Magnetoelasticity
Magnetization of an elastic body affects its state of stress in three ways [25].
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No. 58
HEINZ PARKUS TECHNICAL UNIVERSITY OF VIENNA
VARIATIONAL PRINCIPLES IN THERMO- AND MAGNETO-ELASTICITY
COURSE HELD AT THE DEPARTMENT FOR MECHANICS OF DEFORMABLE BODIES OCTOBER 1970
UDINE 1970
SPRINGER-VERLAG WIEN GMBH
This work is subject to copyright. All rights are reselVed, whetber the whole or part of the material is concemed specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks.
©
1972 by Springer-Verlag Wien
Originally published by Springer-Verlag Wien - New York in 1972
ISBN 978-3-211-81080-4 ISBN 978-3-7091-2941-8 (eBook) DOI 10.1007/978-3-7091-2941-8
P R E F A C E
This short monograph is intented as a textbook for a series of lectures given by the author at the Centre International des Sciences Mecaniques in Udine in the fall of 19?0. While applications of the calculus of variations to problems of continuum mechanics have a long and fascinating history interest in the special subjects treated in this monograph is relatively new. I hope, therefore, that the attempt undertaken here, at a unified presentation of the ma&erial scattered over a large number of scientific journals might serve a useful purpose. The limited time available for the lectures did not permit for the treatment of specific applications. A few references to the pertinent literature are given instead. Some familiarity from the part of the reader with the concepts and techniques of ~he calculus of variations is expected. All mathematical subtleties, however, have been omitted. A certain knowledge of the fundamentals of thermodynamics and electrodynamics will be necessary for an understanding of some parts of the text.I take great pleasure in expressing my sincere gratitude to the Secretary General of CISM, Prof. L. Sobrero, and to the Rector, Prof. W. Olszak, for inviting me to present these lectures.
Udine, October 19?0
C 0 N T E N TS Page Preface .. ..•.•.•••••....•••.•.••....•.•..•..•........ .
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Introduction ••••••••••••••••••••.••••••••••••••.••••••
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Chapter I. Uncoupled Thermoelasticity •••••••••••••••••
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Chapter II. Coupled Thermoelasticity ••••••••••••••••••
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(1) Generalized Hamilton's Principle ••••••••••••••
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(2) Herrmann's combined Biot-Reissner Principle •••
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Chapter III. Thermo-Viscoelasticity •••••••••••••••••••
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(1) The principle by Sanders et al ••••••••••••••••
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(2) The principle by Olszak and Perezyna •••••••••• (3) Schapery 1 s Principle ••••••••••••••••••••••••••
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Chapter IV. Magnetoelasticity •••••••••••••••••••••••••
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Chapter V. Piezoelectricity •••••••••••••••••••••••••••
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References . .•....•••...•....•..•..•..••..••.•........•
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INTRODUCTION Recognition of the fact that boundary value problems of continuum mechanics are equivalent to problems of the calculus of variations goes back to Daniel Bernoulli [1] who considered the special case of the elastic rod. The formulation of the general three-dimensional elastic
