*With Applications to Mechanics, Elasticity and Aeronautics*

**Author**: Aristotle D. Michal

**Publisher:**N.A

**ISBN:**9780486462462

**Category:**Mathematics

**Page:**132

**View:**5636

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# Search Results for: cartesian-tensors-with-applications-to-mechanics-fluid-mechanics-and-elasticity-mathematics-and-its-applications

*With Applications to Mechanics, Elasticity and Aeronautics*

**Author**: Aristotle D. Michal

**Publisher:** N.A

**ISBN:** 9780486462462

**Category:** Mathematics

**Page:** 132

**View:** 5636

This volume offers a working knowledge of the fundamentals of matrix and tensor calculus. Relevant to several fields, particularly aeronautical engineering, the text skillfully combines mathematical statements with practical applications. 1947 edition.

**Author**: Rutherford Aris

**Publisher:** Courier Corporation

**ISBN:** 048613489X

**Category:** Mathematics

**Page:** 320

**View:** 2112

Introductory text, geared toward advanced undergraduate and graduate students, applies mathematics of Cartesian and general tensors to physical field theories and demonstrates them in terms of the theory of fluid mechanics. 1962 edition.

**Author**: C. S. Jog

**Publisher:** CRC Press

**ISBN:** 9780849324130

**Category:** Science

**Page:** 435

**View:** 6515

Foundations and Applications of Mechanics: Volume II, Fluid Mechanics shows how suitable approximations such as ideal fluid flow model, boundary layer methods, and the acoustic approximation, can help solve problems of practical importance. The author proceeds from the general to the particular, making it clear at each stage what assumptions have been made to obtain a particular approximation. In his discussion of compressible fluids, Jog steers away from using gas tables and emphasizes obtaining solutions by numerical techniques - an approach more amenable to computer solutions. He discusses the control volume and the differential equation forms of governing equations in detail and uses examples to demonstrate the advantages and shortcomings of each approach.
*With Applications to Mechanical, Thermomechanical, and Smart Materials*

**Author**: Stephen Bechtel,Robert Lowe

**Publisher:** Academic Press

**ISBN:** 0123948347

**Category:** Science

**Page:** 340

**View:** 2883

Fundamentals of Continuum Mechanics provides a clear and rigorous presentation of continuum mechanics for engineers, physicists, applied mathematicians, and materials scientists. This book emphasizes the role of thermodynamics in constitutive modeling, with detailed application to nonlinear elastic solids, viscous fluids, and modern smart materials. While emphasizing advanced material modeling, special attention is also devoted to developing novel theories for incompressible and thermally expanding materials. A wealth of carefully chosen examples and exercises illuminate the subject matter and facilitate self-study. Uses direct notation for a clear and straightforward presentation of the mathematics, leading to a better understanding of the underlying physics Covers high-interest research areas such as small- and large-deformation continuum electrodynamics, with application to smart materials used in intelligent systems and structures Offers a unique approach to modeling incompressibility and thermal expansion, based on the authors’ own research

**Author**: Martin H. Sadd

**Publisher:** Academic Press

**ISBN:** 0128116498

**Category:** Technology & Engineering

**Page:** 432

**View:** 2165

Continuum Mechanics Modeling of Material Behavior offers a uniquely comprehensive introduction to topics like RVE theory, fabric tensor models, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Contemporary continuum mechanics research has been moving into areas of complex material microstructural behavior. Graduate students who are expected to do this type of research need a fundamental background beyond classical continuum theories. The book begins with several chapters that carefully and rigorously present mathematical preliminaries; kinematics of motion and deformation; force and stress measures; and mass, momentum and energy balance principles. The book then moves beyond other books by dedicating the last chapter to constitutive equation development, exploring a wide collection of constitutive relations and developing the corresponding material model formulations. Such material behavior models include classical linear theories of elasticity, fluid mechanics, viscoelasticity and plasticity, as well as linear and nonlinear theories of solids and fluids, including finite elasticity, nonlinear/non-Newtonian viscous fluids, and nonlinear viscoelastic materials. Finally, several relatively new continuum theories based on incorporation of material microstructure are presented including: fabric tensor theories, micropolar elasticity, elasticity with voids, nonlocal higher gradient elasticity and damage mechanics. Offers a thorough, concise and organized presentation of continuum mechanics formulation Covers numerous applications in areas of contemporary continuum mechanics modeling, including micromechanical and multi-scale problems Integration and use of MATLAB software gives students more tools to solve, evaluate and plot problems under study Features extensive use of exercises, providing more material for student engagement and instructor presentation

**Author**: L. P. Lebedev,Michael J. Cloud

**Publisher:** World Scientific

**ISBN:** 9789812564467

**Category:** Mathematics

**Page:** 191

**View:** 3020

Tensor analysis is an essential tool in any science (e.g. engineering, physics, mathematical biology) that employs a continuumdescription. This concise text offers a straightforward treatment ofthe subject suitable for the student or practicing engineer

**Author**: D. S. Chandrasekharaiah,Lokenath Debnath

**Publisher:** Elsevier

**ISBN:** 1483294684

**Category:** Science

**Page:** 595

**View:** 7015

A detailed and self-contained text written for beginners, Continuum Mechanics offers concise coverage of the basic concepts, general principles, and applications of continuum mechanics. Without sacrificing rigor, the clear and simple mathematical derivations are made accessible to a large number of students with little or no previous background in solid or fluid mechanics. With the inclusion of more than 250 fully worked-out examples and 500 worked exercises, this book is certain to become a standard introductory text for students as well as an indispensable reference for professionals. Key Features * Provides a clear and self-contained treatment of vectors, matrices, and tensors specifically tailored to the needs of continuum mechanics * Develops the concepts and principles common to all areas in solid and fluid mechanics with a common notation and terminology * Covers the fundamentals of elasticity theory and fluid mechanics
*Theory, Applications, and Numerics*

**Author**: Martin H. Sadd

**Publisher:** Elsevier

**ISBN:** 9780080477473

**Category:** Science

**Page:** 480

**View:** 4699

Although there are several books in print dealing with elasticity, many focus on specialized topics such as mathematical foundations, anisotropic materials, two-dimensional problems, thermoelasticity, non-linear theory, etc. As such they are not appropriate candidates for a general textbook. This book provides a concise and organized presentation and development of general theory of elasticity. This text is an excellent book teaching guide. Contains exercises for student engagement as well as the integration and use of MATLAB Software Provides development of common solution methodologies and a systematic review of analytical solutions useful in applications of

**Author**: American Mathematical Society

**Publisher:** N.A

**ISBN:** 9780821801031

**Category:** Mathematics

**Page:** 3998

**View:** 2227

**Author**: W Michael Lai,David H. Rubin,David Rubin,Erhard Krempl

**Publisher:** Butterworth-Heinemann

**ISBN:** 0080942520

**Category:** Science

**Page:** 536

**View:** 828

Continuum Mechanics is a branch of physical mechanics that describes the macroscopic mechanical behavior of solid or fluid materials considered to be continuously distributed. It is fundamental to the fields of civil, mechanical, chemical and bioengineering. This time-tested text has been used for over 35 years to introduce junior and senior-level undergraduate engineering students, as well as graduate students, to the basic principles of continuum mechanics and their applications to real engineering problems. The text begins with a detailed presentation of the coordinate invariant quantity, the tensor, introduced as a linear transformation. This is then followed by the formulation of the kinematics of deformation, large as well as very small, the description of stresses and the basic laws of continuum mechanics. As applications of these laws, the behaviors of certain material idealizations (models) including the elastic, viscous and viscoelastic materials, are presented. This new edition offers expanded coverage of the subject matter both in terms of details and contents, providing greater flexibility for either a one or two-semester course in either continuum mechanics or elasticity. Although this current edition has expanded the coverage of the subject matter, it nevertheless uses the same approach as that in the earlier editions - that one can cover advanced topics in an elementary way that go from simple to complex, using a wealth of illustrative examples and problems. It is, and will remain, one of the most accessible textbooks on this challenging engineering subject. Significantly expanded coverage of elasticity in Chapter 5, including solutions of some 3-D problems based on the fundamental potential functions approach. New section at the end of Chapter 4 devoted to the integral formulation of the field equations Seven new appendices appear at the end of the relevant chapters to help make each chapter more self-contained Expanded and improved problem sets providing both intellectual challenges and engineering applications

**Author**: G. Thomas Mase,George E. Mase

**Publisher:** CRC Press

**ISBN:** 9781439832578

**Category:** Science

**Page:** 400

**View:** 3291

The second edition of this popular text continues to provide a solid, fundamental introduction to the mathematics, laws, and applications of continuum mechanics. With the addition of three new chapters and eight new sections to existing chapters, the authors now provide even better coverage of continuum mechanics basics and focus even more attention on its applications. Beginning with the basic mathematical tools needed-including matrix methods and the algebra and calculus of Cartesian tensors-the authors develop the principles of stress, strain, and motion and derive the fundamental physical laws relating to continuity, energy, and momentum. With this basis established, they move to their expanded treatment of applications, including linear and nonlinear elasticity, fluids, and linear viscoelasticity Mastering the contents of Continuum Mechanics: Second Edition provides the reader with the foundation necessary to be a skilled user of today's advanced design tools, such as sophisticated simulation programs that use nonlinear kinematics and a variety of constitutive relationships. With its ample illustrations and exercises, it offers the ideal self-study vehicle for practicing engineers and an excellent introductory text for advanced engineering students.

**Author**: N.A

**Publisher:** N.A

**ISBN:** N.A

**Category:** Detroit (Mich.)

**Page:** N.A

**View:** 2787

Announcements for the following year included in some vols.

**Author**: Siegfried Hess

**Publisher:** Springer

**ISBN:** 331912787X

**Category:** Science

**Page:** 440

**View:** 8676

This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-trace formulas, coupling of irreducible tensors, rotation of tensors. Constitutive laws for optical, elastic and viscous properties of anisotropic media are dealt with. The anisotropic media include crystals, liquid crystals and isotropic fluids, rendered anisotropic by external orienting fields. The dynamics of tensors deals with phenomena of current research. In the last section, the 3D Maxwell equations are reformulated in their 4D version, in accord with special relativity.

**Author**: James G. Simmonds

**Publisher:** Springer Science & Business Media

**ISBN:** 1441985220

**Category:** Mathematics

**Page:** 114

**View:** 2131

In this text which gradually develops the tools for formulating and manipulating the field equations of Continuum Mechanics, the mathematics of tensor analysis is introduced in four, well-separated stages, and the physical interpretation and application of vectors and tensors are stressed throughout. This new edition contains more exercises. In addition, the author has appended a section on Differential Geometry.

**Author**: P C Kendall

**Publisher:** Routledge

**ISBN:** 1351405616

**Category:** Mathematics

**Page:** 304

**View:** 355

This is a comprehensive and self-contained text suitable for use by undergraduate mathematics, science and engineering students. Vectors are introduced in terms of cartesian components, making the concepts of gradient, divergent and curl particularly simple. The text is supported by copious examples and progress can be checked by completing the many problems at the end of each section. Answers are provided at the back of the book.

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