Tensor Algebra and Tensor Analysis for Engineers

With Applications to Continuum Mechanics

Mikhail Itskov (Autor)

Buch | Hardcover

XIX, 300 Seiten

2018 | 5th ed. 2019
Springer International Publishing (Verlag)
978-3-319-98805-4 (ISBN)

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This is the fifth and revised edition of a well-received textbook that aims at bridging the gap between the engineering course of tensor algebra on the one hand and the mathematical course of classical linear algebra on the other hand. In accordance with the contemporary way of scientific publication, 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. As such, this new edition also discusses such modern topics of solid mechanics as electro- and magnetoelasticity. 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 textbook addresses graduate students as well as scientists working in this field and in particular dealing with multi-physical problems. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

Prof. Itskov studied Automobile Engineering at the Moscow State Automobile and Road Technical University, Russia. In 1990 he received his doctoral degree in mechanics, and in 2002 he obtained his habilitation degree in mechanics from the University of Bayreuth, Germany. Since 2004 he has been full professor for continuum mechanics at the RWTH Aachen University, Germany. His research interests comprise tensor analysis, non-linear continuum mechanics, in particular the application to anisotropic materials, as well as the mechanics of elastomers and soft tissues in a broad sense.

Vectors and Tensors in a Finite-Dimensional Space.- Vector and Tensor Analysis in Euclidean Space.- Curves and Surfaces in Three-Dimensional Euclidean Space.- Eigenvalue Problem and Spectral Decomposition of Second-Order Tensors.- Fourth-Order Tensors.- Analysis of Tensor Functions.- Analytic Tensor Functions.- Applications to Continuum Mechanics.

Erscheinungsdatum	29.09.2018
Reihe/Serie	Mathematical Engineering
Zusatzinfo	XIX, 300 p. 20 illus., 13 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	637 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Themenwelt	Technik ► Maschinenbau
Schlagworte	Christoffel Symbols • Coordinate Transformation • Covariant and Contravariant Derivatives • Derivative of the Stretch and Rotation Tensor • Generalized Rivlin's Identities • Generalized Rivlin’s Identities • matrix theory • Polar Decomposition of the Deformation Gradient • Spectral Decomposition of Second-order Tensors • Tensor Algebra • Tensors in Finite-dimensional Space • Tensor-valued Functions
ISBN-10	3-319-98805-0 / 3319988050
ISBN-13	978-3-319-98805-4 / 9783319988054
Zustand	Neuware