# 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 :**9783642308796

**Genre :**Technology & Engineering

**File Size :**47. 34 MB

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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 Electronic Resource With Applications To Continuum Mechanics

**Author :**Mikhail Itskov

**ISBN :**9783319988061

**Genre :**

**File Size :**80. 12 MB

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## Tensor Analysis And Continuum Mechanics

**Author :**Y.R. Talpaert

**ISBN :**1402010559

**Genre :**Mathematics

**File Size :**20. 35 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 ..

## Tensor Analysis And Elementary Differential Geometry For Physicists And Engineers

**Author :**Hung Nguyen-Schäfer

**ISBN :**9783662484975

**Genre :**Technology & Engineering

**File Size :**39. 85 MB

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This book presents tensors and differential geometry in a comprehensive and approachable manner, providing a bridge from the place where physics and engineering mathematics end, and the place where tensor analysis begins. Among the topics examined are tensor analysis, elementary differential geometry of moving surfaces, and k-differential forms. The book includes numerous examples with solutions and concrete calculations, which guide readers through these complex topics step by step. Mindful of the practical needs of engineers and physicists, book favors simplicity over a more rigorous, formal approach. The book shows readers how to work with tensors and differential geometry and how to apply them to modeling the physical and engineering world. The authors provide chapter-length treatment of topics at the intersection of advanced mathematics, and physics and engineering: • General Basis and Bra-Ket Notation • Tensor Analysis • Elementary Differential Geometry • Differential Forms • Applications of Tensors and Differential Geometry • Tensors and Bra-Ket Notation in Quantum Mechanics The text reviews methods and applications in computational fluid dynamics; continuum mechanics; electrodynamics in special relativity; cosmology in the Minkowski four-dimensional space time; and relativistic and non-relativistic quantum mechanics. Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers benefits research scientists and practicing engineers in a variety of fields, who use tensor analysis and differential geometry in the context of applied physics, and electrical and mechanical engineering. It will also interest graduate students in applied physics and engineering.

## Foundations Of Elastoplasticity Subloading Surface Model

**Author :**Koichi Hashiguchi

**ISBN :**9783319488219

**Genre :**Science

**File Size :**49. 79 MB

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This book is the standard text book of elastoplasticity in which the elastoplasticity theory is comprehensively described from the conventional theory for the monotonic loading to the unconventional theory for the cyclic loading behavior. Explanations of vector-tensor analysis and continuum mechanics are provided first as a foundation for elastoplasticity theory, covering various strain and stress measures and their rates with their objectivities. Elastoplasticity has been highly developed by the creation and formulation of the subloading surface model which is the unified fundamental law for irreversible mechanical phenomena in solids. The assumption that the interior of the yield surface is an elastic domain is excluded in order to describe the plastic strain rate due to the rate of stress inside the yield surface in this model aiming at the prediction of cyclic loading behavior, although the yield surface enclosing the elastic domain is assumed in all the elastoplastic models other than the subloading surface model. Then, the plastic strain rate develops continuously as the stress approaches the yield surface, providing the advantages: 1) The tangent modulus changes continuously, 2) The yield judgment whether the stress reaches the yield surface is not required, 3) The stress is automatically attracted to the yield surface even when it goes out from the yield surface by large loading increments in numerical calculation and 4) The finite strain theory based on the multiplicative decomposition of deformation gradient tensor is formulated exactly. Consequently, the monotonic, the cyclic, the non-proportional loading behaviors for wide classes of materials including soils, rocks and concretes in addition to metals can be described rigorously by the subloading surface model. Further, the viscoplastic constitutive equations in a general rate from the quasi-static to the impact loadings are described, and constitutive equations of friction behavior and its application to the prediction of stick-slip phenomena, etc. are also described in detail. In addition, the return-mapping algorithm, the consistent tangent modulus, etc. are explained for the numerical analyses. Further, the damage, the phase-transformation and the crystal plasticity models are also described in brief. All of them are based on the subloading surface model. The elastoplasticity analysis will be advanced steadily based on the subloading surface model.

## Continuum Mechanics For Engineers Third Edition

**Author :**G. Thomas Mase

**ISBN :**9781420085396

**Genre :**Science

**File Size :**80. 16 MB

**Format :**PDF, Docs

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Continuum Mechanics for Engineers, Third Edition provides engineering students with a complete, concise, and accessible introduction to advanced engineering mechanics. The impetus for this latest edition was the need to suitably combine the introduction of continuum mechanics, linear and nonlinear elasticity, and viscoelasticity for a graduate-level course sequence. An outgrowth of course notes and problems used to teach these subjects, the third edition of this bestselling text explores the basic concepts behind these topics and demonstrates their application in engineering practice. Presents Material Consistent with Modern Literature A new rearranged and expanded chapter on elasticity more completely covers Saint-Venant’s solutions. Subsections on extension, torsion, pure bending and flexure present an excellent foundation for posing and solving basic elasticity problems. The authors’ presentation enables continuum mechanics to be applied to biological materials, in light of their current importance. They have also altered the book’s notation—a common struggle for many students—to better align it with modern continuum mechanics literature. This book addresses students’ need to understand the sophisticated simulation programs that use nonlinear kinematics and various constitutive relationships. It includes an introduction to problem solution using MATLAB®, emphasizing this language’s value in enabling users to stay focused on fundamentals. This book provides information that is useful in emerging engineering areas, such as micro-mechanics and biomechanics. With an abundance of worked examples and chapter problems, it carefully explains necessary mathematics as required and presents numerous illustrations, giving students and practicing professionals an excellent self-study guide to enhance their skills. Through a mastery of this volume’s contents and additional rigorous finite element training, they will develop the mechanics foundation necessary to skillfully use modern, advanced design tools.

## A Math Primer For Engineers

**Author :**C.W. Cryer

**ISBN :**9781614992998

**Genre :**Medical

**File Size :**89. 61 MB

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Mathematics and engineering are inevitably interrelated, and this interaction will steadily increase as the use of mathematical modelling grows. Although mathematicians and engineers often misunderstand one another, their basic approach is quite similar, as is the historical development of their respective disciplines. The purpose of this Math Primer is to provide a brief introduction to those parts of mathematics which are, or could be, useful in engineering, especially bioengineering. The aim is to summarize the ideas covered in each subject area without going into exhaustive detail. Formulas and equations have not been avoided, but every effort has been made to keep them simple in the hope of persuading readers that they are not only useful but also accessible. The wide range of topics covered includes introductory material such as numbers and sequences, geometry in two and three dimensions, linear algebra, and the calculus. Building on these foundations, linear spaces, tensor analysis and Fourier analysis are introduced. All these concepts are used to solve problems for ordinary and partial differential equations. Illustrative applications are taken from a variety of engineering disciplines, and the choice of a suitable model is considered from the point of view of both the mathematician and the engineer. This book will be of interest to engineers and bioengineers looking for the mathematical means to help further their work, and it will offer readers a glimpse of many ideas which may spark their interest.

## Continuum Damage Mechanics

**Author :**Sumio Murakami

**ISBN :**9789400726659

**Genre :**Technology & Engineering

**File Size :**25. 28 MB

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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.

## Continuum Mechanics

**Author :**Anthony James Merrill Spencer

**ISBN :**0486435946

**Genre :**Science

**File Size :**62. 13 MB

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Undergraduate text opens with introductory chapters on matrix algebra, vectors and Cartesian tensors, and an analysis of deformation and stress; succeeding chapters examine laws of conservation of mass, momentum, and energy as well as the formulation of mechanical constitutive equations. 1992 edition.

## An Introduction To Continuum Mechanics

**Author :**Morton E. Gurtin

**ISBN :**0080918492

**Genre :**Science

**File Size :**76. 4 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