Paolo Podio-Guidugli - Böcker

During its 2004 meeting in Warsaw the General Assembly of the International Union of Theoretical and Applied Mechanics (IUTAM) decided to support a proposal of the Georgian National Committee to hold in Tbilisi (Georgia), on April 23-27, 2007, the IUTAM Symposium on the Relation of Shell, Plate, Beam, and 3D Models, dedicated to the Centenary of Ilia Vekua. The sci- ti?c organization was entrusted to an international committee consisting of Philipppe G. Ciarlet (Hong Kong), the late Anatoly Gerasimovich Gorshkov (Russia),JornHansen(Canada),GeorgeV.Jaiani(Georgia,Chairman),Re- hold Kienzler (Germany), Herbert A. Mang (Austria), Paolo Podio-Guidugli (Italy), and Gangan Prathap (India). The main topics to be included in the scienti?c programme were c- sen to be: hierarchical, re?ned mathematical and technical models of shells, plates, and beams; relation of 2D and 1D models to 3D linear, non-linear and physical models; junction problems. The main aim of the symposium was to thoroughly discuss the relations of shell, plate, and beam models to the 3D physicalmodels.Inparticular,peculiaritiesofcuspedshells,plates,andbeams were to be emphasized and special attention paid to junction, multibody and ?uid-elastic shell (plate, beam) interaction problems, and their applications. The expected contributions of the invited participants were anticipated to be theoretical, practical, and numerical in character.

This book deals with an important topic in rational continuum physics, thermodynamics.Although slim, it is fairly well self-contained; some basic notions in continuum mechanics, which a well-intentioned reader should but may not be familiar with, are collected in a final appendix.Modern continuum thermodynamics is a field theory devised to handle a large class of processes that typically are neither spatially homogeneous nor sequences of equilibrium states. The most basic chapter addresses the continuum theory of heat conduction, in which the constitutive laws furnish a mathematical characterization of the macroscopic manifestations of those fluctuations in position and velocity of the microscopic matter constituents that statistical thermodynamics considers collectively. In addition to a nonstandard exposition of the conceptual steps leading to the classical heat equation, the crucial assumption that energy and entropy inflows should be proportional is discussed and a hyperbolic version of that prototypical parabolic PDE is presented. Thermomechanics comes next, a slightly more complex paradigmatic example of a field theory where microscopic and macroscopic manifestations of motion become intertwined. Finally, a virtual power format for thermomechanics is proposed, whose formulation requires that temperature is regarded formally as the time derivative of thermal displacement. It is shown that this format permits an alternative formulation of the theory of heat conduction, and a physical interpretation of the notion of thermal displacement is given.It is addressed to mathematical modelers – or mathematical modelers to be – of continuous material bodies, be they mathematicians, physicists, or mathematically versed engineers.

This book deals in a modern manner with a family of named problems from an old and mature subject, classical elasticity. These problems are formulated over either a half or the whole of a linearly elastic and isotropic two- or three-dimensional space, subject to loads concentrated at points or lines. The discussion of each problem begins with a careful examination of the prevailing symmetries, and proceeds with inverting the canonical order, in that it moves from a search for balanced stress fields to the associated strain and displacement fields.The book, although slim, is  fairly well self-contained; the only prerequisite is a reasonable familiarity with linear algebra (in particular, manipulation of vectors and tensors) and with the usual differential operators of mathematical physics (gradient, divergence, curl, and Laplacian); the few nonstandard notions are introduced with care. Support material for all parts of the book is found in the final Appendix.

This book deals in a modern manner with a family of named problems from an old and mature subject, classical elasticity. These problems are formulated over either a half or the whole of a linearly elastic and isotropic two- or three-dimensional space, subject to loads concentrated at points or lines. The discussion of each problem begins with a careful examination of the prevailing symmetries, and proceeds with inverting the canonical order, in that it moves from a search for balanced stress fields to the associated strain and displacement fields.The book, although slim, is  fairly well self-contained; the only prerequisite is a reasonable familiarity with linear algebra (in particular, manipulation of vectors and tensors) and with the usual differential operators of mathematical physics (gradient, divergence, curl, and Laplacian); the few nonstandard notions are introduced with care. Support material for all parts of the book is found in the final Appendix.

During its 2004 meeting in Warsaw the General Assembly of the International Union of Theoretical and Applied Mechanics (IUTAM) decided to support a proposal of the Georgian National Committee to hold in Tbilisi (Georgia), on April 23-27, 2007, the IUTAM Symposium on the Relation of Shell, Plate, Beam, and 3D Models, dedicated to the Centenary of Ilia Vekua. The sci- ti?c organization was entrusted to an international committee consisting of Philipppe G. Ciarlet (Hong Kong), the late Anatoly Gerasimovich Gorshkov (Russia),JornHansen(Canada),GeorgeV.Jaiani(Georgia,Chairman),Re- hold Kienzler (Germany), Herbert A. Mang (Austria), Paolo Podio-Guidugli (Italy), and Gangan Prathap (India). The main topics to be included in the scienti?c programme were c- sen to be: hierarchical, re?ned mathematical and technical models of shells, plates, and beams; relation of 2D and 1D models to 3D linear, non-linear and physical models; junction problems. The main aim of the symposium was to thoroughly discuss the relations of shell, plate, and beam models to the 3D physicalmodels.Inparticular,peculiaritiesofcuspedshells,plates,andbeams were to be emphasized and special attention paid to junction, multibody and ?uid-elastic shell (plate, beam) interaction problems, and their applications. The expected contributions of the invited participants were anticipated to be theoretical, practical, and numerical in character.

Walter Noll's leadership was central to recent progress in setting the mathematical foundations of continuum physics. In this volume his life and contributions are revisited in an extensive essay that includes a complete list of his research contributions, and the conceptual tools that he provided are put in evidence in original articles pointing to the continuing vitality of his legacy. The volume will appeal to readers with an interest in the many-faceted role that mathematics can play in the advancement of continuum theories of material behavior.This is a reprint of the Journal of Elasticity, Volume 135, Numbers 1-2, April 2019