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E-raamat: Nonsmooth Mechanics and Analysis: Theoretical and Numerical Advances

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Inthecourseofthelast ftyyears, developmentsinnonsmoothana- sisandnonsmoothmechanicshaveoftenbeencloselylinked. Thepresent book acts as an illustration of this. Its objective is two-fold. It is of course intended to help to di use the recent results obtained by various renownedspecialists. ButthereisanequaldesiretopayhomagetoJean Jacques Moreau, who is undoubtedly the most emblematic ?gure in the correlated, not to say dual, advances in these two ?elds. Jean Jacques Moreau appears as a rightful heir to the founders of di erential calculus and mechanics through the depth of his thinking in the ?eld of nonsmooth mechanics and the size of his contribution to the development of nonsmooth analysis. His interest in mechanics has focused on a wide variety of subjects: singularities in ?uid ?ows, the initiation of cavitation, plasticity, and the statics and dynamics of gr- ular media. The 'Ariadne's thread' running throughout is the notion of unilateral constraint. Allied to this is his investment in mathematics in the ?elds of convex analysis, calculus of variations and di erential m- sures. When considering these contributions, regardless of their nature, one cannot fail to be struck by their clarity, discerning originality and elegance. Precision and rigor of thinking, clarity and elegance of style are the distinctive features of his work.
Preface ix
A short biography of Jean Jacques Moreau xiii
Part I Convex and nonsmooth analysis
Moreau's proximal mappings and convexity in Hamilton-Jacobi theory
3(10)
R. T. Rockafellar
Three optimization problems in mass transportation theory
13(12)
G. Buttazzo
Geometrical and algebraic properties of various convex hulls
25(10)
B. Dacorogna
Legendre-Fenchel transform of convex composite functions
35(12)
J.-B. Hiriart-Urruty
What is to be a mean?
47(14)
M. Valadier
Part II Nonsmooth mechanics
Thermoelastic contact with frictional heating
61(10)
L.-E. Andersson
A. Klarbring
J.R. Barber
M. Ciavarella
A condition for statical admissibility in unilateral structural analysis
71(10)
G. Del Piero
Min-max Duality and Shakedown Theorems in Plasticity
81(12)
Q. S. Nguyen
Friction and adhesion
93(14)
M. Raous
The Clausius-Duhem inequality, an interesting and productive inequality
107(12)
M. Fremond
Unilateral crack identification
119(10)
G. E. Stavroulakis
M. Engelhardt
H. Antes
Penalty approximation of Painleve problem
129(16)
M. Schatzman
Discrete contact problems with friction
145(18)
F. Maceri
P. Bisegna
Part III Fluid mechanics
A brief history of drop formation
163(10)
J. Eggers
Semiclassical approach of the ``tetrad model'' of turbulence
173(12)
A. Naso
A. Pumir
Part IV Multibody dynamics: numerical aspects
The geometry of Newton's cradle
185(10)
C. Glocker
U. Aeberhard
Nonsmooth analysis for contact mechanics simulations
195(14)
P. Alart
D. Dureisseix
M. Renouf
Numerical simulation of a multibody gas
209(12)
M. Jean
Granular media and ballasted railway tracks
221(12)
C. Cholet
G. Saussine
P.-E. Gautier
L.-M. Cleon
Scaling behaviour of velocity fluctuations in slow granular flows
233(16)
F. Radjai
S. Roux
Part V Topics in nonsmooth science
Morphological equations and sweeping processes
249(12)
J.-P. Aubin
J. A. Murillo Hernandez
Higher order Moreau's sweeping process
261(18)
V. Acary
B. Brogliato
An existence result in non-smooth dynamics
279(10)
M.D.P. Monteiro Marques
L. Paoli
Finite time stabilization of nonlinear oscillators subject to dry friction
289(16)
S. Adly
H. Attouch
A. Cabot
Canonical duality in nonsmooth, constrained concave minimization
305(10)
D. Y. Gao
Appendix: Theoretical and Numerical Nonsmooth Mechanics International Colloquium 315(4)
Index 319