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Mathematical Theory of Continuum Mechanics

Author: Rabindranath Chatterjee

Publisher: Alpha Science Int'l Ltd.

Published: 1999

Total Pages: 294

ISBN-13: 9788173192449

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.

Mathematical Methods in Continuum Mechanics of Solids

Author: Martin Kružík

Publisher: Springer

Published: 2019-03-02

Total Pages: 617

ISBN-13: 3030020657

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This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear or quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited. This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields.

Continuum Mechanics and Theory of Materials

Author: Peter Haupt

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 666

ISBN-13: 3662047756

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The new edition includes additional analytical methods in the classical theory of viscoelasticity. This leads to a new theory of finite linear viscoelasticity of incompressible isotropic materials. Anisotropic viscoplasticity is completely reformulated and extended to a general constitutive theory that covers crystal plasticity as a special case.

Mathematics Applied to Continuum Mechanics

Author: Lee A. Segel

Publisher: SIAM

Published: 2007-07-12

Total Pages: 598

ISBN-13: 0898716209

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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 Analysis of Continuum Mechanics and Industrial Applications

Author: Hiromichi Itou

Publisher: Springer

Published: 2016-11-18

Total Pages: 229

ISBN-13: 9811026335

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This book focuses on mathematical theory and numerical simulation related to various aspects of continuum mechanics, such as fracture mechanics, elasticity, plasticity, pattern dynamics, inverse problems, optimal shape design, material design, and disaster estimation related to earthquakes. Because these problems have become more important in engineering and industry, further development of mathematical study of them is required for future applications. Leading researchers with profound knowledge of mathematical analysis from the fields of applied mathematics, physics, seismology, engineering, and industry provide the contents of this book. They help readers to understand that mathematical theory can be applied not only to different types of industry, but also to a broad range of industrial problems including materials, processes, and products.

Continuum Mechanics

Author: P. Chadwick

Publisher: Courier Corporation

Published: 2012-08-08

Total Pages: 191

ISBN-13: 048613914X

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DIVComprehensive treatment offers 115 solved problems and exercises to promote understanding of vector and tensor theory, basic kinematics, balance laws, field equations, jump conditions, and constitutive equations. /div

Mathematical Analysis of Continuum Mechanics and Industrial Applications II

Author: Patrick van Meurs

Publisher: Springer

Published: 2017-11-16

Total Pages: 190

ISBN-13: 9811062838

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As the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS15), the proceedings of CoMFoS16 present further advances and new topics in mathematical theory and numerical simulations related to various aspects of continuum mechanics. These include fracture mechanics, shape optimization, modeling of earthquakes, material structure, interface dynamics and complex systems.. The authors are leading researchers with a profound knowledge of mathematical analysis from the fields of applied mathematics, physics, seismology, engineering, and industry. The book helps readers to understand how mathematical theory can be applied to various industrial problems, and conversely, how industrial problems lead to new mathematical challenges.

Mathematical Analysis of Continuum Mechanics and Industrial Applications III

Author: Hiromichi Itou

Publisher: Springer Nature

Published: 2020-08-29

Total Pages: 199

ISBN-13: 9811560625

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This book focuses on mathematical theory and numerical simulation related to various areas of continuum mechanics, such as fracture mechanics, (visco)elasticity, optimal shape design, modelling of earthquakes and Tsunami waves, material structure, interface dynamics and complex systems. Written by leading researchers from the fields of applied mathematics, physics, seismology, engineering, and industry with an extensive knowledge of mathematical analysis, it helps readers understand how mathematical theory can be applied to various phenomena, and conversely, how to formulate actual phenomena as mathematical problems. This book is the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS) 15 and CoMFoS16.

Mathematical Modeling in Continuum Mechanics

Author: Roger Temam

Publisher: Cambridge University Press

Published: 2005-05-19

Total Pages: 356

ISBN-13: 1139443216

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Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.

Tensors

Author: Anadi Jiban Das

Publisher: Springer Science & Business Media

Published: 2007-10-05

Total Pages: 300

ISBN-13: 0387694692

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Here is a modern introduction to the theory of tensor algebra and tensor analysis. It discusses tensor algebra and introduces differential manifold. Coverage also details tensor analysis, differential forms, connection forms, and curvature tensor. In addition, the book investigates Riemannian and pseudo-Riemannian manifolds in great detail. Throughout, examples and problems are furnished from the theory of relativity and continuum mechanics.