Progress in Applied Mechanics: The Chien Wei-zang Anniversary Volume

397 Pages·1987·12.07 MB·English

by  Tai Tien-Min (auth.)

Progress in Applied Mechanics
MECHANICS OF SURFACE STRUCTURES·
Editors: W.A. Nash and G.~. Ora vas
Volume 6
P. Seide, Small elastic deformations of thin shells. 1975. ISBN 90-286-0064-7
V. Panc, Theories of elastic plates. 1975. ISBN 90-286-0104-X
T.L. Nowinski, Theory of thermoelasticity with applications. 1978.
ISBN 9O-286-0457-X
S. Lukasiewicz, Local loads in plates and shells. 1979. ISBN 90-286-0047-7
V. Fift, Statics, formfinding and dynamics of air-supported membrane struc
tures. 1983. ISBN 90-247-2672-7
K.Y. Yeh, Progress in applied mechanics. 1987. ISBN 90-247-3249-2
R. Negrutiu, Elastic analysis of slab structures. 1986. ISBN 90-247-3367-7
• The first four titles in this series were published by Sijthoff and Noordhoff
International Publishers, Alphen aan den Rijn, The Netherlands, Rockville,
Maryland, U.S.A.
Progress in Applied Mechanics
The Chien Wei-zang Anniversary Volume
Edited by
Yeh Kai-yuan
Lanzhou University,
Lanzhou, Gansu 730001
People's Republic of China
1987 MARTINUS NIJHOFF PUBLISHERS .....
1111
a member of the KLUWER ACADEMIC PUBLISHERS GROUP
DORDRECHT / BOSTON / LANCASTER .~
Distributors
for the United States and Canada: Kluwer Academic Publishers, P.O. Box 358,
Accord Station, Hingham, MA 02018-0358, USA
for the UK and Ireland: Kluwer Academic Publishers, MTP Press Limited, Falcon
House, Queen Square, Lancaster LAI lRN, UK
for all other countries: Kluwer Academic Publishers Group, Distribution Center,
P.O. Box 322, 3300 AH Dordrecht, The Netherlands
Library of Congress Cataloging in Publication Data
Main entry under title:
Progress in applied mechanics.
(Mechanics of surface structures ; 6)
Bibliography: p.
1. Mechanics, Applied--Addresses, essays, lectures.
2. Ch'ien, Wei-chIang. I. Ch'ien, Wei-chIang.
II. Yeh, Kai-yuan. III. Series: Mechanics of surface
structures ; v. 6.
TA350.3.P77 1986 620.1 85-21715
ISBN-\3: 978-94-010-806\-3
ISBN-13: 978-94-010-8061-3 e-ISBN-13: 978-94-009-3487-0
DOl: 10.1007/978-94-009-3487-0
Copyright
© 1987 by Martinus Nijhoff Publishers, Dordrecht.
Softcover reprint of the hardcover 1st edition 1987
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, mechanical,
photocopying, recording, or otherwise, without the prior written permission of
the publishers,
Martinus Nijhoff Publishers, P.O. Box 163, 3300 AD Dordrecht,
The Netherlands.
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Contents
Page
Yeh Kai-yuan: foreword IX
The main published works of Professor Chien Wei-zang XI
Continuum mechanics
Tai Tien-min: Variational principles for the linear dynamic theory of micropolar
viscoelasticity 3
Guo Zhong-heng: An extended version of the transfer theorem 15
General mechanics
Yu Xin: On the application of the screw calculus to the mechanics of spatial mechanisms 21
Wong Chia-ho: Main properties of root-loci of time-delay control systems and a method
of finding the stable interval of gain 35
Fluid mechanics
Liu Hsien-chih: Concerning the singularity of non-linear vibration of ideal liquid in
~ommunication tubes with different end cross sections 51
Jiang Fu-ru: Magnetohydrodynamic flow in elliptic ducts 71
Huang Dun: Flow around a cone at supersonic speed 83
Elasticity and plasticity
Fan Wei-xun: A note on biharmonic functions 93
Cheng Chang-jun, Shang Xin-chun, Zhu Jian-gang and Duan Dai-ming: The effect
of transverse shear deformations on ring-shaped elastic plates 97
Generalized variational principles
Long Yu-qiu: Sub-region generalized variational principles in elastic thin plates 121
Liu Dian-kui and Zhang Qi-hao: General variational principles for non-conservative
problems in theory of elasticity and its application to finite element analysis 135
Theory of plates and shells
Sun Huan-chun, Sha De-song, Wang Shou-xin and Tang Li-min: Solution in cosine
series for the bending of a rectangular cantilever plate under the action of arbitrary
transverse loads 147
VII
VIII
Lu Wen-da and Lin Bao-qing: The effect of axisymmetric geometric imperfections on
dynamic response to turbulent wind in a cooling tower 163
Chen Shan-lin: General solution of the bending of ring shells with equations in
complex form 181
ComJMIsite materials
Wang Ren-jie and Loo Tsu-tao: An analytical solution for interlaminar stresses in
symmetric composite laminates 195
Finite deformation of plates and sheDs
Chen Zhi-da: Geometric theory of finite deformation of shells 215
Yeh Kai-yuan, Fan lu-xian and Wang Yun: Perturbation solutions for uniformly
clamped rectangular plates with large deflections 245
Zhou Cheng-ti: The large deflection method in the analysis of elastoplastic instability
of thin shells with initial imperfections 267
Chou Huan-wen: Composite expansion method applied to large deflection problems of
spherical shells 283
Liu Ren-huai: Nonlinear bending of circular sandwich plates under the action of
axisymmetric uniformly distributed line loads 293
Fracture mechanics
Tsai Shu-tang: The physical mechanism of acoustic emission and the difficulty of fracture
mechanics 325
Hsueh Dah-wei: An elastic-plastic analytical analysis near a crack tip 339
Ouyang Chang: On path-independent integrals in fracture dynamics for visco-elastic
plastic media 351
Tang Ren-ji: A fundamental solution for flexural problems of a circular cylinder with
cracks 357
Computational mechanics
Zhong Wan-xie and Lin lia-hao: The whiplash effects on tall buildings 371
Liu Zheng-xing, Feng Tai-hua and Li Ding-xia: Solutions of geometrical non-linear
problems of stiffened plates and shells by the finite element method 379
Author Index 399
Subject Index 403
Foreword
Prof. W. Z. Chien was born on 9 October, 1912 and 1982 saw the 70th anniversary
of his birth. Some of his friends, colleagues, and former students prepared this
special volume in honour of his outstanding contribution to the field of mechanics.
The volume does not contain contributions from all of his students and friends and
for this we apologize.
Prof. Chien's family have lived. in Qufangquiao Village, Hongshengli, Wuxi
County, Jiangsu Province for generations. Many members of his family have been
teachers in this village. When he was 14 years old his father died and for a time it
appeared necessary to terminate his education but, fortunately, an uncle, Chien
Mu, who later became a very famous historian in China, came to his aid and he
was able to continue his studies.
In 1931 he took entrance exams and was simultaneously admitted to five
prestigious Chinese universities. Of these, he chose to enter Tsing-hau University
in Beijing, with major work in physics. He received his baccaulaurate in 1935 and
taught at middle school for a time until he was awarded a Sino:'British scholarship
to study abroad. In the competition for this award, three of the recipients were in
the field of mechanics: Prof. C. C. Lin, Prof. Kuo Yung-huai, and Prof. Chien
Wei-zang. All three arrived in Toronto in August, 1940 and entered the Depart
ment of Applied Mathematics of the University of Toronto to study under
Prof. J. L. Synge.
While still a 90ctoral student, Prof. Chien published in the Th. von Karman
Anniversary Volume, his well-known paper "The Intrinsic Theory of Elastic Plates
and Shells". After receiving his Ph.D. in 1943, Prof. Chien worked as a research
fellow at the Jet Propulsion Laboratory of the California Institute of Technology
in Pasadena. At the end of World War II, Prof. Chien returned to the Department
of Mechanical Engineering at Tsing-hua University in Beijing. There, he taught
many courses in mechanics of solids. His research centred on large deflections of
plates and the hydrodynamic theory oflubrication. In 1952 he was appointed Vice
President of Tsing-hua University, as well as Vice Chairman of the Institute of
Mechanics of the Chinese Academy of Sciences. In 1955 he was elected Academician
of the Mathematics-Physics-Chemistry Department and Technical Science
Department of the Chinese Academy of Sciences. In 1956 he was honoured by
being elected a Foreign Member of the Polish Academy of Sciences. In that same
year he was awarded the second rank National Scientific Prize by the Chinese
Academy of Sciences for his work on buckling of spherical shells. Later in 1956 he
participated in the Ninth International Congress of Theoretical and Applied
Mechanics in Brussels, Belgium, and presented results of his recent studies on large
deflections of thin elastic plates. The year 1957 saw the presentation in Beijing of
special seminars on mechanics led jointly by Prof. Chien and Prof. Tsien Hsue-shen.
IX
x
In the late 1950's Prof. Chien developed new generalized variational principles
in elasticity which, because of the then turbulent conditions in China, remained
unpublished. In 1972 he led a Chinese scientific delegation to England, Sweden,
Canada, and the United States. A particularly happy event occurred in Toronto,
where the visit coincided with the exact date of the award of his doctorate thirty
years previously.
Prof. Chien is editor of the Journal of Applied Mathematics and Mechanics,
issued in simultaneous Chinese and English editions since 1980. Prof. Chien is a
member of the Editorial Board of the International Journal of Engineering Science
as well as one of the editors of Advances in Applied Mathematics. His recent books
have been Variational Methods and Finite Elements, Book One, Singular Pertur
bation Theory, A~ymptotic Solutions of Plates and Shells, and, soon to be released,
Variational Methods and Finite Elements, Book Two, and Mechanics of Armour
Penetration.
To illustrate his endless energy and enthusiasm, in 1982 Prof. Chien took the
position of President of the Shanghai University of Technology as well as serving
as Director of its Institute of Applied Mathematics and Mechanics. The authors
of this book, as well as the many other friends of Prof. Chien wish him a long,
healthy, and happy life.
YEH KAI-YUAN
The main published works of
Professor Chien Wei-zang
1. Monographs
I. Chien Wei-zang, Inventions in Chinese History (in Chinese), Chinese Youth Publications, Beijing
(1954); translated into Mongolian language and other national languages, 200 pages.
2. Chien Wei-zang and Yeh Kai-yuan, Theory of Elasticity (in Chinese), Science Press, Beijing, 1st
Edition (1956); 2nd Edition (1980), 422 pages.
3. Chien Wei-zang, Lin Hung-sun, Hu Hai-chang and Yeh Kai-yuan, Problems of Large Deflection
of Elastic Circular Plates (in Chinese), Science Press, Beijing (1954), 152 pages.
4. Chien Wei-zang, Lin Hung-sun, Hu Hai-chang and Yeh Kai-yuan, Torsion of Elastic Columns (in
Chinese), Science Press, Beijing (1956), 483 pages.
5. Translation of Monograph 3 in Russian (1957), 207 pages.
6. Chien Wei-zang, Variational Principles and Finite Element Methods, Vol. I (in Chinese), Science
Press, Beijing (1980), 599 pages.
7. Chien Wei-zang, Singular Perturbation Theory (in Chinese), to be published in Szechuan People's
Publishing House, Chengtu.
8. Chien Wei-zang and Yeh Kai-yuan, Applied Mathematics (in Chinese), to be published in Shang
hai Science and Technology Publishing House, Shanghai.
9. Chien Wei-zang, Collected Works of Applied Mathematics and Mechanics (in Chinese), Jiangsu
Science and Technology Publishing House, Nanjing (1980), 265 pages.
10. Chien Wei-zang, Armour Penetration Mechanics (in Chinese), to be published in National Defence
Publishing House, Beijing.
II. Edited by Chien Wei-zang, Singular Perturbation Theory and Its Application in Mechanics (in
Chinese), Science Press (1982), Beijing.
12. Chien Wei-zang, The Development of Zinc Air (oxygen) Cells (published with the name of the Zinc
Air Cells Study Group of Tsing Hua University), Science Press, Beijing (1974).
13. Eringen, A. C. (translated by Chien Wei-zang), Tensor Analysis (in Chinese), Jiangsu Science and
Technology Publishing House, Nanjing, (1981), 200 pages.
2. Papers of scientific investigation
I. Chien Wei-zang, Measurement of atmospheric electricity in Peiping (in English), presented in the
193? Annual Meeting of the Chinese Society of Physics (Tsingdao).
2. Chien Wei-zang, The spectrum of double ionized Calcium (Ca III) (in English), Chinese Journal
of Physics, 3, I (1937), 1-13.
3. Chien Wei-zang, Analysis of the spectrum of singly ionized Cerium (in English), Chinese Journal
of Physics, 4 (1939), 86-116.
4. Chien Wei-zang, Highly ionized Potassium and Calcium spectra, (in English), Chinese Journal of
Physics, 4 (1939), 117-147.
5. Synge, J. L. and Chien Wei-zang, The intrinsic theory of elastic shells and plates (in English),
Applied Mechanics, Theodore von Karman Anniversary Volume (1940), 103-120.
6. Weinstein, A. and Chien Wei-zang, On the vibration of a clamped plate under tension (in English),
Quarterly of Applied Mathematics, I, I (1943), 61-{J8.
XI