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Physical Components of Tensors [Kõva köide]

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(Instituto Tecnologico de Aeronautica, Brazil), (Instituto Tecnologico de Aeronautica, Brazil)
  • Formaat: Hardback, 236 pages, kõrgus x laius: 234x156 mm, kaal: 476 g, 1 Tables, black and white; 8 Illustrations, black and white
  • Sari: Applied and Computational Mechanics
  • Ilmumisaeg: 11-Nov-2014
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1482263823
  • ISBN-13: 9781482263824
Teised raamatud teemal:
Physical Components of TensorsSuurem pilt
  • Formaat: Hardback, 236 pages, kõrgus x laius: 234x156 mm, kaal: 476 g, 1 Tables, black and white; 8 Illustrations, black and white
  • Sari: Applied and Computational Mechanics
  • Ilmumisaeg: 11-Nov-2014
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1482263823
  • ISBN-13: 9781482263824
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781482263824.html
Märksõnad:
Illustrating the important aspects of tensor calculus, and highlighting its most practical features, Physical Components of Tensors presents an authoritative and complete explanation of tensor calculus that is based on transformations of bases of vector spaces rather than on transformations of coordinates. Written with graduate students, professors, and researchers in the areas of elasticity and shell theories in mind, this text focuses on the physical and nonholonomic components of tensors and applies them to the theories. It establishes a theory of physical and anholonomic components of tensors and applies the theory of dimensional analysis to tensors and (anholonomic) connections. This theory shows the relationship and compatibility among several existing definitions of physical components of tensors when referred to nonorthogonal coordinates. The book assumes a basic knowledge of linear algebra and elementary calculus, but revisits these subjects and introduces the mathematical backgrounds for the theory in the first three chapters. In addition, all field equations are also given in physical components as well.

Comprised of five chapters, this noteworthy text:





Deals with the basic concepts of linear algebra, introducing the vector spaces and the further structures imposed on them by the notions of inner products, norms, and metrics Focuses on the main algebraic operations for vectors and tensors and also on the notions of duality, tensor products, and component representation of tensors Presents the classical tensor calculus that functions as the advanced prerequisite for the development of subsequent chapters Provides the theory of physical and anholonomic components of tensors by associating them to the spaces of linear transformations and of tensor products and advances two applications of this theory















Physical Components of Tensors

contains a comprehensive account of tensor calculus, and is an essential reference for graduate students or engineers concerned with solid and structural mechanics.

Arvustused

"This book provides a clear explanation of the mathematical properties of tensors, from a physical perspective. The book is rigorous and concise, yet easy to read and very accessible. The reader will enjoy the wide variety of examples and exercises with solution, which make the book very pedagogical. I believe this can be a very useful book for anyone interested in learning about the mathematics of tensors, no matter the field of study or research. I would definitely like to have this book on my shelf, and use it as a reference in my own lectures." Román Orús, Institut für Physik, Johannes Gutenberg-Universität

Foreword xi
J. N. Reddy
Preface xiii
Biographies of the Authors xix
List of Symbols
xxi
1 Finite-Dimensional Vector Spaces
1(26)
1.1 Vector spaces and subspaces
1(6)
1.2 Basis of a vector space
7(2)
1.3 Inner products, norms, and metrics
9(6)
1.4 Contra-variant and covariant components
15(2)
1.5 Coordinate systems
17(2)
1.6 Change of coordinate systems
19(4)
1.7 Exercises
23(4)
2 Vector and Tensor Algebras
27(34)
2.1 Vector algebra
27(7)
2.2 Tensor algebra
34(24)
2.2.1 Dual spaces
34(8)
2.2.2 Duality and inner product
42(4)
2.2.3 Tensors
46(3)
2.2.4 Tensor product
49(4)
2.2.5 Transformation of tensor components due to change of bases
53(2)
2.2.6 Change of bases for tensors
55(1)
2.2.7 Algebraic operations for components of tensors
56(2)
2.3 Exercises
58(3)
3 Tensor Calculus
61(30)
3.1 Tensor fields
61(20)
3.1.1 Gradient of a field
61(3)
3.1.2 Chain rule and product rule
64(2)
3.1.3 Other differential operators
66(1)
3.1.4 Gradient of a field in curvilinear coordinates
67(2)
3.1.5 Christoffel symbols and covariant differentiation of vectors
69(2)
3.1.6 Metric tensors and Christoffel symbols
71(2)
3.1.7 Other differential operators in curvilinear coordinates
73(7)
3.1.8 Riemann--Christoffel tensor
80(1)
3.2 Integral theorems for scalar and vector fields
81(2)
3.3 Exercises
83(8)
4 Physical and Anholonomic Components of Tensors
91(60)
4.1 Physical and anholonomic components of vectors
92(15)
4.2 Physical and anholomic components of tensors
107(5)
4.3 Coordinate transformations of physical components of tensors
112(2)
4.4 Examples of transformation of coordinates for physical components
114(9)
4.4.1 Transformation of covariant components
117(1)
4.4.2 Transformation of second-order tensors
117(4)
4.4.3 Transformation of mixed components
121(1)
4.4.4 Raising and lowering indices
122(1)
4.5 Anholonomic connections
123(10)
4.5.1 Frames and matrices of connections
123(3)
4.5.2 More on Christoffel symbols
126(4)
4.5.3 Anholonomic covariant derivatives of tensors
130(3)
4.6 Strain tensor
133(1)
4.7 Dimensional analysis for tensors
134(12)
4.7.1 Expressions in terms of physical components
141(5)
4.8 Exercises
146(5)
5 Deformation of Continuous Media
151(56)
5.1 Stress tensor and equations of motion
152(14)
5.1.1 Equations of motion referred to two reference frames
160(4)
5.1.2 Equations of motion referred to convected coordinates
164(2)
5.2 Strain-displacement relations for elastic bodies
166(3)
5.3 Characterization of thin shells
169(7)
5.4 Strain-displacement relations for shells
176(5)
5.5 Kinematic relations for shells
181(8)
5.5.1 Linearized kinematics
186(3)
5.6 Equations of motion for shells
189(10)
5.6.1 Linearized equations of motion
194(5)
5.7 Constitutive equations for thermoelastic shells
199(8)
5.7.1 Linear constitutive equations
203(4)
Bibliography 207(4)
Index 211
Wolf Altman obtained his Ph.D. from Stanford University in 1966. His dissertation was published in the Journal of IABSE and became a classic. Professor Altman is an engineering educator and researcher with experience as a consultant in structural mechanics in general and in the City Hall of Sao Caetano do Sul. His research endeavors, which include over 60 articles in international journals, have been mainly on weak variational formulations, including the effects of conservative and nonconservative loads on beams, plates and shells, and on physical and nonholonomic components of tensors with application to the theory of elasticity and shells.







Antonio Marmo De Oliveira

earned his doctorate at the Instituto Tecnologico de Aeronautica in 1977. He was full professor at Instituto Tecnologico de Aeronautica and University of Taubate until his retirement. He performed research in the broad fields of mechanics, applied mathematics, and engineering science, and he has published nine books and over 50 articles in journals and magazines and 300 chronicles in Taubate's newspapers. He was awarded the 1966 Esso Prize of Sciences and some commendations in Taubate city, where he was the head of the university during 2000-2002. He currently works as a consultant for reinforced industrial plastics.