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Applications Of Tensor Analysis In Continuum Mechanics

Released on 2018-07-10
Applications Of Tensor Analysis In Continuum Mechanics

Author: Michael J Cloud

Publisher: World Scientific

ISBN: 9789813238985

Category: Technology & Engineering

Page: 428

View: 851

'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.

Tensor Analysis with Applications in Mechanics

Released on 2010
Tensor Analysis with Applications in Mechanics

Author: L. P. Lebedev

Publisher: World Scientific

ISBN: 9789814313995

Category: Mathematics

Page: 380

View: 547

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.

Applications of Tensor Analysis

Released on 2014-06-10
Applications of Tensor Analysis

Author: A. J. McConnell

Publisher: Courier Corporation

ISBN: 9780486145020

Category: Mathematics

Page: 352

View: 641

DIVTensor theory, applications to dynamics, electricity, elasticity, hydrodynamics, etc. Level is advanced undergraduate. Over 500 solved problems. /div

Vector and Tensor Analysis with Applications

Released on 2012-08-28
Vector and Tensor Analysis with Applications

Author: A. I. Borisenko

Publisher: Courier Corporation

ISBN: 9780486131900

Category: Mathematics

Page: 288

View: 126

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.

Principles & Applications of Tensor Analysis

Released on 1963
Principles & Applications of Tensor Analysis

Author: Matthew S. Smith

Publisher:

ISBN: STANFORD:36105127827157

Category: Calculus of tensors

Page: 128

View: 634

Tensor Analysis and Its Applications

Released on 2015-08-27
Tensor Analysis and Its Applications

Author: Quddus Khan

Publisher: Partridge Publishing

ISBN: 9781482850680

Category: Mathematics

Page: 260

View: 212

This book is intended to serve as a textbook for undergraduate and postgraduate students of mathematics. It will be useful to the researchers working in the field of differential geometry and its applications to general theory of relativity and other applied areas. It will also be helpful in preparing for the competitive examinations like IAS, IES, NET, PCS, and other higher education tests. The text starts with the basic concepts and results, which shall refer throughout this book and is followed by the study of the tensor algebra and its calculus, consisting the notion of tensor, its operations, and its different types; Christoffels symbols and its properties, the concept of covariant differentiation of tensors and its properties, tensor form of gradient, divergence, laplacian and curl, divergence of a tensor, intrinsic derivatives, and parallel displacement of vectors, Riemanns symbols and its properties, and application of tensor in different areas.

Tensor Calculus with Applications

Released on 2003
Tensor Calculus with Applications

Author: Maks A?zikovich Akivis

Publisher: World Scientific

ISBN: 9812385061

Category: Mathematics

Page: 367

View: 307

This textbook presents the foundations of tensor calculus and the elements of tensor analysis, in addition to considering 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. 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 textbook presents the foundations of tensor calculus and the elements of tensor analysis, in addition to considering 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, sincesuch tensors are important in applications to physics and engineering. 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 p

Advances on Tensor Analysis and their Applications

Released on 2020-09-09
Advances on Tensor Analysis and their Applications

Author: Francisco Bulnes

Publisher: BoD – Books on Demand

ISBN: 9781839625558

Category: Mathematics

Page: 140

View: 835

This book brings together recent advances in tensor analysis and studies of its invariants such as twistors, spinors, kinematic tensors and others belonging to tensor algebras with extended structures to Lie algebras, Kac-Moody algebras, and enveloping algebras, among others. Chapters cover such topics as classical tensors and bilinear forms, tensors for exploring space–time, tensor applications in geometry and continuum media, and advanced topics in tensor analysis such as invariant theory, derived categories, hypercohomologies, k-modules, extensions of kinematic tensors, infinite dimensional operators, and more.

Vector and Tensor Analysis with Applications

Released on 1968-01-01
Vector and Tensor Analysis with Applications

Author: Aleksandr Ivanovich Borisenko

Publisher: Courier Corporation

ISBN: 0486638332

Category: Mathematics

Page: 257

View: 151

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.

Tensor Analysis for Engineers and Physicists - With Application to Continuum Mechanics, Turbulence, and Einstein’s Special and General Theory of Relativity

Released on
Tensor Analysis for Engineers and Physicists - With Application to Continuum Mechanics, Turbulence, and Einstein’s Special and General Theory of Relativity

Author: Meinhard T. Schobeiri

Publisher: Springer Nature

ISBN: 9783030357368

Category:

Page:

View: 532

TEXTBOOK OF TENSOR CALCULUS AND DIFFERENTIAL GEOMETRY AND THEIR APPLICATIONS

Released on 2020-12-29
TEXTBOOK OF TENSOR CALCULUS AND DIFFERENTIAL GEOMETRY AND THEIR APPLICATIONS

Author: Quddus Khan

Publisher: Misha Books

ISBN: 9789389055320

Category: Mathematics

Page: 578

View: 281

This book is intended to serve as a Textbook for Undergraduate and Post - graduate students of Mathematics. It will be useful to the researchers working in the field of Differential geometry and its applications to general theory of relativity and other applied areas. It will also be helpful in preparing for the competitive examinations like IAS, IES, NET, PCS, and UP Higher Education exams. The text starts with a chapter on Preliminaries discussing basic concepts and results which would be taken for general later in the subsequent chapters of this book. This is followed by the Study of the Tensors Algebra and its operations and types, Christoffel's symbols and its properties, the concept of covariant differentiation and its properties, Riemann's symbols and its properties, and application of tensor in different areas in part – I and the study of the Theory of Curves in Space, Concepts of a Surface and Fundamental forms, Envelopes and Developables, Curvature of Surface and Lines of Curvature, Fundamental Equations of Surface Theory, Theory of Geodesics, Differentiable Manifolds and Riemannian Manifold and Application of Differential Geometry in Part –II. KEY FEATURES: Provides basic Concepts in an easy to understand style; Presentation of the subject in a natural way; Includes a large number of solved examples and illuminating illustrations; Exercise questions at the end of the topic and at the end of each chapter; Proof of the theorems are given in an easy to understand style; Neat and clean figures are given at appropriate places; Notes and remarks are given at appropriate places.

Tensor Algebra and Tensor Analysis for Engineers

Released on 2009-04-30
Tensor Algebra and Tensor Analysis for Engineers

Author: Mikhail Itskov

Publisher: Springer Science & Business Media

ISBN: 9783540939078

Category: Technology & Engineering

Page: 247

View: 674

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.

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