Mechanics Today

217 Pages·1981·8.317 MB·English

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Mechanics Today
Volume 6
Edited by
S. NEMAT-NASSER, Professor
Department oj Civil Engineering,
The Technological Institute,
Northwestern University,
Evanston, Illinois
Published by Pergamon Press
on behalf of the
AMERICAN ACADEMY OF MECHANICS
PERGAMON PRESS
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Copyright© 1981Pergamon Press Ltd.
All Rights Reserved. No part of this publication may be
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First edition 1981
British Library Cataloguing in Publication Data
Mechanics today.-(Pergamon mechanics today
series)
Vol. 6
1. Mechanics, Applied - Collected works
I. Nemat-Nasser, Siavouche
II. American Academy of Mechanics
620.1 TA350 72-10430
ISBN 0-08-024749-0
Printed in Great Britain by A. Wheaton & Co. Ltd., Exeter
Contributors
The number that follows each author's address refers to the page where his
contribution begins.
I John J. McCoy, Department of Civil Engineering and Mechanics, The
Catholic University of America, Washington, DC 20064, 1.
II M. J. Sewell, Department of Mathematics, University of Reading,
Whiteknights, Reading, UK, 41.
III J. Zarka, Laboratoire de Mecanique des Solides, Ecole Polytech-
nique, 91128 Palaiseau, France, and
J. Casier, Tour EDF GDF, Place des Reflets, 92080 Paris la Defense,
Cedex 08, France, 93.
IV F. Erdogan, Department of Mechanical Engineering and Mechanics,
Lehigh University, Bethlehem, Pennsylvania 18015, 199
xi
Preface
This volume of Mechanics Today includes three comprehensive chapters on
areas in theoretical and applied mechanics and applied mathematics, which
have enjoyed a great deal of attention in the recent past and which are of
considerable scientific, technological, and intellectual value. Chapter I deals
with a general framework within which macroscopic overall response
parameters of continuous bodies with microstructure can be constructed.
Chapter II summarizes essential ingredients necessary to develop a bridge
between the theory of singularities, i.e. the catastrophe theory, and the
calculus of variations, giving several examples of application to applied
mechanics and applied physics problems. In Chapter III the technologically
important problem of the limiting response of elastoplastic structures to
cyclic loading is examined in terms of specific examples, and useful rules for
actual applications are presented. In addition, some supplementary material
to Chapter I of Volume 4 of Mechanics Today is included as Chapter IV.
This volume marks a variation in the style of the Mechanics Today series:
the first five volumes were type-set productions, whereas this is printed
from a camera-ready typed manuscript. I wish to express my sincere
gratitude to Mrs. Erika Ivansons who helped in various editorial tasks and
coordinated and completed the final camera-ready manuscript for the
book.
S. Nemat-Nasser
Wilmette, Illinois
August 1980
xiii
Contents of Volume 1
I Dynamic Effects in Brittle Fracture J. D. ACHENBACH
II Qualitative Theory of the Ordinary Differential Equations of Non-
linear Elasticity STUART S. ANTMAN
III Plastic Waves: Theory and Experiment R. J. CLIFTON
IV Modern Continuum Thermodynamics MORTON E. GURTIN
V General Variational Principles in Nonlinear and Linear Elasticity with
Applications S. NEMAT-NASSER
VI A Survey of Theory and Experiment in Viscometric Flows of Visco-
elastic Liquids A. c. PIPKIN and R. I. TANNER
VII Concepts in Elastic Structural Stability JOHN ROORDA
Contents of Volume 2
I Theory of Creep and Shrinkage in Concrete Structures: A Precis of
Recent Developments ZDENEK P. BAZANT
II On Nonequilibrium Thermodynamics of Continua
S. NEMAT-NASSER
III Mathematical Aspects of Finite-element Approximations in
Continuum Mechanics J. T. ODEN
IV Nonlinear Geometrical Acoustics
BRIAN R. SEYMOUR and MICHAEL P. MORTELL
XV
Contents of Volume 1
I Dynamic Effects in Brittle Fracture J. D. ACHENBACH
II Qualitative Theory of the Ordinary Differential Equations of Non-
linear Elasticity STUART S. ANTMAN
III Plastic Waves: Theory and Experiment R. J. CLIFTON
IV Modern Continuum Thermodynamics MORTON E. GURTIN
V General Variational Principles in Nonlinear and Linear Elasticity with
Applications S. NEMAT-NASSER
VI A Survey of Theory and Experiment in Viscometric Flows of Visco-
elastic Liquids A. c. PIPKIN and R. I. TANNER
VII Concepts in Elastic Structural Stability JOHN ROORDA
Contents of Volume 2
I Theory of Creep and Shrinkage in Concrete Structures: A Precis of
Recent Developments ZDENEK P. BAZANT
II On Nonequilibrium Thermodynamics of Continua
S. NEMAT-NASSER
III Mathematical Aspects of Finite-element Approximations in
Continuum Mechanics J. T. ODEN
IV Nonlinear Geometrical Acoustics
BRIAN R. SEYMOUR and MICHAEL P. MORTELL
XV
Contents of Volume 3
I On Modeling the Dynamics of Composite Materials
A. BEDFORD, D. S. DRUMHELLER and H. J. SUTHERLAND
II The Analysis of Elastodynamic Crack Tip Stress Fields
L. B. FREUND
III Random Vibration of Periodic and Almost Periodic Structures
Y. K. LIN
IV Integral Representations and the Oseen Flow Problem
W. E. OLMSTEAD and A. K. GAUTESEN
V On Nonlinear Gyroscopic Systems
P. R. SETHNA and M. BALUBALACHANDRA
VI Application of the WKB Method in Solid Mechanics
CHARLES R. STEELE
Contents of Volume 4
I Mixed Boundary-value Problems in Mechanics F. ERDOGAN
II On the Problem of Crack Extension in Brittle Solids Under General
Loading K. PALANISWAMY and w. G. KNAUSS
III Scattering of Elastic Waves SUBHENDU K. DATTA
IV Electromagnetic Forces in Deformable Continua YIH-HSING PAO
V Problems in Magneto-solid Mechanics FRANCIS C. MOON
VI On Nonequilibrium Thermodynamics of Continua: Addendum
S. NEMAT-NASSER
xvi
Contents of Volume 3
I On Modeling the Dynamics of Composite Materials
A. BEDFORD, D. S. DRUMHELLER and H. J. SUTHERLAND
II The Analysis of Elastodynamic Crack Tip Stress Fields
L. B. FREUND
III Random Vibration of Periodic and Almost Periodic Structures
Y. K. LIN
IV Integral Representations and the Oseen Flow Problem
W. E. OLMSTEAD and A. K. GAUTESEN
V On Nonlinear Gyroscopic Systems
P. R. SETHNA and M. BALUBALACHANDRA
VI Application of the WKB Method in Solid Mechanics
CHARLES R. STEELE
Contents of Volume 4
I Mixed Boundary-value Problems in Mechanics F. ERDOGAN
II On the Problem of Crack Extension in Brittle Solids Under General
Loading K. PALANISWAMY and w. G. KNAUSS
III Scattering of Elastic Waves SUBHENDU K. DATTA
IV Electromagnetic Forces in Deformable Continua YIH-HSING PAO
V Problems in Magneto-solid Mechanics FRANCIS C. MOON
VI On Nonequilibrium Thermodynamics of Continua: Addendum
S. NEMAT-NASSER
xvi
Contents of Volume 5
I On the "End Problem'' for Thick Rectangular Plates
ROBERT R. ARCHER and NIRMALYA BANDYOPADHYAY
II Aiming an Electromagnetic Beam by Bending the Segments of a
Large Reflecting Surface: A Parameter Study
DAVID BUSHNELL
III 'Taylor Instability" of the Surface of an Elastic-Plastic Plate
DANIEL C. DRUCKER
IV On Pseudo-elasticity of Living Tissues Y. C. FUNG
V Free Vibration Spectrum Structure of a Shell of Revolution
A. L. GOL'DENVEIZER
VI Applicability of Floquet-type Solutions to Bounded Layered
Composites
GEORGE HERRMANN, G. S. BEAUPRE and B. A. AULD
VII Kinematically Unstable Space Frameworks
NICHOLAS J. HOFF and JULIO FERNANDEZ-SINTES
VIII The Momentum-balance Method in Earthquake Engineering
GEORGE W. HOUSNER
IX An Elastic Porous Molecule Model for the Molecular Dynamics
of Polymer Liquids
MILLARD W. JOHNSON JR. and DANIEL SEGALMAN
X The Intrinsic Equations of Shell Theory with Some Applications
W. T. KOITER
XI Self-consistent Scheme in Random Media Elasticity—Exact or
Only Approximate? E. KRONER
XII Compression of Spherical Cells
T. J. LARDNER and P. PUJARA
XIII Progress and Prospects of Stress Analysis in Plasticity
E. H. LEE
xvii
MTV6-B