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Advances in Mechanics and Mathematics #12: Nonsmooth Mechanics and Analysis: Theoretical and Numerical Advances

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Advances in Mechanics and Mathematics #12: Nonsmooth Mechanics and Analysis: Theoretical and Numerical Advances Cover

 

Synopses & Reviews

Publisher Comments:

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.

Table of Contents

From the contents Preface.- A short biography of Jean Jacques Moreau.- Part I. Convex and Nonsmooth Analysis.- Moreau's proximal mappings and convexity in Hamilton-Jacobi theory.- Three optimization problems in mass transportation theory.- Geometrical and algebraic properties of various convex hulls.- Legendre-Fenchel transform of composite functions.- What is to be a mean?- Part II. Nonsmooth Mechanics.- Thermoelastic contact with frictional heating.- A condition for statical admissibility in unilateral structural analysis.- Min-max duality and shakedown theorems in plasticity.- Friction and adhesion.- The Clausius-Duhem inequality, an interesting and productive inequality.- Unilateral crack identification.- Penalty approximation of Painelevé problem.

Product Details

ISBN:
9781441939760
Author:
Alart, Pierre
Publisher:
Springer
Author:
Maisonneuve, Olivier
Author:
Rockafellar, R. Tyrrell
Location:
Boston, MA
Subject:
Mathematical Analysis
Subject:
Analysis
Subject:
Computational Mathematics and Numerical Analysis
Subject:
Computational Mathematics and Numerical Analysis Illustrates links between developments in nonsmooth analysis and nonsmooth mechanics
Subject:
Mathematics-Analysis General
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Global analysis (Mathematics)
Subject:
Computer science_xMathematics
Copyright:
Edition Description:
Softcover reprint of hardcover 1st ed. 2006
Series:
Advances in Mechanics and Mathematics
Series Volume:
12
Publication Date:
20101123
Binding:
TRADE PAPER
Language:
English
Pages:
334
Dimensions:
235 x 155 mm 510 gr

Related Subjects

Engineering » Mechanical Engineering » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » Introduction
Science and Mathematics » Physics » Classical Mechanics

Advances in Mechanics and Mathematics #12: Nonsmooth Mechanics and Analysis: Theoretical and Numerical Advances New Trade Paper
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