Foundations Of Geometric Continuum Mechanics
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Foundations Of Geometric Continuum Mechanics
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Author : Reuven Segev
language : en
Publisher: Springer Nature
Release Date : 2023-10-31
Foundations Of Geometric Continuum Mechanics written by Reuven Segev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-31 with Mathematics categories.
This monograph presents the geometric foundations of continuum mechanics. An emphasis is placed on increasing the generality and elegance of the theory by scrutinizing the relationship between the physical aspects and the mathematical notions used in its formulation. The theory of uniform fluxes in affine spaces is covered first, followed by the smooth theory on differentiable manifolds, and ends with the non-smooth global theory. Because continuum mechanics provides the theoretical foundations for disciplines like fluid dynamics and stress analysis, the author’s extension of the theory will enable researchers to better describe the mechanics of modern materials and biological tissues. The global approach to continuum mechanics also enables the formulation and solutions of practical optimization problems. Foundations of Geometric Continuum Mechanics will be an invaluable resource for researchers in the area, particularly mathematicians, physicists, and engineers interested in the foundational notions of continuum mechanics.
Geometric Continuum Mechanics
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Author : Reuven Segev
language : en
Publisher: Springer Nature
Release Date : 2020-05-13
Geometric Continuum Mechanics written by Reuven Segev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-13 with Mathematics categories.
This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include: Global stress and hyper-stress theories Applications of de Rham currents to singular dislocations Manifolds of mappings for continuum mechanics Kinematics of defects in solid crystals Geometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest.
Geometric Continuum Mechanics And Induced Beam Theories
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Author : Simon R. Eugster
language : en
Publisher: Springer
Release Date : 2015-03-19
Geometric Continuum Mechanics And Induced Beam Theories written by Simon R. Eugster and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-19 with Science categories.
This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.
Geometrical Foundations Of Continuum Mechanics
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Author : Paul Steinmann
language : en
Publisher: Springer
Release Date : 2015-03-25
Geometrical Foundations Of Continuum Mechanics written by Paul Steinmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-25 with Science categories.
This book illustrates the deep roots of the geometrically nonlinear kinematics of generalized continuum mechanics in differential geometry. Besides applications to first- order elasticity and elasto-plasticity an appreciation thereof is particularly illuminating for generalized models of continuum mechanics such as second-order (gradient-type) elasticity and elasto-plasticity. After a motivation that arises from considering geometrically linear first- and second- order crystal plasticity in Part I several concepts from differential geometry, relevant for what follows, such as connection, parallel transport, torsion, curvature, and metric for holonomic and anholonomic coordinate transformations are reiterated in Part II. Then, in Part III, the kinematics of geometrically nonlinear continuum mechanics are considered. There various concepts of differential geometry, in particular aspects related to compatibility, are generically applied to the kinematics of first- and second- order geometrically nonlinear continuum mechanics. Together with the discussion on the integrability conditions for the distortions and double-distortions, the concepts of dislocation, disclination and point-defect density tensors are introduced. For concreteness, after touching on nonlinear fir st- and second-order elasticity, a detailed discussion of the kinematics of (multiplicative) first- and second-order elasto-plasticity is given. The discussion naturally culminates in a comprehensive set of different types of dislocation, disclination and point-defect density tensors. It is argued, that these can potentially be used to model densities of geometrically necessary defects and the accompanying hardening in crystalline materials. Eventually Part IV summarizes the above findings on integrability whereby distinction is made between the straightforward conditions for the distortion and the double-distortion being integrable and the more involved conditions for the strain (metric) and the double-strain (connection) being integrable. The book addresses readers with an interest in continuum modelling of solids from engineering and the sciences alike, whereby a sound knowledge of tensor calculus and continuum mechanics is required as a prerequisite.
Mathematical Foundation Of Railroad Vehicle Systems
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Author : Ahmed A. Shabana
language : en
Publisher: John Wiley & Sons
Release Date : 2021-02-01
Mathematical Foundation Of Railroad Vehicle Systems written by Ahmed A. Shabana and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-01 with Technology & Engineering categories.
MASTER AND INTEGRATE THE GEOMETRY AND MECHANICS OF RAILROAD VEHICLE SYSTEM ENGINEERING WITH ONE PRACTICAL RESOURCE Mathematical Foundation of Railroad Vehicle Systems: Geometry and Mechanics delivers a comprehensive treatment of the mathematical foundations of railroad vehicle systems. The book includes a strong emphasis on the integration of geometry and mechanics to create an accurate and accessible formulation of nonlinear dynamic equations and general computational algorithms that can be effectively used in the virtual prototyping, analysis, design, and performance evaluation of railroad vehicle systems. Using basic concepts, formulations, and computational algorithms, including mechanics-based approaches like the absolute nodal coordinate formulation (ANCF), readers will understand how to integrate the geometry and mechanics of railroad vehicle systems. The book also discusses new problems and issues in this area and describes how geometric and mechanical approaches can be used in derailment investigations. Mathematical Foundation of Railroad Vehicle Systems covers: The mathematical foundation of railroad vehicle systems through the integration of geometry and mechanics Basic concepts, formulations, and computational algorithms used in railroad vehicle system dynamics New mechanics-based approaches, like the ANCF, and their use to achieve an integration of geometry and mechanics Use of geometry and mechanics to study derailments New problems and issues in the area of railroad vehicle systems Designed for researchers and practicing engineers who work with railroad vehicle systems, Mathematical Foundation of Railroad Vehicle Systems: Geometry and Mechanics can also be used in senior undergraduate and graduate mechanical, civil, and electrical engineering programs and courses.
Mathematical Tools For Physicists
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Author : Michael Grinfeld
language : en
Publisher: John Wiley & Sons
Release Date : 2015-01-12
Mathematical Tools For Physicists written by Michael Grinfeld and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-12 with Science categories.
The new edition is significantly updated and expanded. This unique collection of review articles, ranging from fundamental concepts up to latest applications, contains individual contributions written by renowned experts in the relevant fields. Much attention is paid to ensuring fast access to the information, with each carefully reviewed article featuring cross-referencing, references to the most relevant publications in the field, and suggestions for further reading, both introductory as well as more specialized. While the chapters on group theory, integral transforms, Monte Carlo methods, numerical analysis, perturbation theory, and special functions are thoroughly rewritten, completely new content includes sections on commutative algebra, computational algebraic topology, differential geometry, dynamical systems, functional analysis, graph and network theory, PDEs of mathematical physics, probability theory, stochastic differential equations, and variational methods.
Computer Graphics 1987
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Author : Tosiyasu L. Kunii
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computer Graphics 1987 written by Tosiyasu L. Kunii and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
Recent developments in computer graphics have largely involved the following: Integration of computer graphics and image analysis through computer data structure; integration of CAD/CAM as computer-integrated manufacturing (CIM) through the design and simulation of manufacturing processes using computer graphics; progress in basic research on the modeling of complex and mathematical graphic objects, such as computational geometry, graphic data bases, hierarchical windows, and texture; use of computer graphics as an improved human interface to present information visually and multidimensionally; and advancement of industrial technology and computer art based on developments in the areas listed above. These trends are strongly reflected in the contents of the present volume either as papers dealing with one particular aspect of research or as multifaceted studies involving several different areas. The proceedings comprise thirty selected, previously unpublished original papers presented in nine chapters.
The Mathematical World Of Walter Noll
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Author : Yurie A. Ignatieff
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
The Mathematical World Of Walter Noll written by Yurie A. Ignatieff and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
The book stresses particularly Noll's method of axiomatization of physical theories, his axiomatics of continuum mechanics, thermodynamics of materials, special relativity theory, his discovery of the neo-classical space-time of mechanics, his theories of inhomogeneities in simple bodies, fit regions, contact interactions, annihilators of linear differential operators, and finite-dimensional spaces.
Dissipative Ordered Fluids
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Author : André M. Sonnet
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-21
Dissipative Ordered Fluids written by André M. Sonnet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-21 with Science categories.
This is a book on the dissipative dynamics of ordered fluids, with a particular focus on liquid crystals. It covers a whole range of different theories, mainly concerned with nematic liquid crystals in both their chiral and nonchiral variants. The authors begin by giving a detailed account of the molecular origins of orientational order in fluids. They then go on to develop a general framework in which continuum theories for ordered fluids can be phrased. Within this unified setting, they cover both well-established classical theories and new ones with aspects that are not yet completely settled. The book treats a wide range of hydrodynamic theories for liquid crystals, from the original 1960s works by Ericksen and Leslie to new, fast-developing ideas of liquid crystal science. The final chapter is devoted to nematoacoustics and its applications. Old experiments on the propagation of ultrasound waves in nematic liquid crystals are interpreted and explained in the light of a new theory developed within the general theoretical infrastructure proposed in the body of the book. This book is intended both for graduate students and professional scholars in mathematics, physics, and engineering of advanced materials. It delivers a solid framework for liquid crystal hydrodynamics and shows the unifying concepts at the basis of the classical theories. It illustrates how these concepts can also be applied to a wide variety of modern topics. Andre M. Sonnet is in the Department of Mathematics and Statistics at the University of Strathclyde, Glasgow (Scotland) and Epifanio G. Virga is in the Department of Mathematics at the University of Pavia (Italy). They have a long history of working together in liquid crystal science and have contributed, in particular, to the theories of defects and biaxial nematics.
Continuum Mechanics
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Author : Myron B. Allen, III
language : en
Publisher: John Wiley & Sons
Release Date : 2015-07-20
Continuum Mechanics written by Myron B. Allen, III and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-20 with Mathematics categories.
Presents a self-contained introduction to continuum mechanics that illustrates how many of the important partial differential equations of applied mathematics arise from continuum modeling principles Written as an accessible introduction, Continuum Mechanics: The Birthplace of Mathematical Models provides a comprehensive foundation for mathematical models used in fluid mechanics, solid mechanics, and heat transfer. The book features derivations of commonly used differential equations based on the fundamental continuum mechanical concepts encountered in various fields, such as engineering, physics, and geophysics. The book begins with geometric, algebraic, and analytical foundations before introducing topics in kinematics. The book then addresses balance laws, constitutive relations, and constitutive theory. Finally, the book presents an approach to multiconstituent continua based on mixture theory to illustrate how phenomena, such as diffusion and porous-media flow, obey continuum-mechanical principles. Continuum Mechanics: The Birthplace of Mathematical Models features: Direct vector and tensor notation to minimize the reliance on particular coordinate systems when presenting the theory Terminology that is aligned with standard courses in vector calculus and linear algebra The use of Cartesian coordinates in the examples and problems to provide readers with a familiar setting Over 200 exercises and problems with hints and solutions in an appendix Introductions to constitutive theory and multiconstituent continua, which are distinctive for books at this level Continuum Mechanics: The Birthplace of Mathematical Models is an ideal textbook for courses on continuum mechanics for upper-undergraduate mathematics majors and graduate students in applied mathematics, mechanical engineering, civil engineering, physics, and geophysics. The book is also an excellent reference for professional mathematicians, physical scientists, and engineers.