Continuum Mechanics Using Mathematica

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Continuum Mechanics using Mathematica®

Antonio Romano,Addolorata Marasco
Continuum Mechanics using Mathematica Book PDF

Author : Antonio Romano,Addolorata Marasco
Publisher : Springer
Page : 480 pages
File Size : 53,9 Mb
Release : 2014-10-14
Category : Science
ISBN : 9781493916047

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Continuum Mechanics using Mathematica® by Antonio Romano,Addolorata Marasco Pdf

This textbook's methodological approach familiarizes readers with the mathematical tools required to correctly define and solve problems in continuum mechanics. Covering essential principles and fundamental applications, this second edition of Continuum Mechanics using Mathematica® provides a solid basis for a deeper study of more challenging and specialized problems related to nonlinear elasticity, polar continua, mixtures, piezoelectricity, ferroelectricity, magneto-fluid mechanics and state changes (see A. Romano, A. Marasco, Continuum Mechanics: Advanced Topics and Research Trends, Springer (Birkhäuser), 2010, ISBN 978-0-8176-4869-5). Key topics and features: * Concise presentation strikes a balance between fundamentals and applications * Requisite mathematical background carefully collected in two introductory chapters and one appendix * Recent developments highlighted through coverage of more significant applications to areas such as wave propagation, fluid mechanics, porous media, linear elasticity. This second edition expands the key topics and features to include: * Two new applications of fluid dynamics: meteorology and navigation * New exercises at the end of the existing chapters * The packages are rewritten for Mathematica 9 Continuum Mechanics using Mathematica®: Fundamentals, Applications and Scientific Computing is aimed at advanced undergraduates, graduate students and researchers in applied mathematics, mathematical physics and engineering. It may serve as a course textbook or self-study reference for anyone seeking a solid foundation in continuum mechanics.

Continuum Mechanics using Mathematica®

Antonio Romano,Renato Lancellotta,Addolorata Marasco
Continuum Mechanics using Mathematica Book PDF

Author : Antonio Romano,Renato Lancellotta,Addolorata Marasco
Publisher : Birkhäuser
Page : 388 pages
File Size : 50,5 Mb
Release : 2008-11-01
Category : Science
ISBN : 0817670394

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Continuum Mechanics using Mathematica® by Antonio Romano,Renato Lancellotta,Addolorata Marasco Pdf

This book examines mathematical tools, principles, and fundamental applications of continuum mechanics, providing a solid basis for a deeper study of more challenging problems in elasticity, fluid mechanics, plasticity, piezoelectricity, ferroelectricity, magneto-fluid mechanics, and state changes. The work is suitable for advanced undergraduates, graduate students, and researchers in applied mathematics, mathematical physics, and engineering.

Foundations of Fluid Mechanics with Applications

Sergey P. Kiselev,Evgenii V. Vorozhtsov,Vasily M. Fomin
Foundations of Fluid Mechanics with Applications Book PDF

Author : Sergey P. Kiselev,Evgenii V. Vorozhtsov,Vasily M. Fomin
Publisher : Birkhäuser
Page : 575 pages
File Size : 51,6 Mb
Release : 2017-11-02
Category : Mathematics
ISBN : 9783319661490

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Foundations of Fluid Mechanics with Applications by Sergey P. Kiselev,Evgenii V. Vorozhtsov,Vasily M. Fomin Pdf

This textbook presents the basic concepts and methods of fluid mechanics, including Lagrangian and Eulerian descriptions, tensors of stresses and strains, continuity, momentum, energy, thermodynamics laws, and similarity theory. The models and their solutions are presented within a context of the mechanics of multiphase media. The treatment fully utilizes the computer algebra and software system Mathematica® to both develop concepts and help the reader to master modern methods of solving problems in fluid mechanics. Topics and features: Glossary of over thirty Mathematica® computer programs Extensive, self-contained appendix of Mathematica® functions and their use Chapter coverage of mechanics of multiphase heterogeneous media Detailed coverage of theory of shock waves in gas dynamics Thorough discussion of aerohydrodynamics of ideal and viscous fluids an d gases Complete worked examples with detailed solutions Problem-solving approach Foundations of Fluid Mechanics with Applications is a complete and accessible text or reference for graduates and professionals in mechanics, applied mathematics, physical sciences, materials science, and engineering. It is an essential resource for the study and use of modern solution methods for problems in fluid mechanics and the underlying mathematical models. The present, softcover reprint is designed to make this classic textbook available to a wider audience.

Continuum Mechanics

Antonio Romano,Addolorata Marasco
Continuum Mechanics Book PDF

Author : Antonio Romano,Addolorata Marasco
Publisher : Springer Science & Business Media
Page : 353 pages
File Size : 49,8 Mb
Release : 2010-07-23
Category : Science
ISBN : 9780817648701

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Continuum Mechanics by Antonio Romano,Addolorata Marasco Pdf

This book offers a broad overview of the potential of continuum mechanics to describe a wide range of macroscopic phenomena in real-world problems. Building on the fundamentals presented in the authors’ previous book, Continuum Mechanics using Mathematica®, this new work explores interesting models of continuum mechanics, with an emphasis on exploring the flexibility of their applications in a wide variety of fields.

Elasticity with Mathematica ®

Andrei Constantinescu,Alexander Korsunsky
Elasticity with Mathematica Book PDF

Author : Andrei Constantinescu,Alexander Korsunsky
Publisher : Cambridge University Press
Page : 266 pages
File Size : 42,9 Mb
Release : 2007-10-08
Category : Science
ISBN : 0521842018

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Elasticity with Mathematica ® by Andrei Constantinescu,Alexander Korsunsky Pdf

This book is intended for researchers, engineers and students in solid mechanics, materials science and physics who are interested in using the power of modern computing to solve a wide variety of problems of both practical and fundamental significance in elasticity. Extensive use of Mathematica in the book makes available to the reader a range of recipes that can be readily adjusted to match particular tastes or requirements, to visualize solutions, and to carry out symbolic and numerical analysis and optimization.

Foundations of Fluid Mechanics with Applications

Sergey P. Kiselev,Evgenii V. Vorozhtsov,Vasily M. Fomin
Foundations of Fluid Mechanics with Applications Book PDF

Author : Sergey P. Kiselev,Evgenii V. Vorozhtsov,Vasily M. Fomin
Publisher : Springer Science & Business Media
Page : 594 pages
File Size : 42,6 Mb
Release : 1999-12
Category : Computers
ISBN : 0817639950

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Foundations of Fluid Mechanics with Applications by Sergey P. Kiselev,Evgenii V. Vorozhtsov,Vasily M. Fomin Pdf

This book presents the basic concepts of continuum mechanics. The material is presented in a tensor invariant form with a large number of problems with solutions. The book integrates the use of the computer algebra system Mathematica, and contains a large number of programs on the disk that will help clarify the concepts of continuum mechanics.

Elasticity with Mathematica ®

Andrei Constantinescu,Alexander Korsunsky
Elasticity with Mathematica Book PDF

Author : Andrei Constantinescu,Alexander Korsunsky
Publisher : Cambridge University Press
Page : 0 pages
File Size : 55,9 Mb
Release : 2012-08-09
Category : Science
ISBN : 1107406137

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Elasticity with Mathematica ® by Andrei Constantinescu,Alexander Korsunsky Pdf

This book is intended for researchers, engineers and students in solid mechanics, materials science and physics who are interested in using the power of modern computing to solve a wide variety of problems of both practical and fundamental significance in elasticity. Extensive use of Mathematica in the book makes available to the reader a range of recipes that can be readily adjusted to match particular tastes or requirements, to visualize solutions, and to carry out symbolic and numerical analysis and optimization.

Classical Mechanics with Mathematica®

Antonio Romano,Addolorata Marasco
Classical Mechanics with Mathematica Book PDF

Author : Antonio Romano,Addolorata Marasco
Publisher : Springer
Page : 644 pages
File Size : 54,8 Mb
Release : 2018-05-29
Category : Science
ISBN : 9783319775951

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Classical Mechanics with Mathematica® by Antonio Romano,Addolorata Marasco Pdf

This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject. Developed by the authors from over 30 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field—from Newton to Hamilton—while also painting a clear picture of the most modern developments. The text is organized into two parts. The first focuses on developing the mathematical framework of linear algebra and differential geometry necessary for the remainder of the book. Topics covered include tensor algebra, Euclidean and symplectic vector spaces, differential manifolds, and absolute differential calculus. The second part of the book applies these topics to kinematics, rigid body dynamics, Lagrangian and Hamiltonian dynamics, Hamilton–Jacobi theory, completely integrable systems, statistical mechanics of equilibrium, and impulsive dynamics, among others. This new edition has been completely revised and updated and now includes almost 200 exercises, as well as new chapters on celestial mechanics, one-dimensional continuous systems, and variational calculus with applications. Several Mathematica® notebooks are available to download that will further aid students in their understanding of some of the more difficult material. Unique in its scope of coverage and method of approach, Classical Mechanics with Mathematica® will be useful resource for graduate students and advanced undergraduates in applied mathematics and physics who hope to gain a deeper understanding of mechanics.

Elements of Continuum Mechanics and Conservation Laws

S.K. Godunov,Evgenii Romenskii
Elements of Continuum Mechanics and Conservation Laws Book PDF

Author : S.K. Godunov,Evgenii Romenskii
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 44,9 Mb
Release : 2003-05-31
Category : Computers
ISBN : 0306477351

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Elements of Continuum Mechanics and Conservation Laws by S.K. Godunov,Evgenii Romenskii Pdf

Elements of Continuum Mechanics and Conservation Laws presents a systematization of different models in mathematical physics, a study of the structure of conservation laws, thermodynamical identities, and connection with criteria for well-posedness of the corresponding mathematical problems. The theory presented in this book stems from research carried out by the authors concerning the formulations of differential equations describing explosive deformations of metals. In such processes, elasticity equations are used in some zones, whereas hydrodynamics equations are stated in other zones. Plastic deformations appear in transition zones, which leads to residual stresses. The suggested model contains some relaxation terms which simulate these plastic deformations. Certain laws of thermodynamics are used in order to describe and study differential equations simulating the physical processes. This leads to the special formulation of differential equations using generalized thermodynamical potentials.

Elasticity with Mathematica

Andrei Constantinescu,Alexander Korsunsky
Elasticity with Mathematica Book PDF

Author : Andrei Constantinescu,Alexander Korsunsky
Publisher : Unknown
Page : 267 pages
File Size : 54,5 Mb
Release : 2014-05-14
Category : Science
ISBN : 0511355688

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Elasticity with Mathematica by Andrei Constantinescu,Alexander Korsunsky Pdf

This book, first published in 2007, introduces key ideas and principles in the theory of elasticity with the help of symbolic computation. Differential and integral operators on vector and tensor fields of displacements, strains and stresses are considered on a consistent and rigorous basis with respect to curvilinear orthogonal coordinate systems. As a consequence, vector and tensor objects can be manipulated readily, and fundamental concepts can be illustrated and problems solved with ease. The method is illustrated using a variety of plane and three-dimensional elastic problems. General theorems, fundamental solutions, displacements and stress potentials are presented and discussed. The Rayleigh-Ritz method for obtaining approximate solutions is introduced for elastostatic and spectral analysis problems. Containing more than 60 exercises and solutions in the form of Mathematica notebooks that accompany every chapter, the reader can learn and master the techniques while applying them to a large range of practical and fundamental problems.

Micromechanics with Mathematica

Seiichi Nomura
Micromechanics with Mathematica Book PDF

Author : Seiichi Nomura
Publisher : John Wiley & Sons
Page : 290 pages
File Size : 52,9 Mb
Release : 2016-05-02
Category : Science
ISBN : 9781119945031

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Micromechanics with Mathematica by Seiichi Nomura Pdf

Demonstrates the simplicity and effectiveness of Mathematica as the solution to practical problems in composite materials. Designed for those who need to learn how micromechanical approaches can help understand the behaviour of bodies with voids, inclusions, defects, this book is perfect for readers without a programming background. Thoroughly introducing the concept of micromechanics, it helps readers assess the deformation of solids at a localized level and analyse a body with microstructures. The author approaches this analysis using the computer algebra system Mathematica, which facilitates complex index manipulations and mathematical expressions accurately. The book begins by covering the general topics of continuum mechanics such as coordinate transformations, kinematics, stress, constitutive relationship and material symmetry. Mathematica programming is also introduced with accompanying examples. In the second half of the book, an analysis of heterogeneous materials with emphasis on composites is covered. Takes a practical approach by using Mathematica, one of the most popular programmes for symbolic computation Introduces the concept of micromechanics with worked-out examples using Mathematica code for ease of understanding Logically begins with the essentials of the topic, such as kinematics and stress, before moving to more advanced areas Applications covered include the basics of continuum mechanics, Eshelby's method, analytical and semi-analytical approaches for materials with inclusions (composites) in both infinite and finite matrix media and thermal stresses for a medium with inclusions, all with Mathematica examples Features a problem and solution section on the book’s companion website, useful for students new to the programme

Elements of Continuum Mechanics and Thermodynamics

Joanne L. Wegner,James B. Haddow
Elements of Continuum Mechanics and Thermodynamics Book PDF

Author : Joanne L. Wegner,James B. Haddow
Publisher : Cambridge University Press
Page : 279 pages
File Size : 42,6 Mb
Release : 2009-04-13
Category : Science
ISBN : 9781139478380

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Elements of Continuum Mechanics and Thermodynamics by Joanne L. Wegner,James B. Haddow Pdf

This text is intended to provide a modern and integrated treatment of the foundations and applications of continuum mechanics. There is a significant increase in interest in continuum mechanics because of its relevance to microscale phenomena. In addition to being tailored for advanced undergraduate students and including numerous examples and exercises, this text also features a chapter on continuum thermodynamics, including entropy production in Newtonian viscous fluid flow and thermoelasticity. Computer solutions and examples are emphasized through the use of the symbolic mathematical computing program Mathematica®.

Mathematics Applied to Continuum Mechanics

Lee A. Segel
Mathematics Applied to Continuum Mechanics Book PDF

Author : Lee A. Segel
Publisher : SIAM
Page : 598 pages
File Size : 44,6 Mb
Release : 2007-07-12
Category : Science
ISBN : 9780898716207

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Mathematics Applied to Continuum Mechanics by Lee A. Segel Pdf

This classic work gives an excellent overview of the subject, with an emphasis on clarity, explanation, and motivation. Extensive exercises and a valuable section containing hints and answers make this an excellent text for both classroom use and independent study.

Mathematical Theory of Continuum Mechanics

Rabindranath Chatterjee
Mathematical Theory of Continuum Mechanics Book PDF

Author : Rabindranath Chatterjee
Publisher : Alpha Science Int'l Ltd.
Page : 294 pages
File Size : 52,7 Mb
Release : 1999
Category : Mathematics
ISBN : 8173192448

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Mathematical Theory of Continuum Mechanics by Rabindranath Chatterjee Pdf

This text provides an introduction to the theory of continuum mechanics in a logically satisfying form. A simple knowledge of Cartesian tensors is a sufficient prerequisite for this book. The book deals with two major branches of continuum mechanics - the mechanics of elastic solids and the mechanics of fluids providing the basis of civil and mechanical engineering, applied mathematics and physics. Traditional courses in solid mechanics and fluid mechanics are usually taught separately with emphasis on physical behaviour at the cost of rigorous mathematical foundation neglecting the analogies between solids and fluids. The book brings two disciplines under one roof seeking to generalize and unify specialized topics.

Mechanics and Dynamical Systems with Mathematica®

Nicola Bellomo,Luigi Preziosi,Antonio Romano
Mechanics and Dynamical Systems with Mathematica Book PDF

Author : Nicola Bellomo,Luigi Preziosi,Antonio Romano
Publisher : Springer Science & Business Media
Page : 438 pages
File Size : 41,7 Mb
Release : 1999-12-28
Category : Mathematics
ISBN : 081764007X

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Mechanics and Dynamical Systems with Mathematica® by Nicola Bellomo,Luigi Preziosi,Antonio Romano Pdf

Modeling and Applied Mathematics Modeling the behavior of real physical systems by suitable evolution equa tions is a relevant, maybe the fundamental, aspect of the interactions be tween mathematics and applied sciences. Modeling is, however, only the first step toward the mathematical description and simulation of systems belonging to real world. Indeed, once the evolution equation is proposed, one has to deal with mathematical problems and develop suitable simula tions to provide the description of the real system according to the model. Within this framework, one has an evolution equation and the re lated mathematical problems obtained by adding all necessary conditions for their solution. Then, a qualitative analysis should be developed: this means proof of existence of solutions and analysis of their qualitative be havior. Asymptotic analysis may include a detailed description of stability properties. Quantitative analysis, based upon the application ofsuitable methods and algorithms for the solution of problems, ends up with the simulation that is the representation of the dependent variable versus the independent one. The information obtained by the model has to be compared with those deriving from the experimental observation of the real system. This comparison may finally lead to the validation of the model followed by its application and, maybe, further generalization.