Differential Geometry And Kinematics Of Continua
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Differential Geometry And Kinematics Of Continua
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Author : John D Clayton
language : en
Publisher: World Scientific
Release Date : 2014-07-31
Differential Geometry And Kinematics Of Continua written by John D Clayton and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-31 with Mathematics categories.
This book provides definitions and mathematical derivations of fundamental relationships of tensor analysis encountered in nonlinear continuum mechanics and continuum physics, with a focus on finite deformation kinematics and classical differential geometry. Of particular interest are anholonomic aspects arising from a multiplicative decomposition of the deformation gradient into two terms, neither of which in isolation necessarily obeys the integrability conditions satisfied by the gradient of a smooth vector field. The concise format emphasizes clarity and ease of reference, and detailed step-by-step derivations of most analytical results are provided.
A Geometric Approach To Thermomechanics Of Dissipating Continua
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Author : Lalao Rakotomanana
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-08
A Geometric Approach To Thermomechanics Of Dissipating Continua written by Lalao Rakotomanana 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 2012-09-08 with Mathematics categories.
Across the centuries, the development and growth of mathematical concepts have been strongly stimulated by the needs of mechanics. Vector algebra was developed to describe the equilibrium of force systems and originated from Stevin's experiments (1548-1620). Vector analysis was then introduced to study velocity fields and force fields. Classical dynamics required the differential calculus developed by Newton (1687). Nevertheless, the concept of particle acceleration was the starting point for introducing a structured spacetime. Instantaneous velocity involved the set of particle positions in space. Vector algebra theory was not sufficient to compare the different velocities of a particle in the course of time. There was a need to (parallel) transport these velocities at a single point before any vector algebraic operation. The appropriate mathematical structure for this transport was the connection. I The Euclidean connection derived from the metric tensor of the referential body was the only connection used in mechanics for over two centuries. Then, major steps in the evolution of spacetime concepts were made by Einstein in 1905 (special relativity) and 1915 (general relativity) by using Riemannian connection. Slightly later, nonrelativistic spacetime which includes the main features of general relativity I It took about one and a half centuries for connection theory to be accepted as an independent theory in mathematics. Major steps for the connection concept are attributed to a series of findings: Riemann 1854, Christoffel 1869, Ricci 1888, Levi-Civita 1917, WeyJ 1918, Cartan 1923, Eshermann 1950.
Differential Geometry And Continuum Mechanics
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Author : Gui-Qiang G. Chen
language : en
Publisher: Springer
Release Date : 2015-08-11
Differential Geometry And Continuum Mechanics written by Gui-Qiang G. Chen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-11 with Mathematics categories.
This book examines the exciting interface between differential geometry and continuum mechanics, now recognised as being of increasing technological significance. Topics discussed include isometric embeddings in differential geometry and the relation with microstructure in nonlinear elasticity, the use of manifolds in the description of microstructure in continuum mechanics, experimental measurement of microstructure, defects, dislocations, surface energies, and nematic liquid crystals. Compensated compactness in partial differential equations is also treated. The volume is intended for specialists and non-specialists in pure and applied geometry, continuum mechanics, theoretical physics, materials and engineering sciences, and partial differential equations. It will also be of interest to postdoctoral scientists and advanced postgraduate research students. These proceedings include revised written versions of the majority of papers presented by leading experts at the ICMS Edinburgh Workshop on Differential Geometry and Continuum Mechanics held in June 2013. All papers have been peer reviewed.
Generalized Continua From The Theory To Engineering Applications
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Author : Holm Altenbach
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-17
Generalized Continua From The Theory To Engineering Applications written by Holm Altenbach 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 2012-10-17 with Science categories.
On the roots of continuum mechanics in differential geometry -- a review.- Cosserat media.- Cosserat-type shells.- Cosserat-type rods.- Micromorphic media.- Electromagnetism and generalized continua.- Computational methods for generalized continua. The need of generalized continua models is coming from practice. Complex material behavior sometimes cannot be presented by the classical Cauchy continua. At present the attention of the scientists in this field is focused on the most recent research items • new models, • application of well-known models to new problems, • micro-macro aspects, • computational effort, and • possibilities to identify the constitutive equations The new research directions are discussed in this volume - from the point of view of modeling and simulation, identification, and numerical methods.
Kant S Metaphysical Foundations Of Natural Science
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Author : Michael Bennett McNulty
language : en
Publisher: Cambridge University Press
Release Date : 2022-08-11
Kant S Metaphysical Foundations Of Natural Science written by Michael Bennett McNulty and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-11 with Philosophy categories.
In his Metaphysical Foundations of Natural Science (1786), Kant accounts for the possibility of an acting-at-a-distance gravitational force, demonstrates the infinite divisibility of matter, and derives analogues to Newtonian laws of motion. The work is his major statement in philosophy of science, and was especially influential in German-speaking countries in the nineteenth century. However, this complex text has not received the scholarly attention it deserves. The chapters of this Critical Guide clarify the accounts of matter, motion, the mathematization of nature, space, and natural laws exhibited in the Metaphysical Foundations; elucidate the relationship between its metaphysics of nature and Kant's critical philosophy; and describe the historical context for Kant's account of natural science. The volume will be an invaluable resource for understanding one of Kant's most difficult works, and will set the agenda for future scholarship on Kant's philosophy of science.
Sixty Shades Of Generalized Continua
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Author : Holm Altenbach
language : en
Publisher: Springer Nature
Release Date : 2023-02-13
Sixty Shades Of Generalized Continua written by Holm Altenbach and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-13 with Science categories.
In this book, well-known scientists discuss modern aspects of generalized continua, in order to better understand modern materials and advanced structures. They possess complicated internal structure, and it requires the development of new approaches to model such structures and new effects caused by it. This book combines fundamental contributions in honor of Victor Eremeyev and his 60th birthday.
Electrodynamics Of Continua I
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Author : A. Cemal Eringen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Electrodynamics Of Continua I written by A. Cemal Eringen 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 Science categories.
The electrodynamics of continua is a branch ofthe physical sciences concerned with the interaction of electromagnetic fields with deformable bodies. De formable bodies are considered to be continua endowed with continuous distributions of mass and charge. The theory of electromagnetic continua is concerned with the determination of deformations, motions, stress, and elec tromagnetic fields developed in bodies upon the applications of external loads. External loads may be of mechanical origin (e.g., forces, couples, constraints placed on the surface of the body, and initial and boundary conditions arising from thermal and other changes) and/or electromagnetic origin (e.g., electric, magnetic, and current fields). Because bodies of different constitutions respond to external stimuli in a different way, it is imperative to characterize properly the response functions relevant to a given class of continua. This is done by means of the constitutive theory. For example, an elastic dielectric responds to electromagnetic fields in a totally different way than a magnetic fluid. The present book is intended to present a unified approach to the subject matter, based on the principles of contemporary continuum physics.
Kinematics Of Cosserat Continua
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Author : Stephen Corteen Cowin
language : en
Publisher:
Release Date : 1962
Kinematics Of Cosserat Continua written by Stephen Corteen Cowin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Biomechanics categories.
Topological Fluid Mechanics
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Author : International Union of Theoretical and Applied Mechanics
language : en
Publisher: Cambridge University Press
Release Date : 1990-04-12
Topological Fluid Mechanics written by International Union of Theoretical and Applied Mechanics and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-04-12 with Mathematics categories.
There has been developing interest in the aspects of fluid mechanics and of magnetohydrodynamics that can be properly described as topological, rather than exclusively analytical in character. This book contains the proceedings of the IUTAM symposium on Topological Fluid Mechanics held at Cambridge UK, 13-18 August, 1989. Topics covered include the kinematic and dynamical problems in laminar and turbulent flows, as well as the range of problems that arise from the magnetohydrodynamics of highly conducting flows. The papers presented cover all approaches; theoretical, computational and experimental, and each paper has been edited by a member of the International Scientific Committee.
Journal Of The Mechanical Behavior Of Materials
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Author :
language : en
Publisher:
Release Date : 2004
Journal Of The Mechanical Behavior Of Materials written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Deformations (Mechanics) categories.