Nonsmooth Mechanics and Analysis: Theoretical and Numerical Advances

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Pierre Alart, Olivier Maisonneuve, R. Tyrrell Rockafellar
Springer Science & Business Media, Nov 17, 2005 - Technology & Engineering - 320 pages
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This book’s title, Nonsmooth Mechanics and Analysis, refers to a major domain of mechanics, particularly those initiated by the works of Jean Jacques Moreau. Nonsmooth mechanics concerns mechanical situations with possible nondifferentiable relationships, eventually discontinuous, as unilateral contact, dry friction, collisions, plasticity, damage, and phase transition. The basis of the approach consists in dealing with such problems without resorting to any regularization process. Indeed, the nonsmoothness is due to simplified mechanical modeling; a more sophisticated model would require too large a number of variables, and sometimes the mechanical information is not available via experimental investigations. Therefore, the mathematical formulation becomes nonsmooth; regularizing would only be a trick of arithmetic without any physical justification.

Nonsmooth analysis was developed, especially in Montpellier, to provide specific theoretical and numerical tools to deal with nonsmoothness. It is important not only in mechanics but also in physics, robotics, and economics.

 

Audience

This book is intended for researchers in mathematics and mechanics.

 

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Contents

III
3
IV
13
V
25
VI
35
VII
47
VIII
61
IX
71
X
81
XVII
173
XVIII
185
XIX
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XX
209
XXI
221
XXII
233
XXIII
249
XXIV
261

XI
93
XII
107
XIII
119
XIV
129
XV
145
XVI
163
XXV
279
XXVI
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XXVII
305
XXVIII
315
XXIX
319
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