Table Of ContentAPPLIED MECHANICS
PROCEEDINGS OF
THE ELEVENTH INTERNATIONAL CONGRESS OF
APPLIED MECHANICS
MUNICH (GERMANY) 1964
EDITED BY
HENRY GÖRTLER
FREIBURG I. BR.
IN COOPERATION WITH
PETER SORGER
WITH 740 FIGURES
Springer-Verlag Berlin Heidelberg GmbH
1966
ISBN 978-3-662-27863-5 ISBN 978-3-662-29364-5 (eBook)
DOI 10.1007/978-3-662-29364-5
All rights reserved, especially that of translation into foreign langnages.
It is also forbidden to reprodnce this book, cither whole or in part,
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® by Springer-Verlag Berlin Heidelberg 1966
Originally pnblished by Springer-Verlag Berlin Heidelberg New York in 1966
Softcover reprint of the bardeover 1st edition 1966
Library of Congress Catalog Card Nnmber 58-2749
Title No. 1282
IN MEMORIAM
RICHARD GRAMMEL
EHRENPRÄSIDENT DES DEUTSCHEN ORGANISATIONS-KOMITEES
* 3. 3. 1889 t 26. 6. 1964
EXECUTIVE COMMITTEE OF THE INTERNATIONAL COMMITTEE
FOR THE CONGRESSES OF APPLIED MECHANICS
1960-1964
Professor G. ÜOLONNETTI, President
Professor W. T. KOITER, Secretary
Professor G. K. BATCHELOR, Treasurer
EXECUTIVE COMMITTEE OF THE CONGRESS COMMITTEE OF IUTAM
1964-1968
Professor M. RoY (President of IUTAM)
Professor W. T. KOITER, Secretary
Professor G. K. BATCHELOR
Professor H. GöRTLER
CONTENTS
Page
List of Members of the International Committee for the Gongresses of Applied Mechanics . XV
German Organizing Committee . XV
List of Authors. . . XVI
List of Participants . . . . . . . XXI
Opening Addresses
H. GöRTLER: Opening address by the President of the Eleventh Congress 3
G. TEMPLE: Speech at the opening session of the Eleventh Congress 5
General Lectures ·
Chairman: W. T. KolTER
L. I. SEDOV: Some problems of designing new models of continuum media 9
Chairman: G. K. BATCHELOR
E. REISSNER: On the foundations of the theory of elastic shells 20
R. LEGENDRE: Ecoulements instationnaires autour d'obstacles en vibration 31
Chairman: N. J. HoFF
I. N. VEKUA: New methods in mathematical shell theory ... 47
L. J. F. BROER: Some recent advances in the theory of wave propagation 59
Chairman: M. RoY
G. F. CARRIER: Phenomena in rotating fluids ........ . 69
K. MAGNUS: Drehbewegungen starrer Körper im zentralen Schwerefeld 88
Chairman: N. I. MU SKHELISHVILI
H. ZIEGLER: Thermodynamik der Deformationen .. 99
T. B. BENJAMIN: Fluid flow with flexible boundaries ....... . 109
Section 1: Lectures on Mechanics of Solids
August 31
Mechanics of Continua
Chairman: K. MAGNUS
A. C. ERINGEN: Mechanics of micromorphic materials ............ . 131
C. TRUESDELL: Instabilities of isotropic perfectly elastic materials in simple shear 139
Chairman: L. M. MILNE-THOMSON
E. KRÖNER: Das physikalische Problem der antisymmetrischen Spannungen und der sogenannten
Momentenspannungen . · . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
R. A. TOUPIN: On St. Venant's principle . . . . . . . . . . . . . . . . . . . . . . . . . . 151
H. NEUBER: On the general solution of linear-elastic problems in isotropic and anisotropic Gosserat
continua . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Nonlinear Vibrations
Chairman: G. TEMPLE
R. CHALEAT: Les trois premieres approximations de la theoriedes perturbations et leurs applications. 159
YA. G. PANOVKO: A review of applications of the method of direct linearization. . . . . . . . . 167
Chairman: S. H. GRANDALL
R. M. RosENBERG: On motions with a rest point and the existence of normal mode vibrations of non-
linear systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
VIII Contents
Page
V. 0. KoNONENKO: Forced oscillations of the nonlinear quasiharmonical system . . . . . . . . . 173
R. M. DAV IES and T. H. LAMBERT: Transient oscillation of two degree of freedom systems with Cou-
lomb damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Strength of Materials
Chairman: M. REINER
E. H. BROWN: A theory for the mechanical behaviour of sand . . . . . . . . . . . . . . . . . 183
CH. H. LERCHENTHAL: A photoelastic investigation of stress concentration around reinforced cutouts
in stressed sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
Chairman: W. PRAGER
N. ALBERT!: Analisi della distribuzione di tensioni sulla sezione contratta di provini cilindrici di tra-
zione ................................. . 204
Y. OHASHI and S. MURAKAMI: The elasto-plastic bending of a clamped thin circular plate 212
A. SAWCZUK: Large deflections of rigid-plastic plates . . . . . . . . . . . . . . . . 224
September 1
Vibrations
Chairman: K. KLOTTER
F. WEIDENHAMMER: Auswanderungserscheinungen in drehschwingungsfähigen mechanischen und
elektrischen Meßwerken . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
Chairman: R. M. RoSENBERG
V. V. BoLOTIN: On the broadband random vibration of elastic systems 233
S. H. CRANDA.LL: The spectrum of random vibration of a nonlinear oscillator . 239
Chairman: J. P. DEN HARTOG
L. FRYBA: Dynamik des Balkens mit federnder Schicht veränderlicher Steifigkeit unter der Wirkung
eines bewegten Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
0. DANEK und L. SPACEK: Frequenz- und Amplitudenabstimmung gerader Träger . . . . . . . . 252
S. A. AMBA.RTSUMIAN and S. M. DURGARIAN: Some problems of vibration and stability of shallow
shells and plates in a time alternating temperature field . . . . . . . . . . . . . . . . . 257
Theory of Shells
Chairman: K. MARGUERRE
P. M. NAGHDI: On the differential equations of the linear t~eory of elastic shells 262
Chairman: A. L. GoLDENVEIZER
W. FLÜGGE: Concentrated forces on shells ... 270
S. LuKASIEWICZ: Concentrated loadings on shells ....... . 277
Chairman: E. REISSNER
J. G. LEKKERKERKER: Stress concentration around circular holes in cylindrical shells 283
G. N. SAVIN: Goncentration of stresses around curvilinear holes in plates and shells . 289
J. KEMPNER and Y.-N. CHEN: Large deflections of an axially compressed oval cylindrical shell 299
September 2
Chairman: H. NEUBER
A. L. GoLDENVEIZER: The principles of reducing three-dimensional problems of elasticity to two
dimensional problems of the theory of plates and shells . . . . . . . . . . . . . . . . . 306
Chairman: B. BuDIANSKY
G. G. PoPE: The buckling of long, slightly curved panels in axial compression . . . . . . . . . . 312
M. UEMURA: Postbuckling behavior of a circular cylindrical shelllocally buckled under axial com-
pression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Chairman: H. PARKUS
N. J. HoFF: The effect of the edge conditions on the buckling of thin-walled circular cylindrical shells
in axial compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326
M. H; GRADOWCZYK: Thermalstresses in thin elastic shells . . . . . . . . . . . . . . . . . 332
M. A. SAVE and R. T. SHIELD: Minimum-weight design of. sandwich shells subjected to fixed and
moving Ioads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341
Contents IX
Page
Theory of Elasticity
Chairman: H. SCHAEFER
D. RüDIGER t: Zur Trefftzachen Methode in der Elastizitätstheorie 350
Chairman: L. SoBRERO
W. W ALLISCH und E. WEINEL: Ein Beitrag zur Elastomechanik prismatischer und nichtprismatischer
Stäbe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
R. MAzET et G. CouPRY: Sur une conception Mterogime des milieux solides travaillant au dela du
domaine elastique 360
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Chairman: I. N. VEKUA
V. T. BuCHWALD: Eigenfunctions of the full dislocation solution of the annulus in plane elastostatics 368
S. V. SERENSEN and R. M. SHNEIDEROVITCH: The effect of time on stress distribution in the case of cyc
lic deformation 372
Tn. LEHMANN: Formänderungen eines klassischen Kontinuums in vierdimensionaler Darstellung 376
September 3
Elastic-plastic Deformations
Chairman: F. ScnuLTz-GRuNow
B. R. SETH: Generalized strain and transition concepts for elastic-plastic deformation-creep and relax-
ation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
Viscoelasticity and Creep
Chairman: W. FLÜGGE
N. CRISTESCU: Some dynamic problems of onedimensional elasticjviscojplastic bodies 390
E. H. LEE: Some recent developments in linear viscoelastic stress analysis . . . . . 396
Chairman: P. M. NAGHDI
J. BRILLA: Linear viscoelastic bending analysis of anisotropic plates . . . . . . . . . . 403
W. S. NAMESTNIKOW: Kriechen der Metalle beim zusammengesetzten Spannungszustand. 410
Yu. N. RABOTNOV: Creep of shells . . . . . . . . . . . . . . . . . . . . . . 415
Synthesis of Mechanisms
Chairman: E. ME'ITLER
F. FREUDENSTEIN and L. DoBRJANSKYJ: On a theory for the type synthesis of mechanisms 420
Dynamie s
Chairman: H. WITTMEYER
V. A. SARYCHEV: Dynamics of a satellite gravitational stabilization system with consideration of
atmospheric resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429
V. A. ZLATOUSTOV, D. E. 0KHOTSIMSKY, V. A. SARYCHEV and A. P. TüRZHEVSKY: Investigation of a
satellite oscillations in the plane of an elliptic orbit . . . . . . . . . . . . . . . . . . . . 436
Chairman: H. ZIEGLER
J. CRAWLEY and L. MAUNDER: Drift of a vibrating gyroscope supported in gimbals . . . . . . . . 440
V. V. RuMYANTSEV: Non-linear methods in the theory of stability motion of solids with liquid-filled
cavities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
H. LEIPHOLZ: Grundzüge einer Stabilitätstheorie für elastische Systeme unter nichtkonservativer
Belastung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455
Theory or Plates
Chairman: U. WEGNER
M. YosmKI and T. KAWAI: On the method of application of energy principles to problems of elastic
plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461
Propagation of Disturbances in Solids
Chairman: W. 0LSZAK
J. MIKLOWITZ: Scattering of a plane elastic compressional pulse by a cylindrical cavity 469
S. S. GRIGORIAN: On elastic wave radiation at underground explosion ....... . 484
X Contents
Page
Chairman: M. HETENYI
B. J. LAZAN: Damping meohanisms and phenomenology in materials . . . . . . . . . . . . . 493
a
J. MANDEL: Gontribution theorique l'etude de l'eorouissage et des lois de l'eooulement plastique. 502
N. KH. ARUTIUNIAN and B. L. ABRAMIAN: On pressing a rigid punch into an elastic sphere. 510
September 4
Theory of Deformations
Chairman: K. ZoLLER
H. LE BOITEUX: Relation entre les fonotions de transfert et l'experienoe dans la mecanique des solides
deformables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518
Theory of Elasticity and Plasticity
Chairman: F. K. G. 0DQVIST
J. H. ARGYRIS: Three-dimensional anisotropic andinhomogeneaus elastic media matrix analysis for
small and large displacements . . . . . . . . . . 527
R. S. RrvLIN: Mechanics of non-linear viscoelastic solids . . . . . . . . . . . . . . o o o . o 537
Chairman: Goi. BARENBLATT
W. PRAGER: On elastic, perfectly locking materials o o o . o . o o o o o o o 538
0 0 0 0 0 0 0 0 0 0
W. 0LSZAK and Po PERZYNA: The constitutive equations of the flow theory for a non-stationary yield
condition 545
0 0 • 0 • 0 0 0 0 • 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 0
Po Go HoDGE, Jro: Yieldopoint load determination by nonlinear programming . o o o o o . o . 554
0
Thermal Stress
Chairman: Ao SLIBAR
Jo No GooDIER and Ao Lo FLORENCE: Looalized thermal stress at holes, cavities, and inclusions disturb-
ing uniform heat flowo Thermal orack propagation o o o o o o 562
0 • 0 0 0 0 0 0 0 0 0 0 0
Thermal Stress, Theory of Plasticity
Chairman: No KHo ARUTIUNIAN
Po So THEOCARIS: The evolution of the stress distribution in plane-stress contained plasticity problems 569
0
G.l. BARENBLATT: On the structure of fully developed plastic flow in polymerso . 575
0 0 0 0 0 0 0 0
Chairman: So Ao AMBARTSUMIAN
Go DARRIEUS: Deformation thermique d'un arbre 582
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 •
B. A. BoLEY: Estimate of errors in approximate temperature and thermal stress calculations o o . 586
E. Ho MANSFIELD: The effect of a temperature gradient through the thickness of an unsupported
plate o o o o o o o . o . 597
0 0 0 0 0 • 0 0 • 0 0 0 0 0 0 0 0 0 • 0 0 0 0 0 0 0 0 0 0
Theory of Fracture
Chairman: Ho NEUBER
H. FESSLERand Ro Wo WILSON: Strains near cracks in aluminium plates 603
Theory of Fracture, Theory of Plasticity
Chairman: Bo Jo LAZAN
L. Go JAEGER and Jo Oo McCuTCHEON: The elastic analysis of interconnected curved bridge girders 612
Wo So HEMP: Studies in the theory of Michell structures o o o o 621
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Chairman: Ao Co ERINGEN
P. A. KuziN and G. S. SHAPIRO: On dynamic behaviour of plastic structures 629
0 0 • 0 0 0 0 0 •
B. BUDIANSKY and Jo Wo HuTCffiNSON: Dynamic buckling of imperfection-sensitive structures 636
Co MYLONAS: The mechanics of brittle fracture 652
0 0 0 • 0 0 0 0 0 0 0 0 0 0 0 • 0 0 • 0 0
Section 2: Leetores on Mechanics of Fluids and Gases
August 31
Jet Flow
Chairman: Go I. TAYLOR
I. !MAI: On the visoous flow near the trailing edge of a flat plate 663
0
I. TANI and Yo KOMATSU: Impingement of a round jet on a flat surface 672
XI
Contents
Page
Chairman: G. F. CARRIER
S. UomDA and K. W ATANABE: On a similar solution of curved half jet . . . . . . . . 677
J. T. DIEZ RooHE: The peripheral jet theory ...........•.......• 684
A. CRA.YA. et R. MoREA.U: Jetslibres et confines en fluide de forte diffusivite magnetique 696
Laminar Boundary Layer
Chairman: R. LEGENDRE
A. FüRTIER: Sur l'influence de l'instabilite des surfaces de discontinuite de vitesse et de la compressibi-
lite du fluide sur les ecoulements stationnaires en moyenne . . . . . . . . • . . . . . . 707
J. L. PEUBE: Sur les solutions semblables des tiquations de la couche limite Iaminaire bidimensionnelle 8.
masse volumique constante et propriettis physiques variables. Application a la plaqueplane sans
gradient de pression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 713
Chairman: S. A. CHRISTIANOVITOH
L. G. LOITSIANSKI: Sur la mtithode parametrique dans la th6orie de la couche limite Iaminaire 722
S. K.APLUNt: Boundary layers and separation . . . . . . . . . . . . . . . . . . 729
C. BouRQUE: Dticollement de la couche limite Iaminaire devant une jupe ou un diedre 733
September 1
Kinetic Theory of Gases
Chairman: E. MARTENSEN
H. GRAD: Theory of the Boltzmann equation ........ . 741
Super- and Hypersonic Flow
Chairman: M. J. LIGHTHILL
K. I. BA.BENKO: Investigation of a three-dimensional supersonic gas flow around conic bodies 749
W. D. HA.YES: Inviscid hypersonic flows on blunt bodies . . . . . . . . . . . . . . . . 756
Chairman: H. W. LIEPMANN
G. G. CHERNYI: Flat wings in hypersonic flow . . . . . . . . . . . . . . . . . . . . 763
R. HETHERINGTON and M. E. SILVESTER: Transonic flow in plane and axisymmetric nozzles 768
V. V. RusA.Nov: A three-dimensional supersonic gas flow past smooth blunt bodies 774
Meteorology
Chairman: H. SoHLIOHTING
I. A. KIBEL: Short-range weather forecasting as a hydrodynamic problern 779
Hydrodynamic Stability
Chairman: I. TA.NI
G. I. TA.YLOR: Conical free surfaces and fluid interfaces . . . . . . . . • . . . . . . . • . 790
C. C. LIN and D. J. BENNEY: On the instability of shear flows and their transition to turbulence 797
Chairman: R. MIOHEL
P. S. KLEBA.NOFF: The effect of a two-dimensional roughnass element on boundary-layer transition 803
W. VELTE: Beiträge zur hydrodynamischen Stabilität . . . . . . . . . . . . . . . . . . . 806
F. X. WoRTMANN: Experimentelle Untersuchungen laminarer Grenzschichten bei instabiler Schich-
tung . . . . . . . . . . . . . . . . . . . . • . . . . . . . . . . . . . . • . . . 815
Hydrodynsmies
Chairman: G. WEINBLUM
C. WIGLEY: Analysis of the forces and moments on a yawing ship 826
Flow with Mixing
Chairman: T. B. BENJAMIN
P. CARRIERE et M. SIRIEIX: Resultats recents dans l'etude des problemes de melange et de recolle-
ment . • • • . • . • • . • • • • • . • • • • • • . • . • • • • . . . . . . . . • . 837
