الصفحة 1
الصفحة 1
Nonlinear Problems of Elasticity
This second edition is an enlarged, completely updated, and extensively revised version of the authoritative first edition. It is devoted to the detailed study of illuminating specific problems of nonlinear elasticity. The mathematical tools from nonlinear analysis are given self-contained presentations where they are needed. This book begins with chapters on (geometrically exact theories of) strings, rods, and shells, and on the applications of bifurcation theory and the calculus of variations to problems for these bodies. The book continues with chapters on tensors, three-dimensional continuum mechanics, three-dimensional elasticity, large-strain plasticity, general theories of rods and shells, and dynamical problems. Each chapter contains a wealth of interesting, challenging, and tractable exercises.
Mechanical Sytems, Classical Models ; Vol. I : Particle Mechanics
The guideline of the present book is precisely the mathematical model of mechanics. A special accent is put on the solving methodology as well as on the mathematical tools used; vectors, tensors and notions of field theory. Continuous and discontinuous phenomena, various mechanical magnitudes are presented in a unitary form by means of the theory of distributions.
Introduzione alla Teoria della elasticità : Meccanica dei solidi continui in regime lineare elastico = Introduction to the theory of elasticity : Mechanics of continuous solids in linear elastic regime
Introduces the student to the theory of elasticity through the choice of a selected number of topics of paradigmatic conceptual importance and through the performance of numerous exercises and in-depth problems. The topics range from the formal properties of stress and strain tensors, to the theory of linear elastic continuum, to the thermodynamics of deformations, to the propagation of elastic waves, to the theory of brittle fracture in a linear elastic regime.
From Vectors to Tensors
It is true that there exist many books dedicated to linear algebra and some what fewer to multilinear algebra, written in several languages, and perhaps one can think that no more books are needed. However, it is also true that in algebra many new results are continuously appearing, different points of view can be used to see the mathematical objects and their associated structures, and different orientations can be selected to present the material, and all of them deserve publication. he book assumes a certain knowledge of linear algebra, and is intended as a textbook for graduate and postgraduate students and also as a consultation book. It is addressed to mathematicians, physicists, engineers, and applied scientists with a practical orientation who are looking for powerful tensor tools to solve their problems.
Elements for Physics : Quantities, Qualities, and Intrinsic Theories
While usual presentations of physical theories emphasize the notion of physical quantity, this book shows that there is much to gain when introducing the notion of physical quality. The usual physical quantities simply appear as coordinates over the manifolds representing the physical qualities. This allows to develop physical theories that have a degree of invariance much deeper than the usual one. It is shown that properly developed physical theories contain logarithms and exponentials of tensors: their conspicuous absence in usual theories suggests, in fact, that the fundamental invariance principle stated in this book is lacking in present-day mathematical physics. The book reviews and extends the theory if Lie groups, develops differential geometry, proposing compact definitions of torsion and of curvature, and adapts the usual notion of linear tangent application to the intrinsic point of view proposed for physics. As an illustration, two simple theories are studied with some detail, the theory of heat conduction and the theory of linear elastic media. The equations found differ quantitatively and qualitatively from those usually presented.
Creep Mechanics ; 3rd ed.
The third edition of “Creep Mechanics” provides a short survey of recent advances in the mathematical modelling of the mechanical behavior of anisotropic solids under creep conditions, including principles, methods, and applications of tensor functions.
Continuum Mechanics
This book presents an introduction into the entire science of Continuum Mechanics in three parts. PART I: Continuum Mechanics introduces into the Foundations using tensors in Cartesian coordinate systems, classical theory of elasticity, and fluid mechanics. PART II: Mechanics of Materials has chapters on viscoelasticity, plasticity, principles of constitutive modelling, and thermodynamics. PART III presents Tensor Analysis and fundamental equations of Continuum Mechanics in curvilinear coordinates.
Machine learning for risk calculations : A practitioner's view
Fundamental Approximation Methods. Machine Learning -- Deep Neural Nets -- Chebyshev Tensors -- The toolkit - plugging in approximation methods. Introduction: why is a toolkit needed -- Composition techniques -- Tensors in TT format and Tensor Extension Algorithms -- Sliding Technique -- The Jacobian projection technique -- Hybrid solutions - approximation methods and the toolkit.
Basal Implantology
Helps oral implantologists to understand the principles that underlie the use of basal implants as a means to provide simple solutions to complex and highly demanding clinical situations without the need for prior bone grafting.
