Boundary Integral Equation Methods and Numerical Solutions Thin Plat
This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of t
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Christian Constanda Dale Doty William Hamill
Boundary Integral Equation Methods and Numerical Solutions Thin Plates on an Elastic Foundation
Developments in Mathematics VOLUME 35 Series Editors: Krishnaswami Alladi, University of Florida, Gainesville, FL, USA Hershel M. Farkas, Hebrew University of Jerusalem, Jerusalem, Israel
More information about this series at http://www.springer.com/series/5834
Christian Constanda • Dale Doty
•
William Hamill
Boundary Integral Equation Methods and Numerical Solutions Thin Plates on an Elastic Foundation
123
Christian Constanda The Charles W. Oliphant Professor of Mathematical Sciences Department of Mathematics The University of Tulsa Tulsa, Oklahoma, USA
Dale Doty Department of Mathematics The University of Tulsa Tulsa, Oklahoma, USA
William Hamill Department of Mathematics The University of Tulsa Tulsa, Oklahoma, USA
ISSN 1389-2177 ISSN 2197-795X (electronic) Developments in Mathematics ISBN 978-3-319-26307-6 ISBN 978-3-319-26309-0 (eBook) DOI 10.1007/978-3-319-26309-0 Library of Congress Control Number: 2016930553 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www. springer.com)
For Lia, Jennifer, and Kathy
Preface
Many problems in mathematical physics and engineering are modeled by elliptic systems of partial differential equations. Well-known examples in this context are higher-dimensional steady-state heat conduction [11], acoustics (see [8, 15]), gravitational potential [10], fluid mechanics [14], and elasticity theory (plane strain, bending of thin plates, and stationary flexural oscillations—see [11, 12]). Among the solution techniques for such problems, a prominent role is played by boundary integral equation methods (BIEMs), which, apart from being powerful and elegant, have some decisi
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