Tensor Algebra and Tensor Analysis for Engineers: With Applications to Continuum MechanicsSpringer Science & Business Media, 30 avr. 2009 - 247 pages This second edition is completed by a number of additional examples and exercises. In response of comments and questions of students using this book, solutions of many exercises have been improved for a better understanding. Some changes and enhancements are concerned with the treatment of sk- symmetric and rotation tensors in the ?rst chapter. Besides, the text and formulae have thoroughly been reexamined and improved where necessary. Aachen, January 2009 Mikhail Itskov Preface to the First Edition Like many other textbooks the present one is based on a lecture course given by the author for master students of the RWTH Aachen University. In spite of a somewhat di?cult matter those students were able to endure and, as far as I know, are still ?ne. I wish the same for the reader of the book. Although the present book can be referred to as a textbook one ?nds only little plain text inside. I tried to explain the matter in a brief way, nevert- lessgoinginto detailwherenecessary.Ialsoavoidedtediousintroductions and lengthy remarks about the signi?cance of one topic or another. A reader - terested in tensor algebra and tensor analysis but preferring, however, words instead of equations can close this book immediately after having read the preface. |
Table des matières
2 | 26 |
Vector and TensorValued Functions Differential Calculus | 35 |
Curves and Surfaces in ThreeDimensional Euclidean Space | 59 |
Exercises | 79 |
པ | 99 |
Exercises | 111 |
7 | 143 |
8 | 165 |
Solutions 185 | 184 |
References | 239 |
Autres éditions - Tout afficher
Tensor Algebra and Tensor Analysis for Engineers: With Applications to ... Mikhail Itskov Aucun aperçu disponible - 2010 |
Tensor Algebra and Tensor Analysis for Engineers: With Applications to ... Mikhail Itskov Aucun aperçu disponible - 2009 |
Expressions et termes fréquents
A₁ analytic tensor functions arbitrary Cauchy stress Christoffel symbols coefficients components continuum mechanics coordinate lines covariant derivative curvature curve defined denotes dt dt eigenprojections eigenvalues Euclidean space Example Exercise expressed fourth-order tensors further obtain gradient identity tensor Inserting isotropic isotropic functions isotropic tensor function linear combinations linearly independent Linn mapping normal sections Orth orthogonal tensor orthonormal basis polynomial principal invariants Prove QAQT r+sa relation represent representation respect result right eigenvector rotation tensor scalar product scalar-valued second-order tensor shear simple shear sin² skew-symmetric spectral decomposition strain energy function super-symmetric symmetric tensor tangent vectors tensor product tensor-valued function Theorem three-dimensional space vector space virtue yields zero