Beschreibung
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.
Inhaltsverzeichnis
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 Paineleve problem.
Autorenporträt
InhaltsangabeFrom the contents Preface. A short biography of Jean Jacques Moreau. Part I. Convex and Nonsmooth Analysis. Moreau's proximal mappings and convexity in HamiltonJacobi theory. Three optimization problems in mass transportation theory. Geometrical and algebraic properties of various convex hulls. LegendreFenchel 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. Minmax duality and shakedown theorems in plasticity. Friction and adhesion. The ClausiusDuhem inequality, an interesting and productive inequality. Unilateral crack identification. Penalty approximation of Painelevé problem.
