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An Introduction To Continuum Mechanics

Author: Morton E. Gurtin
Publisher: Academic Press
ISBN: 9780080918495
Size: 36.48 MB
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This book presents an introduction to the classical theories of continuum mechanics; in particular, to the theories of ideal, compressible, and viscous fluids, and to the linear and nonlinear theories of elasticity. These theories are important, not only because they are applicable to a majority of the problems in continuum mechanics arising in practice, but because they form a solid base upon which one can readily construct more complex theories of material behavior. Further, although attention is limited to the classical theories, the treatment is modern with a major emphasis on foundations and structure

Introduction To Continuum Mechanics For Engineers

Author: Ray M. Bowen
Publisher: Springer
ISBN: 9781468477634
Size: 29.24 MB
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This textbook is intended to introduce engineering graduate students to the essentials of modern continuum mechanics. The objective of an introductory course is to establish certain classical continuum models within a modern framework. Engineering students need a firm understanding of classical models such as linear viscous fluids (Navier-Stokes theory) and infinitesimal elasticity. This understanding should include an appreciation for the status of the classical models as special cases of general nonlinear continuum models. The relationship of the classical models to nonlinear models is essential in light of the increasing reliance, by engineering designers and researchers, on prepackaged computer codes. These codes are based upon models which have a specific and limited range of validity. Given the danger associated with the use of these computer codes in circumstances where the model is not valid, engineers have a need for an in-depth understanding of continuum mechanics and the continuum models which can be formu lated by use of continuum mechanics techniques. Classical continuum models and others involve a utilization of the balance equations of continuum mechanics, the second law of thermo dynamics, and the principles of material frame indifference and material symmetry. In addition, they involve linearizations of various types. In this text, an effort is made to explain carefully how the governing principles, linearizations, and other approximations combine to yield classical con tinuum models. A fundamental understanding of how these models evolve is most helpful when one attempts to study models which account for a wider array of physical phenomena.

Mathematics Applied To Continuum Mechanics

Author: Lee A. Segel
Publisher: SIAM
ISBN: 0898716209
Size: 30.22 MB
Format: PDF
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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.

An Introduction To Continuum Mechanics

Author: J. N. Reddy
Publisher: Cambridge University Press
ISBN: 1107025435
Size: 32.22 MB
Format: PDF
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This best-selling textbook presents the concepts of continuum mechanics, and the second edition includes additional explanations, examples and exercises.

Continuum Mechanics

Author: Myron B. Allen
Publisher: John Wiley & Sons
ISBN: 1118909348
Size: 31.54 MB
Format: PDF, Kindle
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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.

Tensor Analysis And Continuum Mechanics

Author: Y.R. Talpaert
Publisher: Springer Science & Business Media
ISBN: 9401599882
Size: 70.51 MB
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This book is designed for students in engineering, physics and mathematics. The material can be taught from the beginning of the third academic year. It could also be used for self study, given its pedagogical structure and the numerous solved problems which prepare for modem physics and technology. One of the original aspects of this work is the development together of the basic theory of tensors and the foundations of continuum mechanics. Why two books in one? Firstly, Tensor Analysis provides a thorough introduction of intrinsic mathematical entities, called tensors, which is essential for continuum mechanics. This way of proceeding greatly unifies the various subjects. Only some basic knowledge of linear algebra is necessary to start out on the topic of tensors. The essence of the mathematical foundations is introduced in a practical way. Tensor developments are often too abstract, since they are either aimed at algebraists only, or too quickly applied to physicists and engineers. Here a good balance has been found which allows these extremes to be brought closer together. Though the exposition of tensor theory forms a subject in itself, it is viewed not only as an autonomous mathematical discipline, but as a preparation for theories of physics and engineering. More specifically, because this part of the work deals with tensors in general coordinates and not solely in Cartesian coordinates, it will greatly help with many different disciplines such as differential geometry, analytical mechanics, continuum mechanics, special relativity, general relativity, cosmology, electromagnetism, quantum mechanics, etc ..

A First Course In Continuum Mechanics

Author: Oscar Gonzalez
Publisher: Cambridge University Press
ISBN: 0521886805
Size: 27.77 MB
Format: PDF, ePub, Docs
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A concise account of classic theories of fluids and solids, for graduate and advanced undergraduate courses in continuum mechanics.

Introduction To Continuum Mechanics

Author: Sudhakar Nair
Publisher: Cambridge University Press
ISBN: 0521875625
Size: 62.23 MB
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This textbook treats solids and fluids in a balanced manner, using thermodynamic restrictions on the relation between applied forces and material responses. This unified approach can be appreciated by engineers, physicists, and applied mathematicians with some background in engineering mechanics. It has many examples and about 150 exercises for students to practice. The higher mathematics needed for a complete understanding is provided in the early chapters. This subject is essential for engineers involved in experimental or numerical modeling of material behavior.

Continuum Mechanics And Thermodynamics

Author: Ellad B. Tadmor
Publisher: Cambridge University Press
ISBN: 1107008263
Size: 46.68 MB
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Treats subjects directly related to nonlinear materials modeling for graduate students and researchers in physics, materials science, chemistry and engineering.