# tensor algebra and tensor analysis for engineers with applications to continuum mechanics mathematical engineering

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## Tensor Algebra And Tensor Analysis For Engineers

**Author :**Mikhail Itskov

**ISBN :**9783319163420

**Genre :**Technology & Engineering

**File Size :**30. 26 MB

**Format :**PDF, Kindle

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This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

## Tensor Algebra And Tensor Analysis For Engineers

**Author :**Mikhail Itskov

**ISBN :**9783642308796

**Genre :**Technology & Engineering

**File Size :**53. 78 MB

**Format :**PDF

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There is a large gap between the engineering course in tensor algebra on the one hand and the treatment of linear transformations within classical linear algebra on the other hand. The aim of this modern textbook is to bridge this gap by means of the consequent and fundamental exposition. The book primarily addresses engineering students with some initial knowledge of matrix algebra. Thereby the mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises are provided in the book and are accompanied by solutions, enabling self-study. The last chapters of the book deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and are therefore of high interest for PhD-students and scientists working in this area. This third edition is completed by a number of additional figures, examples and exercises. The text and formulae have been revised and improved where necessary.

## Tensor Algebra And Tensor Analysis For Engineers

**Author :**Mikhail Itskov

**ISBN :**9783540939078

**Genre :**Technology & Engineering

**File Size :**51. 70 MB

**Format :**PDF, Docs

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There is a large gap between engineering courses in tensor algebra on one hand, and the treatment of linear transformations within classical linear algebra on the other. This book addresses primarily engineering students with some initial knowledge of matrix algebra. Thereby, mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling autonomous study. The last chapters deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area.

## Tensor Analysis And Continuum Mechanics

**Author :**Y.R. Talpaert

**ISBN :**1402010559

**Genre :**Mathematics

**File Size :**53. 82 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 ..

## From Vectors To Tensors

**Author :**Juan R. Ruiz-Tolosa

**ISBN :**9783540270669

**Genre :**Computers

**File Size :**55. 46 MB

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This textbook deals with tensors that are treated as vectors. Coverage details such new tensor concepts as the rotation of tensors, the transposer tensor, the eigentensors, and the permutation tensor structure. The book covers an existing gap between the classic theory of tensors and the possibility of solving tensor problems with a computer. A complementary computer package, written in Mathematica, is available through the Internet.

## A First Course In Continuum Mechanics

**Author :**Oscar Gonzalez

**ISBN :**9780521886802

**Genre :**Science

**File Size :**68. 13 MB

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A concise account of classic theories of fluids and solids, for graduate and advanced undergraduate courses in continuum mechanics.

## Continuum Mechanics For Engineers Third Edition

**Author :**G. Thomas Mase

**ISBN :**1439832579

**Genre :**Science

**File Size :**59. 7 MB

**Format :**PDF, ePub

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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.

## Continuum Mechanics

**Author :**P. Chadwick

**ISBN :**9780486139142

**Genre :**Science

**File Size :**58. 77 MB

**Format :**PDF, ePub

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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

## Continuum Damage Mechanics

**Author :**Sumio Murakami

**ISBN :**9789400726659

**Genre :**Technology & Engineering

**File Size :**65. 86 MB

**Format :**PDF, Mobi

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Recent developments in engineering and technology have brought about serious and enlarged demands for reliability, safety and economy in wide range of fields such as aeronautics, nuclear engineering, civil and structural engineering, automotive and production industry. This, in turn, has caused more interest in continuum damage mechanics and its engineering applications. This book aims to give a concise overview of the current state of damage mechanics, and then to show the fascinating possibility of this promising branch of mechanics, and to provide researchers, engineers and graduate students with an intelligible and self-contained textbook. The book consists of two parts and an appendix. Part I is concerned with the foundation of continuum damage mechanics. Basic concepts of material damage and the mechanical representation of damage state of various kinds are described in Chapters 1 and 2. In Chapters 3-5, irreversible thermodynamics, thermodynamic constitutive theory and its application to the modeling of the constitutive and the evolution equations of damaged materials are descried as a systematic basis for the subsequent development throughout the book. Part II describes the application of the fundamental theories developed in Part I to typical damage and fracture problems encountered in various fields of the current engineering. Important engineering aspects of elastic-plastic or ductile damage, their damage mechanics modeling and their further refinement are first discussed in Chapter 6. Chapters 7 and 8 are concerned with the modeling of fatigue, creep, creep-fatigue and their engineering application. Damage mechanics modeling of complicated crack closure behavior in elastic-brittle and composite materials are discussed in Chapters 9 and 10. In Chapter 11, applicability of the local approach to fracture by means of damage mechanics and finite element method, and the ensuing mathematical and numerical problems are briefly discussed. A proper understanding of the subject matter requires knowledge of tensor algebra and tensor calculus. At the end of this book, therefore, the foundations of tensor analysis are presented in the Appendix, especially for readers with insufficient mathematical background, but with keen interest in this exciting field of mechanics.

## Tensor Analysis With Applications In Mechanics

**Author :**L. P. Lebedev

**ISBN :**9789814313995

**Genre :**Mathematics

**File Size :**60. 63 MB

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The tensorial nature of a quantity permits us to formulate transformation rules for its components under a change of basis. These rules are relatively simple and easily grasped by any engineering student familiar with matrix operators in linear algebra. More complex problems arise when one considers the tensor fields that describe continuum bodies. In this case general curvilinear coordinates become necessary. The principal basis of a curvilinear system is constructed as a set of vectors tangent to the coordinate lines. Another basis, called the dual basis, is also constructed in a special manner. The existence of these two bases is responsible for the mysterious covariant and contravariant terminology encountered in tensor discussions. A tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. This book is a clear, concise, and self-contained treatment of tensors, tensor fields, and their applications. The book contains practically all the material on tensors needed for applications. It shows how this material is applied in mechanics, covering the foundations of the linear theories of elasticity and elastic shells. The main results are all presented in the first four chapters. The remainder of the book shows how one can apply these results to differential geometry and the study of various types of objects in continuum mechanics such as elastic bodies, plates, and shells. Each chapter of this new edition is supplied with exercises and problems most with solutions, hints, or answers to help the reader progress. An extended appendix serves as a handbook-style summary of all important formulas contained in the book.