Saint-Venant's Problem
This monograph is concerned with the equilibrium of linearly elastic cylinders. It gives an up-to-date and systematic treatment of extension, bending, torsion and flexure of cylinders, including the deformation of homogeneous and nonhomogeneous anisotropi
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1279 Dorin lesan
Saint-Venant's Problem
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann
1279 Dorin lesan
Saint-Venant's Problem
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Author
Dorin lesan Department of Mathematics, University of lasi 6600 lasi, Rumania
Mathematics Subject Classification (1980): 73C10, 73C20, 73C25, 73C30, 73C40, 73K05, 73B25,35J55 ISBN 3-540-18361-2 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-18361-2 Springer-Verlag New York Berlin Heidelberg
Library of Congress Cataloging-in-Publication Data. lesan, Dorin. Saint-Venant's problem. (Lecture notes in mathematics; 1279) Bibliography: p. Includes index. 1. Saint-Venant's principle. 2. Elasticity. 3. Cylinders. I. Title. II. Series: Lecture notes in mathematics (Springer-Verlag; 1279. QA3.L28 no. 1279 [QA931] 510 s 87-23553 ISBN 0-387-18361-2 (U.S.) [624.1 '772] 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, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1987 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210
INTRODUCTION A major concern througbout the bistory of elasticity bas been witb problems dictated by the demands of engineering. Interest in tbe construction of a tbeory for the deformation of elastic cylinders dates back to Coulomb, Navier and Cauchy. However, only SaintVenant has been able to give a solution of the problem. The importance of SaintVenant's celebrated memoirs [132,133], on what has long since become known as SaintVenant's problem requires no emphasis. To review the vast literature to which the work contsined in [132,133] has given impetus is not our inteniion. An account of the historical developments as well as references to various contributions, may be found in tbe books and in some of the papers cited. We recall that SaintVenant's problem consists in determining the equilibrium of a homogeneous and isotropic linearly elastic cylinder, loaded by surface forces distributed over its plane ends. SaintVenant proposed an approximation to the solution of tbe tbreedimensional problem, wbich only requires tbe solution of twodimensional problems in the cross section of the cylinder. formulation leads to tbe four basic problems of extension, bending. torsion and flexure. His analysis is founded on pbysical intuition and e1ementRry beam tbeory. SaintVenant's extension, bending, tortion, and flexure solutions are wellknown (see, for example, Love (981, Chapters 14,15
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