Cusped Shell-Like Structures
The book is devoted to an up-dated exploratory survey of results concerning elastic cusped shells, plates, and beams and cusped prismatic shell-fluid interaction problems. It contains some up to now non-published results as well. Mathematically the corres
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George Jaiani
Cusped Shell-Like Structures
123
Prof. Dr. George Jaiani I. Vekua Institute of Applied Mathematics Iv. Javakhishvili Tbilisi State University University Street 2 0186 Tbilisi Georgia e-mail: [email protected]
ISSN 2191-530X ISBN 978-3-642-22100-2 DOI 10.1007/978-3-642-22101-9
e-ISSN 2191-5318 e-ISBN 978-3-642-22101-9
Springer Heidelberg Dordrecht London New York Ó George Jaiani 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: eStudio Calamar, Berlin/Figueres Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
This work is devoted to an updated exploratory survey of results concerning elastic cusped shells, plates, and beams and cusped prismatic shell-fluid interaction problems. It also contains some up to now non-published results and new problems to be investigated. Mathematically, the corresponding problems lead to nonclassical, in general, boundary value and initial-boundary value problems for governing degenerate elliptic and hyperbolic systems in static and dynamical cases, respectively. Two principally different approaches of investigation are used: (1) to get results for 2D (two-dimensional) and 1D (one-dimensional) problems from results of the corresponding 3D (three-dimensional) problems and (2) to investigate directly governing degenerate and singular systems of 2D and 1D problems. In both the cases, it is important to study the relationship of 2D and 1D problems with 3D problems. On the one hand, it turned out that the second approach allows to investigate such 2D and 1D problems whose corresponding 3D problems are not possible to study within the framework of the 3D model of the theory of elasticity. On the other hand, the second approach is historically approved, since first the 1D and 2D models were created and only then the 3D model was constructed. Hence, the second approach gives a good chance for the further development (generalization) of the 3D model. The present work is addressed to engineers interested in the mathematical aspects of practical problems and mathematicians interested in engineering applications. Both can find new challenging pr
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