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Cartesian Tensors In Engineering Science

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Cartesian Tensors In Engineering Science

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Author : L. G. Jaeger
language : en
Publisher: Elsevier
Release Date : 2015-09-03

Cartesian Tensors In Engineering Science written by L. G. Jaeger and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-03 with Technology & Engineering categories.

Cartesian Tensors in Engineering Science provides a comprehensive discussion of Cartesian tensors. The engineer, when working in three dimensions, often comes across quantities which have nine components. Variation of the components in a given plane may be shown graphically by a familiar construction called Mohr's circle. For such quantities it is always possible to find three mutually perpendicular axes, called principal axes, with respect to which the six ""paired up"" components are all zero. Such quantities are called symmetric tensors of the second order. The student may at this stage be struck by the fact that the physical quantities with which he normally deals have either one component, three components or nine components, being respectively scalars, vectors, and what have just been called second order tensors. The family of quantities having 1, 3, 9, 27, ... components does exist. It is the tensor family in three dimensions. The book discusses the ""tests"" a given quantity must pass in order to qualify as a member of the family. The products of tensors, elasticity, and second moment of area and moment of inertia are also covered. Although written primarily for engineers, it is hoped that students of various branches of physical science may find this book useful.

Cartesian Tensors In Engineering Science

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Author : L. G. Jaeger
language : en
Publisher: Elsevier
Release Date : 2016-06-06

Cartesian Tensors

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Author : George Frederick James Temple
language : en
Publisher: Courier Corporation
Release Date : 2004-09-01

Cartesian Tensors written by George Frederick James Temple and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-01 with Mathematics categories.

An introduction to the theory of Cartesian tensors, this text notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. Covers isotropic tensors and spinor analysis within the confines of Euclidean space; and tensors in orthogonal curvilinear coordinates. Examples. 1960 edition.

Cartesian Tensors In Engineering Science

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Author : Leslie Gordon JAEGER
language : en
Publisher: Pergamon
Release Date : 1966-01

Cartesian Tensors In Engineering Science written by Leslie Gordon JAEGER and has been published by Pergamon this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966-01 with categories.

Tensors For Physics

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Author : Siegfried Hess
language : en
Publisher: Springer
Release Date : 2015-04-25

Tensors For Physics written by Siegfried Hess and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-25 with Science categories.

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.

Tensor Calculus For Engineers And Physicists

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Author : Emil de Souza Sánchez Filho
language : en
Publisher: Springer
Release Date : 2016-05-20

Tensor Calculus For Engineers And Physicists written by Emil de Souza Sánchez Filho and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-20 with Technology & Engineering categories.

This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of n-dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without needing to resort to other bibliographical sources on tensors. Chapter 1 deals with Fundamental Concepts about tensors and chapter 2 is devoted to the study of covariant, absolute and contravariant derivatives. The chapters 3 and 4 are dedicated to the Integral Theorems and Differential Operators, respectively. Chapter 5 deals with Riemann Spaces, and finally the chapter 6 presents a concise study of the Parallelism of Vectors. It also shows how to solve various problems of several particular manifolds.

Guide To The Literature Of Engineering Mathematics And The Physical Sciences

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Author : Sylvia Weiser
language : en
Publisher:
Release Date : 1972

Guide To The Literature Of Engineering Mathematics And The Physical Sciences written by Sylvia Weiser and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Engineering categories.

The Mechanical Behaviour Of Engineering Materials

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Author : W. D. Biggs
language : en
Publisher: Elsevier
Release Date : 2013-10-22

The Mechanical Behaviour Of Engineering Materials written by W. D. Biggs and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Technology & Engineering categories.

The Mechanical Behaviour of Engineering Materials aims to relate properties and structure, and to provide a theoretical basis upon which to extrapolate when conditions or materials outside previous experience arise. The present text refers primarily to metals and alloys, other (non-crystalline) solids are treated rather less fully. This is largely dictated by the state of knowledge at the present time, for although there is a large mass of data concerning the properties of non-metallic materials, much of this is empirical and a full explanation is made difficult by the complexities of an irregular initial structure. The book can be divided into the three sections covering constitution, properties, and significance of test data. Separate chapters discuss properties such as heterogeneity, elasticity, plasticity, and fracture. Subsequent chapters deal with tensile and hardness tests; creep, fatigue and impact tests; and the selection of engineering materials. Throughout the text the author has endeavored to confine the discussion to those aspects of materials science which appear to be reasonably well understood at the present time.

Tensor Analysis With Applications In Mechanics

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Author : L. P. Lebedev
language : en
Publisher: World Scientific
Release Date : 2010

Tensor Analysis With Applications In Mechanics written by L. P. Lebedev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

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

Iaeng Transactions On Engineering Sciences

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Author : Sio-Iong Ao
language : en
Publisher: CRC Press
Release Date : 2014-04-07

Iaeng Transactions On Engineering Sciences written by Sio-Iong Ao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-07 with Computers categories.

Two large international conferences on Advances in Engineering Sciences were held in Hong Kong, March 13-15, 2013, under the International MultiConference of Engineers and Computer Scientists (IMECS 2013), and in London, U.K., 3-5 July, 2013, under the World Congress on Engineering 2013 (WCE 2013) respectively. IMECS 2013 and WCE 2013 were organize

Cartesian Tensors In Engineering Science

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