous seem to have b e e n a c c o m ­ in case - w h e n an elas tic body to a static c o n s e r v a t i v e discrete is s u b jected the so - c a l l e d energ y criterion is g e n erally ac c e p t e d for the v e r i f i c a t i o n of stability, require s the total po t e n t i a l ene rgy of the bod y which to assu me a relat ive m i n i m u m at the e q u i l i b r i u m po sition W i t h the adve nt of air craft nume r o u s r esear ches struct ure s in w e i g h t l i g h t-weight and st ruc tures stiffness, which every field of industry tures in the b e g i n n i n g of this century, have been co n d u c t e d to deve lop mos t e ffective are incr e a s i n g l y used In general, are c o mposed of sle nder columns shells, which are stiff in axial or flex ible in b e n d i n g defor mat ion s bers le ading to the p r e s e n t - d a y can be ea sily d e f o r m e d tions w i t h i n the range of to v a rious ins t a b i l i t y phenome na jec ted axia l or to in- plane at fairl y low stress mation s either levels, and and thin-walled pla tes states strains, behavior usually are rota­ s u s c eptible associated or calle d has load limit and be en one the d e v e l o p m e n t of with b r a n c h i n g of a respectively afte r b u c k l i n g for finite are they o ften lose st ab ility e q u i l i b r i u m load b i f u r c a t i o n buckl ing , impo rta nt p r oblems with they r e s u l t i n g in large b e n d i n g d e f o r ­ b u c k l i n g p r o b l e m to d etermine the critical the ensuing defo r m a t i o n s but In fact, w h e n they are s u b ­ forces, n e w e q u i l i b r i u m fig uration, w h i c h buckling struc­ Sin ce these st ructural m e m ­ The loss of s tability is an ex tr emal of the almo st lig h t - w e i g h t in- plane into small in the poin t Thus, the to clarif y of the m o s t lig h t - w e i g h t struc­ tures It is quite d ifficult to solve the foregoing buckling p r o b ­ lem through a direct a p p l i c a t i o n of the gene ral n o n l i n e a r ry of elasticity interes t is On the other hand, g e n erally nite deform a t i o n of restricted ela sti c beams, to theo­ the p r o b l e m of pract i c a l c o m p a r a t i v e l y small f i ­ plat es and shells, and for CHAPTER 544 Fig 6.43a One - c o n fig u tio n s of -B , : ( i) = L = mm ; ( i i ) 2 N, N = 9, P = 259 tie r th e N = , 2000 P = 2 L = O , = mm N, p o s tb u c k lin g s p ec im en ; ( i i i ) = N, Fig 6.4 3b Two - c o n fig u la tio n s -B when o f = mm t ie r th e : P = 11, P = 321.0 N ; ( i i ) L = , 11, P = 298.9 N ; ( i i i ) 11, P = 318.5 N N = 8, mm p o s tb u c k lin g s p e c im e n ( i) 2000 L = , L =O L0 = , , N = N = N = BUCKLING OF PA R T IA L L Y L I Q U I D - F I L L E D C YLIN D ER S 545 Finally, we shall compare the critical compressive load Pc here observed with the corresponding theoretical one stated in the preceding section For that purpose, we shall employ the notation (6.7.1) where kc and k° have been defined by equation (6.6.14) and where P° denotes the critical compressive load theoretically predict­ ed for the test cylinder when it is empty The results are shown in Fig 6.44 , (a) through (c) , in which the curves rep­ resent the theoretical results while small circles indicate the experimental ones The critical loads here observed for the cases Z = 500, 1000 and 2000, respectively, amount to 0.80 to 0.87, 0.80 to 0.82 and 0.88 to 0.90, of the corresponding theoretical ones, which seems to indicate a reasonable agreement cn O O < ) , - , O 1) O ( I cr - KI r ' r = 1000,1Ρ χ · P? = 3 O c _L 0.6 1.2 Ra 1.0 II o 0.6 L 1.2 0.8 *> Ρ χ = P ° = N (α) z ) , Ο- .1 (C ) Z = 0 , o o ! - 0.8J Ra 1.0 r.τ- 1.2 Ra 1.0 - Λ\ Ω · N (S on _ L J _ Ρ χ = , p £ = 11 N 0.8 - : Theory , o : Experiment j F ig 4 re s u lts the fo r f i l l i n g I I I I I _i _ IL _ 0.6 0.2 C om parison the 0.4 of v a r ia tio n r a tio L 0.6 , 0.8 Lo th e o re tic a l of the and c r it ic a l I.O e x p e rim e n ta l lo ad Ra w ith CHAPTER 546 between theory and experiment Comparison of the critical wave numbers theoretically predicted and experimentally observed was not made since the former correspond to the snapping critical state while the latter to the postbuckled stable state after snap-through buckling, which are not necessarily coincident It is to be added that the postbuckling relations here obtained for the shells with Z = 500 and 1000 when L q = are ascertain­ the corresponding theoretical ed to be in good agreement with ones presented non-dimensional in § 3.7, when forms, using the former the instead of Ρ , and Wm , respectively are represented in parameters Σ, and w m , REFERENCES CHAPTER NONLINEAR THEORY OF CIRCULAR CYLINDRICAL SHELLS S Timoshenko and J N Goodier , T h e o r y - H il l Book Company, I S Sokolnikoff , M a th e m a tic a l - H il l 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20 D Brush and B M c G w -H ill Company, Book Almroth, B u c k lin g 1975 547 of B ars, P la te s and S h e lls , REFERENCES 548 21 22 A S Wolmir,B i e g s a m e Kh.M Mushtari and K S h e lls , 23 24 Is e l P rogram W.T Koiter, T h e s is , 26 VEB N o n -L in e a r S c ie n tific S ta b ility G en eral E d , : D V e rla g 1962 Theory of T n s la tio n s M u s te r, D o n n e ll, (1 ), B.Budiansky, of E la s tic e q u a tio n s P roc Symp -2 , of on E la s tic 1962 1968 of S tru c tu re s , E q u ilib riu m U n iv e la s tic th e s ta b ility Theory H o u sto n , (in D u tch ), of fo r S h e lls th in s h e lls , to Honor L lo y d 1967 P o s tb u c k lin g T h eo ry, A p p l Mech 353-1366 Theory of Advances B u c k lin g in A p p l and W ile y & S J Britvec, Sons, The P o s t-B u c k lin g M e c h , J.M T Thompson and G W Hunt, John T h in L td , 1945 J.W Hutchinson and W T Koiter, ity , 30 th e in S tru c tu re s , 29 fo r U n iv e rs ity , W T Koiter, R e v , 28 S c h a le n , 1975 On D e lft H a m ilto n 27 und Galimov, J J Stoker,N o n l i n e a r E l a s t i c i t y , G o r d o n a n d B r e a c h , M Esslinger and B Geier, P o s tb u c k lin g B e h a v io r S p rin g e r-V e rla g , 25 P la tte n Z (1 ), A G en eral B e h a v io r of E la s tic E la s tic S ta b il­ -6 Theory of 1973 S ta b ility of E la s tic S ys te m s, P ergam on P ress In c , 1973 31 K Huseyin, n a tio n a l 32 V V Bolotin, b i l i t y , 33 M e c h a n ic s P ress, of On The s ta b ility , P ro b le m s E la s tic of S ta b ility U n iv e rs ity N o o rd h o ff In te r ­ th e Theory of E la s tic S ta ­ D yn am ic of Under N o n c o n s e rv a tiv e W a te rlo o , S ta b ility of Loads , 1973 E la s tic S ys te m s, H o ld e n -D a y , 1964 36 G Herrmann3 Ed., D y n a m i c S t a b i l i t y E H Dowell, A e r o e l a s t i c i t y o f 37 R D Blevins, 35 e la s tic 1963 D iv is o n , V V Bolotin, In c , th e o ry 1975 N o n c o n s e rv a tiv e Pergam on S Nemat-Nasser, S o lid 34 N o n lin e a r P u b lis h in g , n a tio a n l P u b lis h in g , of S tru c tu re s , p la te s and P ergam on s h e lls , P ress, N o o rd h o ff 1967 In te r - 1975 flo w -in d u c e d v ib tio n , Van N o s tra n d R e in h o ld Company, 1977 38 L H Donnell, No 39 479 S ta b ility of T h in -W a lle d Tubes under T o rs io n , NACA Rep (1 3 ) W Flügge, D ie S ta b ilitä t der K re is z y lin d e rs c h a le , In g -A rc h , (1 ), -5 40 J L Sanders, Jr., (1 ), 41 J L Sanders3 Jr., S h e lls , 42 NASA Tech A th in s h e lls , e la s tic T h in E la s tic An Rep W T Koiter, of N o n lin e a r T h e o rie s fo r T h in S h e lls , Q A p p l M a th , 21-36 Im p ro v e d R -24 c o n s is te n t in S h e lls , : F ir s t A p p ro x im a tio n Theory fo r T h in (1 9 ) f i r s t a p p ro x im a tio n W K o ite r, T 12-33, E d , N o rth -H o lla n d in th e P roc general Symp P u b lis h in g on th e o ry th e Company, of Theory 1960 REFERENCES 549 CHAPTER BUCKLING OF CIRCULAR CYLINDRICAL SHELLS UNDER FUNDAMENTAL LOADS 43 E Sehwerin, (1 ), 44 A Kromm, D ie spruchu ng durch (1 ), 45 S ta b ilitä ts g re n z e S ch u b -u n d S ta b ility (1 ), des d ü n n w a n d ig e n der ZAMM, Jb d e u ts ch b e i L u f tf Bean­ -F o rs c h , of T h in C y lin d ric a l S h e lls in T o rs io n , B u c k lin g 1, in T o rs io n , P roc 71 -4 95 C y lin d e rs N Yamaki , R ep o rt R ohres, K re is z y lin d e rs c h a le L ä n g s k rä fte , S B Batdorf_, M Stein and M Schildcrout, -W a lle d 47 T o r s io n s s ta b ilitä t 02 -6 16 R C Sturm, ASCE, 46 D ie -2 Rep of In s t NACA C irc u la r H ig h Speed TN No C r itic a l 1344, C y lin d ric a l M e c h a n ic s , S tre s s of T h in 1947 S h e lls Tohoku Under U n iv , T o rs io n / 17 (1 6 ), -1 48 N Yamaki and S Kodama, T o rs io n /R e p o rt 49 R V Mises, (1 ), 50 A W A Nash, B u c k lin g J A eron 55 T h in on th e Rep S h e lls (1 ), -1 z y lin d ris c h e r P roc R ohre, Z Under V D I., of of J B u c k lin g of (1 ), J , B P C Ho and S Cheng, C y lin d ric a l M e c h , Some A n a ly s is fo r S u b je c t to H y d ro s ta tic C o n d itio n s of (1 ), T h in and C y lin d e rs I n i t i a l S u b je c t to 51 -3 58 S h e lls Under E x te rn a l -1 C y lin d ric a l S h e ll under P ressu re by U s in g 104 9-10 P ro b le m s S h e lls S h e lls B oundary B u c k lin g 89-E M 3(1 ), A IA A S ta b ility T h in -W a lle d A p p l S and ers' Theory, E la s tic 54 -3 55 E ffe c ts S tre n g th P res su re , ASCE, of C y lin d ric a l Tsai-Chen Soong, (1 ), C y lin d ric a l M e c h , (1 ) (1 ), A E Armenäkas and G Herrmann, A e o lo tro p ic 56 of M e th o d NACA S e i., H y d ro s ta tic P ressu re, 54 C irc u la r Speed A ussendruck G D, Galletly and R Bart, E x te rn a l of H ig h S im p lifie d S h e lls , O u t-o f-R o u n d n e ss 53 B u c k lin g In s t K ritis c h e C y lin d ric a l P res su re , 52 Der Rep -7 5 S B Batdorf, T h in 51 2, under in S ta b ility C o m b in e d of H ete ro g en eo u s L o a d in g , A IA A J , 60 3-16 L H Sobel, E ffe c ts in d e rs to S u b je c t of B oundary L a te l and C o n d itio n s A x ia l on P ressu re, th e S ta b ility A IA A J , of (1 ), C y l­ 1437— 1440 57 58 W Thielemann and M Esslinger, E in flu s s B e u lla s t Der W Schnell, s c h a le n 59 von E in f lu s s u n te r N Yamaki, P ressu re, 60 K re is z lin d e rs c h a le n , B u c k lin g Rep G Fischer, S t a b ilitä t In n e n d ru c k , der R a n d v e rw ö lb u n g a u f M a n te ld ru c k , In s t Ueber of H ig h den d ü n n w a n d ig e r Z f Der S ta h lb a u , C irc u la r Speed R a n d b e d in g u n g e n d ie 3 (1 ), B e u lw e rte (1 ), C y lin d ric a l M e c h , E in flu s s der S ta h lb a u , der (1 9 ), F lu g w is s e n s c h a fte n , 1 (1 ), d ie von Z y lin d e r- -1 S h e lls Under E x te rn a l 5-55 g e le n k ig e n K re is z y lin d e rs c h a le n auf -3 Lagerun g u n te r 1 -1 auf d ie A x ia lla s t und 550 61 REFERENCES G Fischer, -W a lle d A IA A 62 J , (1 ), M Stein , th e 63 The B u c k lin g S 65 N a t M e c h , N.J Hoff, A x ia l In flu e n c e H, Ohira, N J Hoff, Low J A p p l a t M e c h , A p p l In t of 1, M e c h , Edge (1 6 ), A n a ly s is — A on G en eral P roc th U S ta b ility of A x ia lly -1 on th e P ressu re, T h in 1961, th S tre ss es C irc u la r B u c k lin g Rep In s t C y lin d ric a l (1 6 ), of H ig h S h e lls -2 C om pressed C y lin d e rs , P roc 7-41 of A x ia lly In t Sym p of J A x ia lly A p p l B u c k lin g S m a lle r th an Com pressed Space C y lin d e rs T e c h n o lo g y and C om pressed M e c h , of A x ia lly th e C irc u la r (1 ), C om pressed C la s s ic a l Cy­ 3 -5 C r itic a l C y lin ­ V a lu e , -5 u c k lin g Mech of S e i., B u c k lin g of C irc u la r (1 ), C irc u la r Bases R o ta tio n s ), on C y lin d ric a l S h e lls in 89 -5 20 C y lin d ric a l th e Rep (1 ), 11 -1 42 D o n n e ll In s t S h e lls under E q u a tio n s H ig h Neg­ Speed M e c h , P e rfe c t S h e lls Mode Under Shape A x ia l in L in e a r th e C o m p re ss io n , J -8 2, B u c k lin g of (S o lu tio n s Edge Mangelsdorf, C y lin d ric a l The C y lin d ric a l (1 ), P re b u c k lin g P S tre ss es E nergy, D e fo rm a tio n s Theory (S o lu tio n s C irc u la r le c tin g la r S tra in A x ia lly L e n g th , J N Yamaki and S Kodama, C and 99-123 C o m p re s s io n /R e p o rt 75 J , of Mann-Naohbar and W Naohbar, B u c k lin g B u c k lin g th e E x te rn a l of P roc F in ite P re b u c k lin g (1 ), P T h in 1 -5 N Yamaki and S Kodama, le c tin g of P ressu re, 1964 C o n d it io n s on th e M e c h , B u c k lin g (1 ), C o m p re s s io n , R -190, T e c h n o lo g y , Theory S tre s s e s C o m p re s s io n /R e p o rt 74 J N J Hoff and T C Soong , B A x ia l of B e h a v io r B u c k lin g of D e fo rm a tio n s TR S h e ll A IA A N J Hoff and L W Rehfield, S h e lls S ta b ility In te rn a l 97 -5 05 under A p p l Local S h e lls Edge Is e l 1963, T h in P re b u c k lin g E ig e n v a lu e s , Tokyo, on and 81-10 C ong r L in e a r V a rio u s of B u c k lin g N a t NASA 1962, of P e rp le x in g Local Japan Load P re b u c k lin g S h e lls , (1 ), The C o n d itio n s A x ia l V a ria tio n S h e lls C o m p re ss io n , H Ohira, d ric a l 73 of M e c h , In flu e n c e lin d r ic a l 72 A p p l C y lin d ric a l S c ie n c e , 71 under C y lin d e rs , Second N Yamaki, and 70 th e C y lin d ric a l 11th 69 P e rfe c t C om pressed in 68 fo r B Almroth, Speed 67 B oundary -7 In flu e n c e of C ong r C irc u la r 66 of S h e lls D Brush and B Almroth, E x p re s s io n 64 In flu e n c e C y lin d ric a l The S h e lls , C irc u la r Based R o ta tio n s ), Rep M o rle y -K o ite r P a rt and on C y lin d ric a l th e In s t E q u a tio n s 2, J F lü g g e H ig h fo r A p p l S h e lls under E q u a tio n s Speed T h in -W a lle d M e c h , Neg­ M e c h , 24 C irc u ­ (1 ), 961— 970 76 W T Koiter , T h in S h e ll G en eral T heory, New Theory of Trends and S h e ll S ta b ility , A p p lic a tio n s , in : 65-87, W O ls z a k , E d , S p rin g e r-V e rla g , 1980 77 J G Simmonds and D A Danielson, of A x ia lly C o n d itio n s , Com pressed J A p p l C y lin d ric a l M e c h , New S h e lls (1 ), R e s u lts fo r S u b je c t 93-100 th e to B u c k lin g R e la x e d Loads B oun dary REFERENCES 78 D J Gorman and R M Evan-Iwanowski, In v e s tig a tio n of B u c k lin g of to L o a d in g A x ia l M e c h , 79 th e C la m p ed (1 ), E ffe c ts (1 ), and In te rn a l Edge P re b u c k lin g Th von Karman, M a th e m a tis c h e n 83 K Marguerre, in Edge Ebene und B u c k lin g der A p p l In s t th e of 3rd U Rep In s t OF Speed M e c h , S h e lls F lü g g e H ig h under E q u a tio n s Speed M e c h , C IR C U L A R FUNDAMENTAL im LOADS M a s c h in e n b a u , P la tte C a m b rid g e ASME, m it g rosser sehr N a t Form änderun g, 3-10 TheS tre n g th dünnem of T h in S te g b le c h , Z f 200 B e n d in g C ong r der 3-57 (1 9 ), N o n -L in e a r S E n c y k l o p ä ’d i e (1 ), (1 ), E x a m in a tio n EM3, and A p p l B u c k lin g M e c h , of C ir ­ P ro v id e n c e New ST3, S tre n g th TR 473 Y ork, P o s t-B u c k lin g Behav­ Mode In te c tio n , 117— in : J G ranada Local and O ver­ Rhodes and A P u b lis h in g C L im ite d , 1980 of T h in S e c tio n s in C o m p re ss io n , T e sts of T h in -W a lle d D u lu m in C y lin d e rs in (1 3 ) New Theory and B e n d in g , fo r th e Trans T von Karman and H S Tsien9 T h e C o m p re s s io n , B e tw e en P a n e ls , 5 -4 A J A eron B u c k lin g ASME, B u c k lin g S o c , N J Hoffj W A Madsen and J Mayers, C om pressed IV In te c tio n A n a ly s is C o m p re s s io n A x ia l P la te S tru c tu re s , C o m p re s s io n N o n lin e a r NACA of -4 S tru c tu re s , -8 , Sydney, (1 ), L H Donnell, -1 3 under E q u a tio n s 1976 T h in -W a lle d T o ro n to , A S C E , A x ia lly th e A p p l S h e lls C y lin d ric a l g e krü m m te n B u c k lin g o f S tiffe n e d E E Lundquist, under and Type H ig h M o d ifie d -3 M e c h , Trans (1 7 ), G J Hancock, A x ia l 93 on B E H A V IO R B le c h w a n d trä g e r P roc ASCE, C o m p re ss io n , 92 Rep D o n n e ll (1 ), W T Koiter and A van der Neut, P roc Th eo r C y lin d ric a l th e C irc u la r UNDER M o to r lu fts h iffa h r t, S p rin g e r-V e rla g , London, on S u b je c te d -3 W a lk e r, E d , 91 T h e o rie C ong r B Budiansky3 Ed., a l l 90 of Based F e s tig k e its p ro b le m e Zur P la te s , P roc 171, 89 SHELLS J Rhodes and J Μ Harvey, io r , 88 on R o ta tio n s ), H B Keller and E L Reiss, (1 ), 87 C irc u la r Based P O S T B U C K L IN G C o m p re ss io n , H Wagner, c u la r 86 of B u c k lin g W is s e n s c h a fte n , In t F lu g te c h n ik 85 S h e lls in Th von KarmanE E Seohler and L H Donnell, P la te s 84 D e v e lo p , R o ta tio n s ), (S o lu tio n s C Y L IN D R IC A L th E x p e rim e n ta l -3 CHAPTER P roc and D e fo rm a tio n s C y lin d ric a l P res su re , (S o lu tio n s P re b u c k lin g C o n s id e rin g 82 A n a ly tic a l 9-14 C o m p re s s io n /R e p o rt , 81 An P re b u c k lin g C irc u la r B u c k lin g 3, N Yamaki and S Kodama, (1 ), Large T h in -W a lle d N Yamaki and S Kodama, C o n s id e rin g of 15 -4 26 C o m p re s s io n /R e p o rt 80 551 C irc u la r C y lin d ric a l o f T h in (1 ), of T h in (1 ), Under 95 -8 C y lin d ric a l S h e lls 3 -3 P o s tb u c k lin g S h e lls , C y lin d e rs A IA A E q u ilib riu m J , of (1 6 ), REFERENCES 552 94 R C Tennyson, lin d r ic a l 95 A N ote S h e lls S ta b ility p re s s io n , of in : F th e C irc u la r N io rd s o n , E d , Load J , of T h in N a c h b e u lla s te n a ls von Com­ 64 -2 93 , u n tere K re is z y lin d e rn , Der G renze S ta h lb a u -3 N, Yamaki and K Otomo, C y lin d ric a l E x p e rim e n ts S h e lls Under on th e P o s tb u c k lin g H y d ro s ta tic B e h a v io r of P res su re , Exp M e c h , of C y lin d ric a l 99 -3 N Yamaki and J Tani, under P o s tb u c k lin g H y d ro s ta tic P res su re , B e h a v io r ZAMM, N, Yamaki_, K Otomo and K Matsuda, of (1 ), C irc u la r C y lin d ric a l C irc u la r (1 ), E x p e rim e n ts S h e lls Under 09 -7 on th e P o s tb u c k lin g C o m p re s s io n , E x p M e c h , 23-28 N Yamaki and S Kodama, c a l A x ia l S h e lls , G erech n ete B e h a v io r Cy­ -4 E q u ilib riu m under B e u lla s te n S h e lls C irc u la r P o s tb u c k lin g C y lin d e rs Theory of (1 ), 1969 e x p e rim e n te lle n a x ia le n (1 ), 100 On A IA A der C irc u la r 99 I B u c k lin g M Esslinger and B Geier, (1 ), 98 C la s s ic a l C o m p re s s io n , T h in -W a lle d S p rin g e r-V e rla g , 97 th e A x ia l W F Thielemann and M E Esslinger, and 96 on under S h e lls Under P o s tb u c k lin g C o m p re s s io n , In t J B e h a v io r of N o n -L in e a r C irc u la r M e c h , C y lin d ri­ 1 (1 ), 99- 111 101 N Yamaki, lin d r ic a l E x p e rim e n ts S h e lls S tru c tu re s , 102 103 -3 , on th e P o s tb u c k lin g T o rs io n , in : B S p rin g e r-V e rla g , B e h a v io r B u d ia n s k y , P o s tb u c k lin g B e h a v io r c a l In g (1 ), S h e lls Under T o rs io n , Y C Fung and E E Sechler, N G o o d ie r P ergam on and P ress N L td , J -A rc h , In s ta b ility H o ff, E d , and C irc u la r Cy­ B u c k lin g of of of C irc u la r C y lin d r i­ 79-89 T h in E la s tic S h e lls , S tru c tu l M e c h a n ic s , T h in -S h e ll S tru c tu re s in : 1 -1 , 1960 Y C Fung and E E Sechler3 Ed,, E x p e rim e n t of E d , 1976 N Yamaki' and K, Matsuda, J 104 under D e s ig n , P r e n tic e -H a ll, In c , E n g le w o o d — T h eo ry, C lif f s , N J , A n a ly s is fo r 1974 105 S B Batdorf, T h in 106 E E Lundquist, T o rs io n , 107 P roc to No U S of N a t of J L arge C o n g r of under T o rs io n , of on 874, D e fle c tio n s Under A p p l M e c h , D u lu m in Japan and T o rs io n M e c h , C y lin d e rs (1 ), Soc Im p e rfe c tio n s and (1 ), Im p e rfe c t P o s tb u c k lin g Trans S ta b ility 1947 T h in -W a lle d I n i t i a l l y A p p l E la s tic No in 1932 C y lin d e rs T Hayashi and Y Hirano, ders Rep T ests 427, B u c k lin g T o rs io n , M eth o d NACA S tre n g th E ffe c ts B u c k lin g 2nd S im p lifie d S h e lls , T N W A Nash, je c t 109 NACA Τ T Loo, E la s tic 108 A C y lin d ric a l on th e C o m p re s s io n , -3 C y lin d ric a l S h e lls Sub­ -1 B e h a v io r A ero A x ia l of Space O rth o tro p ic S e i., C y lin ­ (1 ), 47 -5 110 W A Nash, ly An Im p e rfe c t S tre s s A n a l., E x p e rim e n ta l C y lin d ric a l (1 9 ), A n a ly s is S h e lls 55-68 of S u b je c t th e to B u c k lin g T o rs io n , of T h in P roc I n i t i a l ­ Soc Exp REFERENCES 111 V I Weingarten, on th e N a t 112 C ong r I E ffe c t of M e c h , S h e a rin g E d , In te rn a l S h e lls (1 ), Theory of ZA M M and T o rs io n , a C la m p ed (1 6 ), B e h a v io r of P ressu re Under A x ia l P roc T e n s io n th U S -8 B e h a v io r Forces, P o s tb u c k lin g N io rd s o n , of C y lin d ric a l P o s tb u c k lin g A c tio n B Budiansky, F The of A p p l N Yamaki, the 113 B u c k lin g 553 T h in of In f in it e C y lin d e rs S h e lls , S trip Under -2 in 2 -2 3 , T o rs io n , S p rin g e r in : V e rla g , 1969 114 D W Windenburg and C Trilling, C y lin d ric a l S h e lls Under E x te rn a l C o lla p s e by P ressu re, In s ta b ility Trans ASME , of T h in 56(1934) , -8 115 R G Sturm, d e rs, 116 Eng T h in B u c k lin g P ressu re, H y d ro s ta tic J P and C o m p re s s io n , to of T h in -W a lle d I l lin o is E x te rn a l Spannungen of C y lin ­ (1 ) S n ap -T h ro u g h P ressu re, J , M e c h , P roc A c tio n SESA 14 E ffe c t of S h e lls J A p p l B e h ä lte rn C o m b in e d T o rs io n 92 -1 S ta b ility of T h in -W a lle d E x te rn a l P ressu re Cy­ and -9 o f T h in -W a lle d Mech Im p e rfe c tio n s J Under C o m b in e d (1 ), B e h a v io r z y lin d ris c h e n -3 (1 ), E la s tic under P ressu re, P res su re , von (1 ), C y lin d ric a l Exp S h e lls A IA A E x te rn a l E x te rn a l Engng on M e c h , C y lin d ric a l S h e lls S e i.,1 (1 9 ), 0-56 B u c k lin g (1 ), o f T h in C y lin d e rs 69 -5 75 Kempner, K A V Pandalai, S A Patel and J Crouzet-Pascal3 s ta tic B e h a v io r P ressu re, J o f C irc u la r A eron S e i., u n ter A ussendruck, B e u l-u n d Der S ta h lb a u , H R Meyer-Piening, T h e o re tis c h e N a c h b e u lv e rh a lte n s d ü n n w a n d ig e r R ändern u n ter -W ilh e lm in a C y lin d ric a l (1 ), W Thielemann and M Esslinger, Z y lin d e r 125 of E x p e rim e n ta l P o s tb u c k lin g 124 C o n ic a l L H Donnell, J P ressu re U n iv O b s e rv a tio n s VDI Weingarten and P Seide, Montague, Under 123 und and S u b je c te d 122 329, Under Z e its c h r R E Ekstrom, A x ia l 121 C o lla p s in g No S h e lls B e u ld ru c k A ussendruck, lin d r ic a l 120 th e B u ll -2 H Meineke, u n te r 119 of S ta C y lin d ric a l (1 ), 118 S tu d y A, F Kirstein and E Wenk3 Jr., in 117 A Exp und A u s s e n d ru c k b e la s tu n g , zu B u n s c h w e ig (1 ) , S h e lls Under (1 ), H ydro­ U n tersu ch u n g m it D is s e rta tio n , is o tro p e r -1 e x p e rim e n te lle der e in g e s p a n n te n Tech U n iv C a ro lo 89pp I n i t i a l E x te rn a l under N a c h b e u lv e rh a lte n K re is z y lin d e r B Budiansky and J C Amazigo, C y lin d ric a l S h e lls -2 P o s tb u c k lin g P res su re , J M a th B e h a v io r P h y s , of (1 ), 2 -2 126 J C Amazigo and W B Fraser, C y lin d ric a l S o lid s 127 S h e lls S tru c tu re s , D im p le (1 ), M Esslinger and B Geier, S p rin g e r-V e rla g 128 w ith (1 ), R C Tennyson, A x ia l C o m p re s s io n , pp B u c k lin g A IA A J , B u c k lin g Shaped under I n i t i a l E x te rn a l P ressu re Im p e rfe c tio n s , In t of J 83 -9 00 P o s tb u c k lin g B e h a v io r of S tru c tu re s , 2-91 Modes of (1 9 ), C irc u la r C y lin d ric a l 1481-1487 S h e lls under REFERENCES 554 129 R C Tennyson _, M Booton and K H Chan , Under C o m b in e d L o a d in g , J A p p l B u c k lin g M e c h , of Trans S hort ASME , C y lin d e rs E (1 ), -5 130 J Kempner , C y lin d ric a l 131 P roc 133 of New C e n te n n ia l B, Almroth, B u c k lin g J , (1 ), P o s tb u c k lin g B u c k le d (1 ), Under a C y lin d ric a l L T h in 138 C irc u la r New J , J (1 ), M Esslinger , Engng A n a ly s is and CHAPTER and Z y lin d e r, 142 Der IN IT IA L 144 of S h e ll Cong fo r (1 6 ), A p p l A x ia lly 152 6-15 lä n g s g e d ru c k te n (1 ), 20-24 P o s tb u c k lin g B e h a v io r -E M (1 ), -6 E la s tic under S ta b ility A x ia l (1 ), P o s tb u c k lin g C y lin d ric a l of of C o m p re s s io n , 73-76 E q u ilib r ia S h e lls E x p e rim e n ts , AND : J A p p l A of A x ia lly F in ite -E le m e n t M e c h , Speed M e c h , Tohoku Trans ASME, W T K o ite r N o rth -H o lla n d U n iv , and of G E -3 B Budiansky and P u b lis h in g B a rre le d (1 9 ), and S h e lls E ffe c t D e fle c tio n s T o rs io n , Rep 53-71 A n a ly s e s Company, I n i t i a l under (1 ), fo r th e C y lin d ric a l M ik h a ilo v , C y lin d ric a l of S h e lls C irc u la r K S E N S IT IV IT Y LOADS P e rtu rb a tio n S e n s itiv ity 35 -6 67 , S tiffe n e d IM P E R FE C TIO N C y lin d ric a l J W Hutchinson and J, C Frauenthal, 2 -2 In t C rite rio n J , S h e lls FUNDAMENTAL C irc u la r in : C y lin d ric a l C irc u la r C y lin d ric a l 11th P Seide, Watanabe and S Kodama, B u c k lin g Im p e rfe c tio n M e c h , Com pressed S ta h lb a u , ASCE, S ta h lb a u , P O S TB U C K LIN G T o rs io n , of A IA A Der P roc S ta b le W ith N Yamaki and S Kodama, and 143 Länge, C o n ic a l C irc u la r C o m p a ris o n H ig h C y lin d e r -4 N Y a m a k i T In s t C irc u la r 0 -5 UNDER th e th e H o c h g e s c h w in d ig k e ita u fn a h m e n vom B e u lv o rg a n g d ü n n w a n d ig e r, E la s tic E -4 (1 7 ), of A s tro n a u tic s , (1 ) C irc u la r P roc B u c k lin g S h e lls , D iv , A Maewal and W Nachbar, on 3366 A x ia lly a S n ap -T h ro u g h e n d lic h e r C y lin d ric a l C om pressed, 141 U n ifo rm de Neufville and J J Connory J r , C y lin d e rs , a x ia lb e la s te te r 140 of of V I Weingarten, E J Morgan and A IA A a No B e i t r a g zum N a c h b e u l v e r h a l t e n v o n d ü n n w a n d ig e n T h in -W a lle d 139 of M , C o m p re ss io n , C om pressed R T h e o rie s and -3 K re is z y lin d e rs c h a le n 137 N o n lin e a r 6-121 B e h a v io r R M Jones , T o w a r d H, Appel, th e A e ro n a u tic s C irc u la r 342 -6 3 B e h a v io r A x ia l Com pressed -3 , , S tre n g th and A x ia lly in (1 9 ), R P o s tb u c k lin g A IA A M Uemura, S h e lls C o n f., The A x ia l of (1 ), D e v e lo p m e n ts C o m p re ss io n , in S e i., C y lin d ric a l Loaded Mech 136 B e h a v io r A eron A J Sobey , L o c a lly 135 T h in D urand C y lin d e rs , 134 J W F Thielemann , B u c k lin g 132 P o s tb u c k lin g S h e lls , E d , P o s tb u c k lin g S h e lls Theory of under S h e lls , 1980 E la s tic S h e lls , P o s tb u c k lin g Trans ASME, B e h a v io r J A p p l -7 J C Amazigo, under E x te rn a l I n i t i a l P res su re , P o s t-B u c k lin g J M a th P h y , B e h a v io r 47(1968) of , REFERENCES 145 J C Amazigo and W B.Fraser, C y lin d ric a l S o lid s 146 S h e lls w ith S tru c tu re s , G A Cohen, -S tiffe n e d D im p le (1 ), C o m p u ter O rth o tro p ic 555 B u c k lin g Shaped under I n i t i a l E x te rn a l P ressu re Im p e rfe c tio n s , of In t J 83 -9 00 A n a ly s is S h e lls of of Im p e rfe c tio n R e v o lu tio n , S e n s itiv ity A IA A J , of R in g (1 ), 1032- 1039 147 L H Donnell and C C Wan, T h in C y lin d e rs (1 ), 148 P roc 149 2nd U S of L arge of A x ia l N a t.C ong r S tiffe n e d under A p p l B u c k lin g under (1 ), The E ffe c t of C y lin d ric a l S h e lls Under B66 (1 ), C irc u la r (1 9 ), 1954, A x ia l A IA A J on th e C o m p re ss io n , S e n s itiv ity J , (1 ), B e h a v io r A p p l of of O val M e c h , Ec­ -4 C y lin ­ Trans ASME, A x is y m m e tric A x ia l Im p e rfe c tio n s C o m p re ss io n , on Buck­ th e P roc Kon Ned 265 C y lin d ric a l S h e lls B u c k lin g under of A x ia l A x is y m m e tric C o m p re ss io n , Im p e r­ A IA A J , 2127-2131 J W Hutohinson3 R C, Tennyson and D B Muggeridge, E ffe c t Local of la r of M e c h , -3 P o s tb u c k lin g C o m p re s s io n , R C Tennyson and D B Muggeridge, fe c t B u c k lin g A p p l 66-72 W T Koiter, W e t, on J Im p e rfe c tio n s and Im p e rfe c tio n S h e lls , and and T o rs io n M e c h , C y lin d ric a l A x ia l S h e lls of Im p e rfe c tio n s C o m p re ss io n , D e fle c tio n s C y lin d e rs d r ic a l Ak 153 of J, W Hutohinson, lin g 152 E ffe c t under J W Hutohinson and J.C Amazigo, E -3 151 E ffe c ts B u c k lin g c e n tr ic a lly 150 C o lu m n s 73-83 Tsu-Tao Loo, E la s tic and A x is y m m e tric C y lin d ric a l Im p e rfe c tio n S h e ll under on A x ia l th e B u c k lin g C o m p re ss io n , B e h a v io r A IA A J , F o rm u la s fo r a of a C irc u ­ (1 ), 48 52 154 J C Amazigo and B Budiansky, S tre s s e s of A x ia lly A x is y m m e tric Com pressed Im p e rfe c tio n s , J A s y m p to tic C y lin d e rs A p p l w ith M e c h , th e L o c a liz e d Trans B u c k lin g or Random ASME, E -3 (1 ), c ir c u la r c y lin d r ic a l -1 155 B Budiansky and J W Hutchinson, s h e lls under a ir c r a f t B u c k lin g A x ia l S h e lls to of A 8-38 der and In t o f A x ia lly L e n g th , J P e rtu rb a tio n C om pressed A p p l M e c h , T h in N e u t, R in g J th e th e o ry -2 , S tiffe n e d S o lid s C y lin d ric a l S h e lls of S o lu tio n s C y lin d ric a l (1 ), of D e lft C y lin d r i­ S tru c tu re s , fo r S h e lls th e of B u c k lin g In f in it e or 54 -7 S n a p p in g F in ite of L e n g th , Im p e rfe c t J A p p l T h in -W a lle d M e c h , 38 -1 J Arbocz and C D Babcock3 Jr., T h e th e van to -6 C irc u la r on of C o n trib u tio n U n s tiffe n e d Κ Y Narasimhan and N J Hoff, (1 ), B u c k lin g : C o m p re s s io n , C L Dym and N J Hoff, F in ite 159 Under in 1972 c a l P ro b le m s 158 P ress, p re s e n te d P T Pedersen, (1 ), 157 c o m p re s s io n , s tru c tu re s , U n iv e rs ity 156 a x ia l B u c k lin g of C y lin d ric a l S h e lls , E ffe c t J of G eneral A p p l Im p e rfe c tio n s M e c h , (1 9 ), REFERENCES 556 160 P Bhatia and C D Babcock_, Jr , A x ia l S h e lls J W ith P ris m a tic Im p e rfe c tio n s , B u c k lin g A p p l of M e c h , C y lin d ric a l (1 ), 731— 736 161 J Arbocz and E E Sechler, Im p e rfe c t 162 C y lin d ric a l J S Hansen, C y lin d ric a l 163 R C Tennyson, th e of 164 165 B u c k lin g S tru c tu re s , J Arbocz, J A IA A P as t, J , of P resen t S tiffe n e d of W et S h e lls and under A p p lie d F u tu re and 1976 of M e c h a n ic s , The E ffe c t of S h e lls Under of S h e ll B66, 265, in A x ia l C o m b in e d T o rs io n M e c h , B u c k lin g C o n g r AND in : Trans and 61 -4 76 , A x ia l B u c k lin g C Ho and S Cheng, C y lin d ric a l 1469 Z Is e l M easure­ J T e c h , T o f K o ite r, C irc u la r E d , N o rth -H o lla n d Theo­ P u b lis h in g Im p e rfe c tio n s on P roc th e Kon Buck­ Ned of of Rep OF C O M B IN E D S ta b ility L a te l of or No S tre ss 887, of T h in 1947 C IR C U L A R LOADS T h in -W a lle d C y lin d e rs H y d ro s ta tic P ressu re, -1 In te rn a l S h e lls 1962, C r itic a l NACA P ressu re under T o rs io n , and A x ia l P roc T e n s io n th U S -8 C y lin d ric a l Exp M e c h , Some P ro b le m s S h e lls under S h e lls (1 ), in Under S ta b ility C o m b in e d C o m b in e d T o rs io n -1 of L o a d in g H e te ro g en eo u s , A IA A J , 603-1607 G J Simitses, C o m b in e d A n a ly s is , Im p e rfe c tio n C o m p re ss io n , (1 9 ), C y lin d ric a l P res su re , A e o lo tro p ic The E ffe c t M e c h , UNDER E x te rn a l ASME, The of A p p l H y d ro s ta tic (1 ), Based -ft-D ia m e te r S e n s itiv ity W P O S TB U C K LIN G SHELLS and P a S ta b ility I n i t i a l C o m p re s s io n , B U C K LIN G R E Ekstrom,_ B on Loads -3 1 1963 V I Weingarten, N a t Ib id , P re d ic tio n s , A x is y m m e tric H S Suer and L A Harris, th e B u c k lin g S urveys Im p e rfe c tio n C o m p re s s io n , C Y L IN D R IC A L on on B u c k lin g 35 -3 48 B u c k lin g C y lin d ric a l C y lin d e rs A p p l E d , 1977 CHAPTER J S tiffe n in g B u d ia n s k y , S B Batdorfj M Schildcrout and M Stein, Under and Loaded 122 3-12 3 9 -9 (1 ), P o s tb u c k lin g S h e lls and -W a lle d 175 and A x ia lly 24 -3 W T Koiter, Ak 174 B Im p e rfe c tio n (1 7 ), W e ltra u m fo rs c h , N Yamaki, lin g 173 : Singer_, H Abramovich and R, Yaffe, Company, 172 I n i t i a l in Com pressed 37 -7 1 (1 ), Im p e rfe c tio n s in S p rin g e r-V e rla g , J Arbocz and J G Williams, r e tic a l 171 Shape C y lin d e rs , M easured A x ia lly Im p e rfe c tio n s S tru c tu re s , Im p e rfe c tio n s , C y lin d ric a l 170 of (1 ), P re d ic tio n E x p e rim e n ta lly 17 (1 ), 169 of B u c k lin g M e c h , on m en ts 168 S o lid s E ffe c t -2 , th e A p p l G en eral J C irc u la r J J Arbocz and C D Babcock3 Jr., F lu g w is s 167 of In t The of S tru c tu re s , S h e ll 166 In flu e n c e S h e lls , On S h e lls , T o rs io n In s ta b ility and of H y d ro s ta tic O rth o tro p ic P res su re , C y lin d ric a l A IA A J , S h e lls (1 ), under 1463- REFERENCES 176 177 M Booton and R C Tennyson, B u c k lin g of c u la r L o a d in g , A IA A C y lin d e rs o f 179 C o m b in e d 181 th e In s t 183 H ig h of Speed C irc u la r In t N o n -L in e a r J B u c k lin g P ressu re M e c h , C y lin d ric a l of and M e c h a n ic s , (1 ), U n iv , C y lin d ric a l M e c h , Trans B u c k lin g S h e lls ASME, Under under A x ia l S h e lls , (1 ), J , J Hutchinson, T h eo ry, C o m p o s ite and C o m b in e d I of P res­ E x p e rim e n t In t , J N o n -L in e a r Homogeneous L o a d in g , Is o ­ J A p p l of C y lin ­ -7 of S ta b ility C o m p re s s io n , of A IA A A n a ly s is J , P re s s u riz e d (1 ), 2259-2263 Im p e rfe c t C y lin d ric a l 1461-1466 E x te rn a l of Im p e rfe c t P ressu re, L o a d in g , and R a d ia l C y lin d ric a l A IA A J , R C Tennyson_, M Booton and Κ H Chan, under 57-76 B e h a v io r — M e m o irs 3 -3 of M e th o d B u c k lin g B u c k lin g and A B ia x ia l J Hutchinson, A IA A T o rs io n I I A x ia l E -3 (1 9 ), M Zyczkowski and S Bucko, S h e lls — S h e lls J a p a n e s e ), (1 9 ), C ir ­ -2 C y lin d ric a l (in P o s tb u c k lin g under A n is o tro p ic (1 9 ), 55 -3 M M Lei and S Cheng, tro p ic J , C irc u la r (1 ), Ib id Im p e rfe c t T o rs io n Tohoku S h e lls S Kodama and N Yamaki, C o m p re s s io n 184 A c tio n s u riz e d d r ic a l 182 C o m b in e d S KodamaK Otomo and N Yamaki, M e c h a n ic s , 180 under S Kodama and N Yamaki, under 178 557 J A p p l M e c h , S h e lls (1 ), B u c k lin g Trans under A x ia l 1968-1970 of ASME, S hort C y lin d e rs E -4 (1 ), 574- 578 185 V I Weingarten and P Seide, lin d r ic a l A x ia l 186 and C o m p re ss io n , P ressu re A IA A and A x ia l C o m p re ss io n , S ta h lb a u , (1 9 ), Mech and -A (1 ), S Kodama and N Yamaki, C y lin d ric a l S h e lls Trans S Y Lu, End Load, Soc Mech B u c k lin g A IA A P Schroder, J , Ueber of Soc d ie E E Lundquist, C o m b in e d and S ta b ility C o m b in e d of In te rn a l 111 8-11 B e u lla s te n — Neue of a x ia l V ersuche Shear (in und g e d rü c k te r V o rs c h rifte n , C y lin d ric a l S h e lls J a p a n e s e ), T n s Japan B e h a v io r Mech E n g rs , Ib id : : R eport -A (1 ), of R eport P re s s u riz e d 1, -A (1 ), 2, C irc u ­ E x p e rim e n t Theory (in -9 (in J ap a n e se ), -9 C y lin d ric a l S h e ll w ith a T ran sverse 2350-2351 S ta b ilitä t ZAMM, C irc u la r L o a d in g s C a n tile v e r S tre n g th T ran servse Cy­ 6 -3 E n g rs , (1 ), K re is z y lin d e rs c h a le , P ressu re E la s tic under (1 ), C o m p re s s io n S Kodama and N Yamaki, Japan J , P o s tb u c k lin g under Japan T h in -W a lle d -2 P ressu re E n g rs , S h e lls Reif, A In n e n d ru c k B u c k lin g T ran s 193 A IA A A x ia l C o m b in e d J ap a n e se ), 192 m it of E x te rn a l Seide, P C o n ic a l under la r 191 and S ta b ility C o m b in e d 13 -9 20 S Kodama and N Yamaki, Soc 190 under (1 ), Von H Saal, H Kahmer and Der 189 J , C y lin d ric a l K re is z y lin d e rs c h a le n 188 E la s tic S h e lls V I Weingarten, E J Morgan and T h in -W a lle d 187 C o n ic a l der (1 ), Test and of q u e rk ftb e la s te te n d ü n n w a n d ig e n T -T T h in -W a lle d B e n d in g , NACA D u lu m in Tech N o te C y lin d e rs No 523, in 1935 REFERENCES 558 194 N Yamaki3 K Naito and S h e lls s ta tic under P res su re , S tru c tu re s , 195 C o m b in e d in : -2 , E S a t o , A c tio n J a Rhodes G ranada B u c k lin g of and A and A n a ly s is , C P u b lis h in g B Almroth and A M C Holmes , E x p e rim e n t In t of T ran sverse L im ite d , S o lid s C y lin d ric a l Load W a lk e r, B u c k lin g J C irc u la r Edge and E d , H ydro­ T h in -W a lle d 1980 of S h e lls S tru c tu re s , w ith C u to u ts , (1 ), 1057- 1071 196 B Almrothj F A Brogan and M B Marlowe , C y lin d e rs 197 198 w ith C irc u la r C y lin d ric a l A IA A J , (1 ), S u b je c te d (in U n iv , Soc Edge and th e of Load In s t C o lla p s e P ressu re C irc u la r and H ig h P O S TB U C K LIN G Z y lin d e r Der m it SHELLS OF of Loads, C y lin d ric a l H y d ro s ta tic Speed P A R T IA L L Y UNDER M e c h , P res­ Tohoku Spannungs - b e lie b ig e r L IQ U ID -F IL L E D FUNDAMENTAL und LOADS S ta b ilitä ts n a c h w e is F lü s s ig k e its fü llu n g , Mech E n g rs , S h e lls B u c k lin g under -A (1 ), of T o rs io n P a r t ia lly (in Der fü r S ta h lb a u , L iq u id -F ille d (in Trans Japan 208-1217 C irc u la r J ap a n e se ), L iq u id -F ille d J a p a n e s e ), H Dokij N Yamaki3 J Tani and K Otomo, No P o s tb u c k lin g C y lin d ric a l T ran s Japan Soc S h e lls Mech B e h a v io r under E n g rs , of T o rs io n — -A (1 ), 449 H Doki3N Yamaki and J Tani, C irc u la r Trans C y lin d ric a l Japan Soc S h e lls Mech B u c k lin g under E n g rs , of P ressu re L iq u id -F ille d -A (1 ), — E x p e rim e n t -A (1 984), No C irc u la r (in Trans J a p a n e s e ), p re s s io n In s t Soc S h e lls Mech L iq u id -F ille d — E x p e rim e n t H ig h Speed J a p a n e se ), 129 1-12 9 P o s tb u c k lin g T ran s S h e lls Japan B u c k lin g under E n g rs , A x ia l B e h a v io r of under H y d ro s ta tic Soc of Mech -A (1 ), C irc u la r (in M e c h , E n g rs , U n iv , To 52 L iq u id -F ille d ( in P o s tb u c k lin g be Japanese ) , 130 0-13 C y lin d ric a l J ap a n e se ) Tohoku P a r t ia lly C o m p re s s io n H Dokij N Yamaki3 J Tani andK Otomo, P a r t ia lly L iq u id -F ille d (in 453 C y lin d ric a l Japan P ressu re C y lin d ric a l H Doki3 N Yamaki and J Tani, C irc u la r P a r t ia lly H y d ro s ta tic H Ooki3 N Yamaki3 J Tani andK Otomo, P a r t ia lly 205 AND C Y L IN D R IC A L C y lin d ric a l E x p e rim e n t 204 B Almroth , B e n d in g of -1 P a r tia lly 203 of H DokijN Yamaki and J Tani, C irc u la r A n a ly s is 1582-1584 1-59 H Saal and A Reif, (1 ), S ta b ility 1 (1 ), B u c k lin g T ran sverse M e m o irs B U C K LIN G h o riz o n ta le and C o m b in e d E Sato , B oth J a p a n e s e ), C IR C U L A R 202 under J , 20-25 to (1 ), CHAPTER 201 S h e lls N Yamakij K Naito and sure 200 A IA A W B Stephens3 J H Starnes _, Jr Long S h e lls 199 C u to u ts , S h e lls p u b lis h e d (1 ) B e h a v io r under in A x ia l M e m o irs of Com­ o f th e ... shells (North- Holiand series in applied mathematics and mechanics ; v 27) Includes bibliographical references Shells (Engineering) Cylinders Buckling (Mechanics) I Title II Series -2 ^ TA660.S5Y36... PUBLISHING COMPANY, INC 52 Vanderbilt Avenue New York, N.Y 10017 U.S.A Library of Congress Cataloging in Publication Data Yamaki, N (Noboru), 192 0Elastic stability of circular cylindrical shells (North- Holiand... effects of the contained liquid on the buckling and postbuckling of clamped cylindrical loads are tanks under each of examined in Chapter the three fundamental In each case above stated, the buckling