Table Of ContentTRENDS IN STRUCTURAL MECHANICS
SOLID MECHANICS AND ITS APPLICATIONS
Volume 54
Series Editor: G.M.L. GLADWELL
Solid Mechanics Division, Faculty of Engineering
University of Waterloo
Waterloo, Ontario, Canada N2L 3G1
Aims and Scope of the Series
The fundamental questions arising in mechanics are: Why?, How?, and How much?
The aim of this series is to provide lucid accounts written by authoritative research
ers giving vision and insight in answering these questions on the subject of
mechanics as it relates to solids.
The scope of the series covers the entire spectrum of solid mechanics. Thus it
includes the foundation of mechanics; variational formulations; computational
mechanics; statics, kinematics and dynamics of rigid and elastic bodies; vibrations
of solids and structures; dynamical systems and chaos; the theories of elasticity,
plasticity and viscoelasticity; composite materials; rods, beams, shells and
membranes; structural control and stability; soils, rocks and geomechanics;
fracture; tribology; experimental mechanics; biomechanics and machine design.
The median level of presentation is the first year graduate student. Some texts are
monographs defining the current state of the field; others are accessible to final
year undergraduates; but essentially the emphasis is on readability and clarity.
For a list of related mechanics titles, see final pages.
Trends in
Structural Mechanics
Theory, Practice, Education
Edited by
J. ROORDA
Department of Civil Engineering,
University of Waterloo,
Waterloo, Ontario, Canada
and
N. K. SRIVASTAVA
School of Engineering,
Universite de Moncton,
Moncton, New Brunswick, Canada
KM
W
SPRINGER SCIENCE+BUSINESS MEDIA, B.V.
LLiibbrraarryy ooff CCoonnggrreessss CCaattaallooggiinngg--iinn--PPuubblliiccaattiioonn DDaattaa
IISSBBNN 997788--9944--001100--66330033--66 IISSBBNN 997788--9944--001111--55447766--55 ((eeBBooookk))
DDOOII 1100.1.1000077//997788--9944--001111--55447766--55
PPrriinntteedd o onn a accidid-f-rferee pea ppaepr er
AAlIlI RRiigghhttss RReesseerrvveedd
©© 11999977 SSpprriinnggeerr SScciieennccee++BBuussiinneessss MMeeddiiaa DDoorrddrreecchhtt
OOrriiggiinnaallllyy ppuubblliisshheedd bbyy KKlluuwweerr AAccaaddeemmiicc PPuubblliisshheerrss iinn 11999977
SSooffttccoovveerr rreepprriinntt ooff tthhee hhaarrddccoovveerr 1lsstt eeddiittiioonn 11999977
NNoo ppaarrtt ooff tthhee mmaatteerriiaall pprrootteecctteedd bbyy tthhiiss ccooppyyrriigghhtt n noottiiccee mmaayy b bee r erepprorodduucceedd o or r
uuttii1liizzeedd iinn aannyy ffoorrmm oorr bbyy aannyy mmeeaannss, ,e elleeccttrroonniicc oOrf mmeecchhaanniiccaall,,
iinncc1luuddiinngg pphhoottooccooppyyiinngg,, rreeccoorrddiinngg oorr bbyy aannyy iinnffoorrmmaattiioonn ssttoorraaggee a anndd
rreettrriieevvaall ssyysstteemm,, wwiitthhoouutt wwrriitttteenn ppeerrmmiissssiioonn ffrroomm tthhee ccooppyyrriigghhtt oowwnneerr. .
PROFESSOR ARCHIBALD NORBERT SHERBOURNE
This international symposium is organized to
honour Professor A.N. Sherbourne, who
recently retired from a long and active career in
the Department of Civil Engineering of the
University of Waterloo, Canada.
The purpose of the symposium is threefold:
i) To reunite those who have been associated
with Prof. Sherbourne over the years in an
academic or professional capacity.
ii) To discuss trends in structural mechanics
in relation to past, present and future
developments.
iii) To publish a volume of papers, prepared by
experts in structural mechanics from the
perspectives of theory, practice and
education, dedicated to Professor A.N.
Sherbourne.
Archibald Sherbourne is well known for his research in structural mechanics,
particularly in the areas of elasticity and plasticity of solids and structures, fatigue,
stability and buckling, vibrations, plates and shells, connections, steel structures and
composite materials. His scientific contributions include more than two hundred
publications, active participation in more than twenty national and international
committees and supervision of numerous graduate research students.
Professor Sherbourne was born on July 8, 1929. He attended the University of
London, England, where he obtained his first degree in science in 1953. He then went
to Lehigh University in the United States as a research assistant, and obtained his BS
(1955) and MS (1957) in civil engineering and mechanics. He earned his PhD in
structural engineering in 1960 from the University of Cambridge, England. Between
studies, he worked for British Railways, Greater London Council, US Steel
Corporation (American Bridge Division) Los Angeles, and as a senior research
assistant at the University of Cambridge. He came to Canada in June 1961 and joined
the University of Waterloo as an Associate Professor in the Department of Civil
Engineering. For his continuous achievements in research, he was honoured with a
DSc (Science) in 1970 by the University of London.
At the University of Waterloo, Professor Sherbourne occupied many posts, while he
continued his teaching and research as professor. He served as Chair of the
Department of Civil Engineering, Warden of the University Residences and Dean of
the Faculty of Engineering (1966-1974). He played a key part in the phenomenal
growth of the Engineering Faculty of the University of Waterloo into one of the
largest and best known co-operative engineering education and research intitutions in
Canada.
Professor Sherbourne has been advisor to many scientific and technical institutions
world wide, including the University ofIbadan (Nigeria) 1971, the State University of
New York (Buffalo) 1971, Ministry of Science and Technology (Canada) 1972,
Federal University of Paraiba (Brazil) 1.972 and 1979, the University of Havana
(Cuba) 1972, the University of West Indies (Trinidad) 1973-75, the Commonwealth
Secretariat (London, Nigeria) 1978, the University of Victoria (Canada) 1980 and Tata
Sons Ltd., Rand D Unit (India). He established other strong links with universities in
USA, Europe, Australia, Asia, Central and South America, and provided valuable
advice to several third world countries for development in technical and engineering
education via CIDA, CUSO, OAS, and the Commonwealth Secretariat.
Professor Sherbourne is a member of several learned societies and professional
associations. He is Fellow of the Institute of Structural Engineers (London), Fellow of
the Royal Society of Arts (London) and Fellow of the Canadian Society for Civil
Engineering. He is a Founder Member of the American Academy of Mechanics, a
Chartered Engineer (UK) and a Member-Specialist of the Professional Engineers of
Ontario. He has been a consultant on several engineering education projects in
Canada. He is listed in at least six international biographical publications.
Dr. Sherbourne has been a great teacher, researcher and leader throughout his career.
He has always been forthright in demanding quality from himself, as well as from
others with compassion and understanding.
J Roorda, N.K. Srivastava
CONTENTS
1. Solid Mechanics
T. BARTA ................................................................................................................. 1
Cosserat Continuum and Shell Theory
R.N. DUBEY, H. JAHED, A. KUMAR ................................................................... .15
A Technique for Solving Nonlinear Problems
M. GRIGORIU ......................................................................................................... 21
Solution of Solid Mechanics Problems by Random Walk
T. KAWAI, N. TAKEUCHI. ..................................................................................... 31
Development and Progress of the Discrete Method of Limit Analysis using
"Rigid Bodies -Spring Models"
E.A.W. MAUNDER ................................................................................................. 41
Dual Analysis with Equilibrium Finite Elements
A. NOORZAD, H. POOROOSHASB ........................................................................ 51
Yielding and Flow of Sand
A.P.S. SELV ADURAI .............................................................................................. 57
Mechanics of Buried Flexible Structures
2. Modern Materials
F. ELLY IN ............................................................................................................... 67
Designing with Fibre-Reinforced Composites: Advantages and Pitfalls
I. EMRI. .................................................................................................................... 75
Use of Polymers and Polymer-Based Composites in Structural Mechanics
M.Z. KABIR ............................................................................................................. 95
A Finite Element Presentation of Optimum Design for Filament
Winding Composite Cylindrical Pressure Vessels.
M.Z. KABIR ........................................................................................................... 10 5
Interactive Buckling in Fibrous Pultruded I-Section Composite Beams
J.T. PINDERA ........................................................................................................ 115
Theories Behind the Development of Constitutive Relations
K.A. SOUDKI. ........................................................................................................ 125
Rehabilitation of Structures by Fibre Reinforced Plastic Laminates
3. Buckling and Instability
C. MARSH ............................................................................................................. 135
A Coherent Code for Structural Design Against Buckling
F.PJ. RIMROTT, G. FRITZSCHE ......................................................................... 143
Large Twisting and Kinking of Thin-Walled Elastic Ribbons
S. SRIDHARAN ..................................................................................................... 153
Stiffened Plates and Cylindrical Shells under Interactive Buckling
J.C. THOMPSON, C.S. LEE ................................................................................... 165
Parametric Studies of the Factors Affecting the Stability of Segmental Dome
Structures
viii CONIENTS
4. Structural Systems
LM. ALLISON, R. MACKAy ............................................................................... 175
Impact Damage Sustained During Vehicle Rollover
M. BURT ................................................................................................................ 185
Periodic Table of the Polyhedral Universe
M.Z. COHN ............................................................................................................ 199
Optimizing Structural Systems
B. TABARROK, Z. QIN ......................................................................................... 211
Static and Dynamic Analysis of Tension Structures
5. Structural Components
E. ANDERHEGGEN .............................................................................................. 225
Finite Elements, Plasticity Theory and Linear Programming for Dimensioning
Reinforced Concrete Slabs and Walls
F. ARBABI, J.H. PECK ......................................................................................... 235
Steel Satchel Connections
M.R. BAHAARI ..................................................................................................... 245
A Study of M -<I> Behaviour of Flush Endplate Connections
W.F. CHEN ............................................................................................................ 255
Moment Frame Connections Revisited: A Fundamental Fracture
Mechanics Approach
D.H. CLYDE .......................................................................................................... 273
Lower Bound Moment Fields -A New Approach
R. GREEN ........... ;. . ~ ............................................................................................... 281
Reinforced Concrete Column Design
GJ. TURVEY, M. SALEHI .................................................................................... 289
Full-Section Yield Analysis of Uniformly Loaded Sector Plates
6. Reliability and Seismic Design
S.E. CHIDIAC, M.S. CHEUNG, N.P. MAILVANGANAM .................................... 299
Service Life of Patches in Concrete Flat Slabs
H.P. HONG ............................................................................................................. 309
Reliability-Based Nondestructive Inspection Planning
L.G. JAEGER, A.A. MUFTI ................................................................................... 319
The Earthquake-Resistant Design of Critically-Important Concrete
Structures
M. PANDEy ........................................................................................................... 329
An Improved Approximation for the Multinormal Integral with
Applications to System Reliability Computation
J.L. URRUTIA-GALICIA ....................................................................................... 339
New Developments in the Theory of Dynamics for Seismic Analysis
of Buildings
CONTENTS ix
7. Engineering Design and Education
S.T. ARIARATNAM .............................................................................................. 353
On the Moment Distribution Method of Structural Analysis
R.N. DUBEY .......................................................................................................... 357
Role of Higher Education
D. GRIERSON ........................................................................................................ 359
Some Musings About a Difficult Design Problem
J. ROORDA ............................................................................................................ 367
Engineering Design and Computers
N.K. SRIVASTAVA ............................................................................................... 379
Learning Conceptual Design
COSSERAT CONTINUUM AND SHELL THEORY
THOMAS BARTA
Department of Civil and Environmental Engineering
University College London
London, U.K.
1 Introduction
LION SHELL THEORY
Shell theory is the creation of H. Aron (1874) and was rederived and elucidated by
Love (1888) and further improved by Lamb (1890).
Koiter (1960) rederived and corrected the Aron-Love theory and established that
differences of the type (J{ (in the definition of,,) are immaterial from the point of
view of a first approximation" , (( and" are strains and curvature-changes and K is a
normal curvature of the undeformed surface). Later (1963) Budiansky and Sanders
and Naghdi(1963) investigating consistency and adequacy of the theory concluded
that Koiter's (1960) theory (derived also independently by Sanders) is the "best".
Consistency means compliance with the general principles of physics and adequacy
could be equated with manageability. In the early days there were many doubts
if the static geometric analogy is a general principle of physics. This has been
proved convincingly by Tonti (1976), while Oden and Reddy (1974) established the
corresponding dual-complementary variational principles. (The author gratefully
acknowledges private discussions with A.Sherbourne, in 1963 a visiting professor at
University College London, who pointed out that duality is a fundemental property
of field-theories, and thus prompted his interest in the Cosserat-continuum.
Unfortunately the "manageability" criterion, ie. the possibility to reduce the
canonic equations of the theory to a set of two equations was not satisfied by the
Koiter's-Sanders theory. John (1969)produced such "horribly complicated" equa
tions.
Barta (1968) (based on an earlier report in 1966) used Koiter's order of magni
tude criterion to obtain a consistent and manageable theory, independent of Pois
son's ratio, very similar to the one presented here. Unfortunately one of the three
operators involved contained a numerical error.
Lukasiewicz (1965) derived a similar but incosistent, non-dual theory.
Koiter (1969) produced a theory similar to Barta's approach with two of the
operators correct, but one (and its dual) depending on Poisson's ratio, Koiter (1981)
presented these equations again, still containing the" obnoxious terms" containing
Poisson's ratio. We comment on these terms in chapter 7.10. Koiter refers to the
1
1. Roorda and N.K. Srivastava (eds.), Trends in Structural Mechanics, 1-14.
© 1997 Kluwer Academic Publishers.
