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A One Dimensional Introduction To Continuum Mechanics

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A One Dimensional Introduction To Continuum Mechanics

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Author : Tony A J Roberts
language : en
Publisher: World Scientific
Release Date : 1994-10-25

A One Dimensional Introduction To Continuum Mechanics written by Tony A J Roberts and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-25 with Mathematics categories.

Many textbooks on continuum mechanics plunge students in at the ‘deep end’ of three-dimensional analysis and applications. However a striking number of commonplace models of our physical environment are based entirely within the dynamics of a one-dimensional continuum. This introductory text therefore approaches the subject entirely within such a one-dimensional framework.The principles of the mathematical modeling of one-dimensional media constitute the book's backbone. These concepts are elucidated with a diverse selection of applications, ranging from tidal dynamics and dispersion in channels to beam bending, algal blooms, blood flow, and the greenhouse effect.The book is ideally suited to elementary undergraduate courses as it makes no use of multivariable calculus. A number of graded problems are included at the end of each section.

A One Dimensional Introduction To Continuum Mechanics

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Author : Anthony John Roberts
language : en
Publisher: World Scientific
Release Date : 1994

A One Dimensional Introduction To Continuum Mechanics written by Anthony John Roberts and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.

Many textbooks on continuum mechanics plunge students in at the ?deep end? of three-dimensional analysis and applications. However a striking number of commonplace models of our physical environment are based entirely within the dynamics of a one-dimensional continuum. This introductory text therefore approaches the subject entirely within such a one-dimensional framework.The principles of the mathematical modeling of one-dimensional media constitute the book's backbone. These concepts are elucidated with a diverse selection of applications, ranging from tidal dynamics and dispersion in channels to beam bending, algal blooms, blood flow, and the greenhouse effect.The book is ideally suited to elementary undergraduate courses as it makes no use of multivariable calculus. A number of graded problems are included at the end of each section.

Soil Mechanics

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Author : David Muir Wood
language : en
Publisher: Cambridge University Press
Release Date : 2009-09-28

Soil Mechanics written by David Muir Wood 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 2009-09-28 with Science categories.

"This introductory course on soil mechanics presents the key concepts of stress, stiffness, seepage, consolidation, and strength within a one-dimensional framework. Consideration of the mechanical behaviour of soils requires us to consider density alongside stresses, thus permitting the unification of deformation and strength characteristics. Soils are described in a way which can be integrated with concurrent teaching of the properties of other engineering materials. The book includes a model of the shearing of soil and some examples of soil-structure interaction which are capable of theoretical analysis using one-dimensional governing equations. The text contains many worked examples, and exercises are given for private study at the end of all chapters. Some suggestions for laboratory demonstrations that could accompany such an introductory course are sprinkled through the book." --Book Jacket.

Nonlinear Continuum Mechanics And Large Inelastic Deformations

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Author : Yuriy I. Dimitrienko
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-25

Nonlinear Continuum Mechanics And Large Inelastic Deformations written by Yuriy I. Dimitrienko 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 2010-12-25 with Science categories.

The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics – kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead to different results. The analysis is accompanied by experimental data and detailed numerical results for rubber, the ground, alloys, etc. The book will be an invaluable text for graduate students and researchers in solid mechanics, mechanical engineering, applied mathematics, physics and crystallography, as also for scientists developing advanced materials.

Continuum Mechanics Volume I

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Author : José Merodio
language : en
Publisher: EOLSS Publications
Release Date : 2011-11-30

Continuum Mechanics Volume I written by José Merodio and has been published by EOLSS Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with categories.

The main objective of continuum mechanics is to predict the response of a body that is under the action of external and/or internal influences, i.e. to capture and describe different mechanisms associated with the motion of a body that is under the action of loading. A body in continuum mechanics is considered to be matter continuously distributed in space. Hence, no attention is given to the microscopic (atomic) structure of real materials although non-classical generalized theories of continuum mechanics are able to deal with the mesoscopic structure of matter (i.e. defects, cracks, dispersive lengths, ...). Matter occupies space in time and the response of a body in continuum mechanics is restricted to the Newtonian space-time of classical mechanics in this volume. Einstein’s theory of relativity is not considered. In the classical sense, loading is considered as any action that changes the motion of the body. This includes, for instance, a change in temperature or a force applied. By introducing the concept of configurational forces a load may also be considered as a force that drives a change in the material space, for example the opening of a crack. Continuum mechanics refers to field descriptions of phenomena that are usually modeled by partial differential equations and, from a mathematical point of view, require non-standard knowledge of non-simple technicalities. One purpose in this volume has been to present the different subjects in a self-contained way for a general audience. The organization of the volume is as follows. Mathematically, to predict the response of a body it is necessary to formulate boundary value problems governed by balance laws. The theme of the volume, that is an overview of the subject, has been written with this idea in mind for beginners in the topic. Chapter 1 is an introduction to continuum mechanics based on a one-dimensional framework in which, simultaneously, a more detailed organization of the chapters of this volume is given. A one-dimensional approach to continuum mechanics in some aspects maybe misleading since the analysis is oversimplified. Nevertheless, it allows us to introduce the subject through the early basic steps of the continuum analysis for a general audience. Chapters 3, 4 and 5 are devoted to the mathematical setting of continuum analysis: kinematics, balance laws and thermodynamics, respectively. Chapters 6 and 7 are devoted to constitutive equations. Chapters 8 and 9 deal with different issues in the context of linear elastostatics and linear elastodynamics and waves, respectively, for solids. Linear Elasticity is a classical and central theory of continuum mechanics. Chapter 10 deals with fluids while chapter 11 analyzes the coupled theory of thermoelasticity. Chapter 12 deals with nonlinear elasticity and its role in the continuum framework. Chapters 13 and 14 are dedicated to different applications of solid and fluid mechanics, respectively. The rest of the chapters involve some advanced topics. Chapter 15 is dedicated to turbulence, one of the main challenges in fluid mechanics. Chapter 16 deals with electro-magneto active materials (a coupled theory). Chapter 17 deals with specific ideas of soft matter and chapter 18 deals with configurational forces. In chapter 19, constitutive equations are introduced in a general (implicit) form. Well-posedness (existence, time of existence, uniqueness, continuity) of the equations of the mechanics of continua is an important topic which involves sophisticated mathematical machinery. Chapter 20 presents different analyses related to these topics. Continuum Mechanics is an interdisciplinary subject that attracts the attention of engineers, mathematicians, physicists, etc., working in many different disciplines from a purely scientific environment to industrial applications including biology, materials science, engineering, and many other subjects.

Model Emergent Dynamics In Complex Systems

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Author : A. J. Roberts
language : en
Publisher: SIAM
Release Date : 2014-12-18

Model Emergent Dynamics In Complex Systems written by A. J. Roberts and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-18 with Mathematics categories.

Arising out of the growing interest in and applications of modern dynamical systems theory, this book explores how to derive relatively simple dynamical equations that model complex physical interactions. The author’s objectives are to use sound theory to explore algebraic techniques, develop interesting applications, and discover general modeling principles. Model Emergent Dynamics in Complex Systems unifies into one powerful and coherent approach the many varied extant methods for mathematical model reduction and approximation. Using mathematical models at various levels of resolution and complexity, the book establishes the relationships between such multiscale models and clarifying difficulties and apparent paradoxes and addresses model reduction for systems, resolves initial conditions, and illuminates control and uncertainty. The basis for the author’s methodology is the theory and the geometric picture of both coordinate transforms and invariant manifolds in dynamical systems; in particular, center and slow manifolds are heavily used. The wonderful aspect of this approach is the range of geometric interpretations of the modeling process that it produces—simple geometric pictures inspire sound methods of analysis and construction. Further, pictures drawn of state spaces also provide a route to better assess a model’s limitations and strengths. Geometry and algebra form a powerful partnership and coordinate transforms and manifolds provide a powerfully enhanced and unified view of a swathe of other complex system modeling methodologies such as averaging, homogenization, multiple scales, singular perturbations, two timing, and WKB theory. Audience Advanced undergraduate and graduate students, engineers, scientists, and other researchers who need to understand systems and modeling at different levels of resolution and complexity will all find this book useful.

Principles Of Engineering Mechanics

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Author : H. Harrison
language : en
Publisher: Elsevier
Release Date : 2012-12-02

Principles Of Engineering Mechanics written by H. Harrison and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Technology & Engineering categories.

Students of engineering mechanics require a treatment embracing principles, practice an problem solving. Each are covered in this text in a way which students will find particularly helpful. Every chapter gives a thorough description of the basic theory, and a large selection of worked examples are explained in an understandable, tutorial style. Graded problems for solution, with answers, are also provided. Integrating statistics and dynamics within a single volume, the book will support the study of engineering mechanics throughout an undergraduate course. The theory of two- and three-dimensional dynamics of particles and rigid bodies, leading to Euler's equations, is developed. The vibration of one- and two-degree-of-freedom systems and an introduction to automatic control, now including frequency response methods, are covered. This edition has also been extended to develop continuum mechanics, drawing together solid and fluid mechanics to illustrate the distinctions between Eulerian and Lagrangian coordinates.Supports study of mechanics throughout an undergraduate courseIntegrates statics and dynamics in a single volumeDevelops theory of 2D and 3D dynamics of particles and rigid bodies

Continuum Mechanics Volume Ii

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Author : José Merodio
language : en
Publisher: EOLSS Publications
Release Date : 2011-11-30

Continuum Mechanics Volume Ii written by José Merodio and has been published by EOLSS Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with categories.

Continuum Mechanics Volume Iii

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Author : José Merodio
language : en
Publisher: EOLSS Publications
Release Date : 2011-11-30

Continuum Mechanics Volume Iii written by José Merodio and has been published by EOLSS Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with categories.

Waves And Rays In Seismology Answers To Unasked Questions Second Edition

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Author : Michael A Slawinski
language : en
Publisher: World Scientific
Release Date : 2018-05-04

Waves And Rays In Seismology Answers To Unasked Questions Second Edition written by Michael A Slawinski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Science categories.

'In summary, Professor Slawinski has written an engaging volume covering an unfamiliar topic in a highly accessible fashion. Non-specialists will gain a significant appreciation of the unique complexities associated with seismology.'Contemporary PhysicsThe author dedicates this book to readers who are concerned with finding out the status of concepts, statements and hypotheses, and with clarifying and rearranging them in a logical order. It is thus not intended to teach tools and techniques of the trade, but to discuss the foundations on which seismology — and in a larger sense, the theory of wave propagation in solids — is built. A key question is: why and to what degree can a theory developed for an elastic continuum be used to investigate the propagation of waves in the Earth, which is neither a continuum nor fully elastic. But the scrutiny of the foundations goes much deeper: material symmetry, effective tensors, equivalent media; the influence (or, rather, the lack thereof) of gravitational and thermal effects and the rotation of the Earth, are discussed ab initio. The variational principles of Fermat and Hamilton and their consequences for the propagation of elastic waves, causality, Noether's theorem and its consequences on conservation of energy and conservation of linear momentum are but a few topics that are investigated in the process to establish seismology as a science and to investigate its relation to subjects like realism and empiricism in natural sciences, to the nature of explanations and predictions, and to experimental verification and refutation.In the second edition, new sections, figures, examples, exercises and remarks are added. Most importantly, however, four new appendices of about one-hundred pages are included, which can serve as a self-contained continuum-mechanics course on finite elasticity. Also, they broaden the scope of elasticity theory commonly considered in seismology.

A One Dimensional Introduction To Continuum Mechanics

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