E-Book, Englisch, 236 Seiten
Altman / Oliveira Physical Components of Tensors
1. Auflage 2014
ISBN: 978-1-4822-6383-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
E-Book, Englisch, 236 Seiten
ISBN: 978-1-4822-6383-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
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.
Zielgruppe
Researchers and engineers working in engineering mechanics, professors and graduate students in mechanical, aerospace, automotive, civil engineering; and engineering mechanics/engineering science, and applied mathematicians working in the area of engineering analysis.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Finite-Dimensional Vector Spaces
Vector spaces and subspaces
Basis of a vector space
Inner products, norms, and metrics
Contravariant and covariant components
Coordinate systems
Change of coordinate systems
Exercises
Vector and Tensor Algebras
Vector Algebra
Tensor Algebra
Exercises
Tensor Calculus
Tensor fields
Integral theorems for scalar and vector fields
Exercises
Physical and Anholonomic Components of Tensors
Physical and anholonomic components of vectors
Physical and anholomic components of tensors
Coordinate transformations of physical components of tensors
Examples of transformation of coordinates for physical components
Anholonomic connections
Strain tensor
Dimensional analysis for tensors
Exercises
Deformation of Continuous Media
Stress tensor and equations of motion
Strain-displacement relations for elastic bodies
Characterization of thin shells
Strain-displacement relations for shells
Kinematic relations for shells
Equations of motion for shells
Constitutive equations for thermoelastic shells
Bibliography
Index