Tensor Analysis With Applications In Mechanics

Author : L. P. Lebedev,Michael J. Cloud,Victor A. Eremeyev
Publisher : World Scientific
Page : 378 pages
File Size : 42,8 Mb
Release : 2010
Category : Mathematics
ISBN : 9789814313995

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Tensor Analysis with Applications in Mechanics by L. P. Lebedev,Michael J. Cloud,Victor A. Eremeyev Pdf

1. Preliminaries. 1.1. The vector concept revisited. 1.2. A first look at tensors. 1.3. Assumed background. 1.4. More on the notion of a vector. 1.5. Problems -- 2. Transformations and vectors. 2.1. Change of basis. 2.2. Dual bases. 2.3. Transformation to the reciprocal frame. 2.4. Transformation between general frames. 2.5. Covariant and contravariant components. 2.6. The cross product in index notation. 2.7. Norms on the space of vectors. 2.8. Closing remarks. 2.9. Problems -- 3. Tensors. 3.1. Dyadic quantities and tensors. 3.2. Tensors from an operator viewpoint. 3.3. Dyadic components under transformation. 3.4. More dyadic operations. 3.5. Properties of second-order tensors. 3.6. Eigenvalues and eigenvectors of a second-order symmetric tensor. 3.7. The Cayley-Hamilton theorem. 3.8. Other properties of second-order tensors. 3.9. Extending the Dyad idea. 3.10. Tensors of the fourth and higher orders. 3.11. Functions of tensorial arguments. 3.12. Norms for tensors, and some spaces. 3.13. Differentiation of tensorial functions. 3.14. Problems -- 4. Tensor fields. 4.1. Vector fields. 4.2. Differentials and the nabla operator. 4.3. Differentiation of a vector function. 4.4. Derivatives of the frame vectors. 4.5. Christoffel coefficients and their properties. 4.6. Covariant differentiation. 4.7. Covariant derivative of a second-order tensor. 4.8. Differential operations. 4.9. Orthogonal coordinate systems. 4.10. Some formulas of integration. 4.11. Problems -- 5. Elements of differential geometry. 5.1. Elementary facts from the theory of curves. 5.2. The torsion of a curve. 5.3. Frenet-Serret equations. 5.4. Elements of the theory of surfaces. 5.5. The second fundamental form of a surface. 5.6. Derivation formulas. 5.7. Implicit representation of a curve; contact of curves. 5.8. Osculating paraboloid. 5.9. The principal curvatures of a surface. 5.10. Surfaces of revolution. 5.11. Natural equations of a curve. 5.12. A word about rigor. 5.13. Conclusion. 5.14. Problems -- 6. Linear elasticity. 6.1. Stress tensor. 6.2. Strain tensor. 6.3. Equation of motion. 6.4. Hooke's law. 6.5. Equilibrium equations in displacements. 6.6. Boundary conditions and boundary value problems. 6.7. Equilibrium equations in stresses. 6.8. Uniqueness of solution for the boundary value problems of elasticity. 6.9. Betti's reciprocity theorem. 6.10. Minimum total energy principle. 6.11. Ritz's method. 6.12. Rayleigh's variational principle. 6.13. Plane waves. 6.14. Plane problems of elasticity. 6.15. Problems -- 7. Linear elastic shells. 7.1. Some useful formulas of surface theory. 7.2. Kinematics in a neighborhood of [symbol]. 7.3. Shell equilibrium equations. 7.4. Shell deformation and strains; Kirchhoff's hypotheses. 7.5. Shell energy. 7.6. Boundary conditions. 7.7. A few remarks on the Kirchhoff-Love theory. 7.8. Plate theory. 7.9. On Non-classical theories of plates and shells

Author : Mikhail Itskov
Publisher : Springer
Page : 0 pages
File Size : 47,7 Mb
Release : 2015-04-07
Category : Technology & Engineering
ISBN : 3319163418

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Tensor Algebra and Tensor Analysis for Engineers by Mikhail Itskov Pdf

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.

Author : Michael J Cloud,Victor A Eremeyev,Leonid P Lebedev
Publisher : World Scientific
Page : 428 pages
File Size : 55,6 Mb
Release : 2018-07-10
Category : Technology & Engineering
ISBN : 9789813238985

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Applications Of Tensor Analysis In Continuum Mechanics by Michael J Cloud,Victor A Eremeyev,Leonid P Lebedev Pdf

'A strong point of this book is its coverage of tensor theory, which is herein deemed both more readable and more substantial than many other historic continuum mechanics books. The book is self-contained. It serves admirably as a reference resource on fundamental principles and equations of tensor mathematics applied to continuum mechanics. Exercises and problem sets are useful for teaching … The book is highly recommended as both a graduate textbook and a reference work for students and more senior researchers involved in theoretical and mathematical modelling of continuum mechanics of materials. Key concepts are well described in the text and are supplemented by informative exercises and problem sets with solutions, and comprehensive Appendices provide important equations for ease of reference.'Contemporary PhysicsA 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. 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.This book provides a clear, concise, and self-contained treatment of tensors and tensor fields. It covers the foundations of linear elasticity, shell theory, and generalized continuum media, offers hints, answers, and full solutions for many of the problems and exercises, and Includes a handbook-style summary of important tensor formulas.The book can be useful for beginners who are interested in the basics of tensor calculus. It also can be used by experienced readers who seek a comprehensive review on applications of the tensor calculus in mechanics.

Author : Aleksandr Ivanovich Borisenko,Ivan Evgen?evich Tarapov
Publisher : Courier Corporation
Page : 292 pages
File Size : 54,7 Mb
Release : 1968-01-01
Category : Mathematics
ISBN : 0486638332

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Vector and Tensor Analysis with Applications by Aleksandr Ivanovich Borisenko,Ivan Evgen?evich Tarapov Pdf

Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 46,7 Mb
Release : 2024-05-12
Category : Electronic
ISBN : 9789814464505

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Tensor Analysis with Applications in Mechanics by Anonim Pdf

Author : Mikhail Itskov
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 47,8 Mb
Release : 2009-04-30
Category : Technology & Engineering
ISBN : 9783540939078

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Tensor Algebra and Tensor Analysis for Engineers by Mikhail Itskov Pdf

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.

Author : Ivan Stephen Sokolnikoff
Publisher : Unknown
Page : 0 pages
File Size : 45,6 Mb
Release : 1951
Category : Electronic
ISBN : OCLC:253723474

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Tensor Analysis by Ivan Stephen Sokolnikoff Pdf

Author : John G. Papastavridis
Publisher : Routledge
Page : 435 pages
File Size : 41,6 Mb
Release : 2018-12-12
Category : Mathematics
ISBN : 9781351411622

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Tensor Calculus and Analytical Dynamics by John G. Papastavridis Pdf

Tensor Calculus and Analytical Dynamics provides a concise, comprehensive, and readable introduction to classical tensor calculus - in both holonomic and nonholonomic coordinates - as well as to its principal applications to the Lagrangean dynamics of discrete systems under positional or velocity constraints. The thrust of the book focuses on formal structure and basic geometrical/physical ideas underlying most general equations of motion of mechanical systems under linear velocity constraints. Written for the theoretically minded engineer, Tensor Calculus and Analytical Dynamics contains uniquely accessbile treatments of such intricate topics as: tensor calculus in nonholonomic variables Pfaffian nonholonomic constraints related integrability theory of Frobenius The book enables readers to move quickly and confidently in any particular geometry-based area of theoretical or applied mechanics in either classical or modern form.

Author : A. J. McConnell
Publisher : Courier Corporation
Page : 353 pages
File Size : 53,6 Mb
Release : 1957-01-01
Category : Mathematics
ISBN : 9780486603735

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Applications of Tensor Analysis by A. J. McConnell Pdf

Standard work applies tensorial methods to subjects within realm of advanced college mathematics. Text explains fundamental ideas and notation of tensor theory; covers geometrical treatment of tensor algebra; introduces theory of differentiation of tensors; and applies mathematics to dynamics, electricity, elasticity and hydrodynamics. 685 exercises, most with answers.

Author : I. S. Sokolnikoff
Publisher : Unknown
Page : 128 pages
File Size : 46,6 Mb
Release : 1951
Category : Electronic
ISBN : OCLC:729241083

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Tensor Analysis by I. S. Sokolnikoff Pdf

Author : Zafar Ahsan
Publisher : Anshan Pub
Page : 0 pages
File Size : 52,7 Mb
Release : 2008
Category : Calculus of tensors
ISBN : 1905740867

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Tensor Analysis with Applications by Zafar Ahsan Pdf

The principal aim of tensor analysis is to investigate the relations which remain valid when we change from one coordinate system to another. Albert Einstein found it to be an excellent tool for the presentation of his general theory of relativity and consequently tensor analysis came to prominence in mathematics. It has applications in most branches of theoretical physics and engineering. This present book is intended as a text for postgraduate students of mathematics, physics and engineering. It is self-contained and requires prior knowledge of elementary calculus, differential equations and classical mechanics. It consists of five chapters, each containing a large number of solved examples, unsolved problems and links to the solution of these problems. "Tensor Analysis with Applications" can be used on a selection of university courses, and will be a welcome addition to the library of maths, physics and engineering departments.

Author : A. I. Borisenko,I. E. Tarapov
Publisher : Courier Corporation
Page : 288 pages
File Size : 40,8 Mb
Release : 2012-08-28
Category : Mathematics
ISBN : 9780486131900

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Vector and Tensor Analysis with Applications by A. I. Borisenko,I. E. Tarapov Pdf

Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.

Author : Ivan Stephen Sokolnikoff
Publisher : Unknown
Page : 128 pages
File Size : 53,5 Mb
Release : 1983
Category : Calculus of tensors
ISBN : OCLC:1090659422

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Tensor Analysis by Ivan Stephen Sokolnikoff Pdf

Author : Goldberg Vladislav V,Akivis Maks A
Publisher : World Scientific Publishing Company
Page : 380 pages
File Size : 45,7 Mb
Release : 2003-09-29
Category : Science
ISBN : 9789813102255

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Tensor Calculus With Applications by Goldberg Vladislav V,Akivis Maks A Pdf

This textbook presents the foundations of tensor calculus and the elements of tensor analysis. In addition, the authors consider numerous applications of tensors to geometry, mechanics and physics.While developing tensor calculus, the authors emphasize its relationship with linear algebra. Necessary notions and theorems of linear algebra are introduced and proved in connection with the construction of the apparatus of tensor calculus; prior knowledge is not assumed. For simplicity and to enable the reader to visualize concepts more clearly, all exposition is conducted in three-dimensional space. The principal feature of the book is that the authors use mainly orthogonal tensors, since such tensors are important in applications to physics and engineering.With regard to applications, the authors construct the general theory of second-degree surfaces, study the inertia tensor as well as the stress and strain tensors, and consider some problems of crystallophysics. The last chapter introduces the elements of tensor analysis.All notions introduced in the book, and also the obtained results, are illustrated with numerous examples discussed in the text. Each section of the book presents problems (a total over 300 problems are given). Examples and problems are intended to illustrate, reinforce and deepen the presented material. There are answers to most of the problems, as well as hints and solutions to selected problems at the end of the book.

Author : Mikhail Itskov
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 54,5 Mb
Release : 2012-08-13
Category : Science
ISBN : 9783642308796

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Tensor Algebra and Tensor Analysis for Engineers by Mikhail Itskov Pdf

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.