Nonsmooth Mechanics and Applications
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NONSMOOTH MECHANICS AND APPLICATIONS
EDITED BY
J.J. MOREAU UNIVERSITY OF MONTPELLIER
P.O. PANAGIOTOPOULOS ARISTOTLE UNIVERSITY AND R.W.T.H.
SPRINGER-VERLAG WIEN GMBH
Le spese di stampa di questo volume sono in parte coperte da contributi dei Consiglio Nazionale delle Ricerche.
This volume contains 77 illustrations.
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Cl
1988 by Springer-Verlag Wien
Originally published by Springer Verlag Wien-New York in 1988
ISBN 978-3-211-82066-7 DOI 10.1007/978-3-7091-2624-0
ISBN 978-3-7091-2624-0 (eBook)
PREFACE
This book is devoted to problems of Mechanics involving nonsmooth relations. In place of classical derivatives current concepts of Nonsmooth Analysis are used, such as subdifferentials, generalized gradients,fans or quasidifferentials. The corresponding problems may take the form of variational or hemivariational inequalities or of dif./erential and integral inclusions. Other mechanical topics investigated in the present volume lead to the determination of saddle points for non-differentiable functions. In Dynamics, velocity is not supposed to be a smooth function of time, but only to have locally bounded variation, so that acceleration is a vector-valued measure on the concerned interval of time. Evolution is thus governed by measure differential equations or by measure differential inclusions. The formalism used makes easy to discretize for numerical treatment. Generally, the practice/ Nonsmooth Analysis requires the handling ofmultivalued mappings (i.e. set-valued mappings, also called multifunctions). In Mechanics, this concept has for long been implicit in such classical domains as Plasticity of Dry Friction. Its use in a formalizedway provides a new insight into these subjects and concurrently proves to be operationally efficient. The same is true for a number of mechanical or thermodynamical topics. Chapter l by J.J. Moreau, concerns the Dynamics ofsystems with afinite number ofdegrees of freedom, involving unilateral contact whereupon possible friction is assumed to obey Coulomb's law. New formulations of the corresponding evolution problems are developed which lead to effective numerical algorithms. These numerical techniques in particular prove effective in the handling of the catastrophic events which may be manifested in the presence of dry friction. Chapter Il by P. D. Panagiotopoulos, deals with mechanicalproblems admitting variational formulations in terms of Hemivariational Inequalities. The notions of substationarity and quasidifferentiability are introduced and some new nonclassical variational principles in inequality form are presented. Chapter Ill by M. Fremond, develops the use of nonsmooth potentials in reversible or irreversible Thermodynamics. This provides new approaches to subjects such as Phase Changes
