Continuum Mechanics
This book presents an introduction into the entire science of Continuum Mechanics in three parts. PART I: Continuum Mechanics introduces into the Foundations using tensors in Cartesian coordinate systems, classical theory of elasticity, and fluid mechanic
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Fridtjov Irgens
Continuum Mechanics With 279 Figures and 4 Tables
Fridtjov Irgens Wolffsgate 12 5006 Bergen Norway [email protected]
ISBN: 978-3-540-74297-5
e-ISBN: 978-3-540-74298-2
Library of Congress Control Number: 2007936609 c 2008 Springer-Verlag Berlin Heidelberg 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: Steinen-Broo, e Studio Calamar, Girona Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com
Preface
Students of engineering and engineering science are early in their studies exposed to Applied Mechanics: Statics and Dynamics of rigid bodies, Strength of Materials and Fluid Mechanics. As a teacher of these subjects for many years at the Norwegian University of Science and Technology, and for students of most special branches of engineering, I have found that it is highly relevant and important that students who want to obtain a better understanding of the mechanics of materials or of the mechanics of fluids, should take a course in Continuum Mechanics, a discipline that synthesizes the basic concepts of the mechanics of solids and fluids. The pioneers in natural science were experts in many different disciplines of physics and mechanics. Leonhard Euler [1707–1783] is an example of a scientist who has made permanent contributions both in Solid Mechanics: the Euler theory of column buckling, and Fluid Mechanics: the Euler equations of inviscid fluids. Later came times when special fields like the Theory of Elasticity, Hydrodynamics, and Gas Dynamics dominated. Classical Theory of Elasticity is the mechanics of isotropic and linearly elastic materials, for which the behavior is based on extensions of Hooke’s law, and where deformations are assumed to be small. Hydrodynamics is the mechanics of liquids, and Gas Dynamics is the thermomechanics of gasses. These two disciplines are joined in the science of Fluid Mechanics, the term fluid being a common name for liquids and gasses. Although these separate parts of mechanics still exist as important special fields, a need for unification of the mechanics of solids and fluids became important in modern times, let us say in the last 60 years or so. New and complex materials have been invented and made available, and a better utilization o
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