Vibrations of Thin Elastic Shells
In this introductory Chapter, we first give some information about the history of shell dynamics, and then make remarks concerning the scope of these lectures. The description of the elastic shell as it shall be considered here is followed by the equation
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CENTRE
C0 URSES AND
FOR MECHANICAL
SCIENCES
L E C T U R E S - No. 240
THIN SHELL THEORY NEW TRENDS AND APPLICATIONS
EDITED BY
W. OLSZAK POLISH ACADEMY OF SCIENCES INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES UDINE
Springer-Verlag Wien GmbH
This work is lllbject to copyrigh l All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. ISBN 978-3-211-81602-8 ISBN 978-3-7091-2442-0 (eBook) DOI 10.1007/978-3-7091-2442-0
© 1980 Springer-Verlag Wien Originally published by CISM, Udine in 1980.
PREFACE
The design of thin shell structures constitutes one of the most challenging fields in modern civil engineering, architecture, and aeronautics. With .ever increasing spans and the shapes always more fanciful, the shell thickness is continually decreasing. Research and design face difficult and responsible problems. The texts included in this volume are intended to present some characteristic trends of the present-day developments. In the last two decades, several international meetings of various kinds have been organized in order to formulate and discuss some particular questions of the shell theory. One of them, held in 1963 in Warsaw under the auspices of the International Association for Shell and Spatial Structures (lASS), was focussed on "Nonclassical Shell Problems" being mainly interested in some new trends of this theory and the ensuing engineering applications.(* l Somewhat on similar lines much effort has been made in the last years to further deepen our understanding of the response of thin shell structures under condictions which previously were not taken into consideration and to find answers to virtually open questions. The present volume offers seven contributions delivered during the CISM Huber Session on the above topics; they reflect the state-ofthe-art in some "nonclassical" fields of the shell theory and/or present new results of recent research work in this challenging domain. The contribution by W.B. Kratzig offers a short introduction into the variables and gor;erning equations of the genera/linear shell theory. Starting with a review of differential geometry of surfaces, the variables of the dynamic field are defined and the corresponding equations of motion and dynamic boundary conditions are formulated. Thereafter the kinematic field is treated in the same way. Constitutive equations for hypere/astic shells are then derived from a rate of energy equation as a first order approximation. Finally, two consistent formulations of Kirchhoff Love-type shell theories and of those including shear deformation are formulated by virtue of the corresponding variational principles, their
II
Preface
primal operators are derived and presented in a matrix notation.
For a long time the diverse and often precocious buckling behaviour of shell structures seemed to defy rational analysis. Great efforts, theoretical
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