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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Irgens, Fridtjov Tensor Analysis Cham : Springer,c2018 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Fridtjov Irgens |

ISBN: | 9783030034122 3030034127 |

OCLC Number: | 1080074438 |

Notes: | Includes index. 6 General Coordinates in Euclidean Space E3 |

Description: | 1 online resource |

Contents: | Intro; Preface; A Short Presentation of the Contents of This Book; References; Contents; Symbols; 1 Mathematical Foundation; 1.1 Matrices and Determinants; 1.2 Cartesian Coordinate Systems. Scalars and Vectors; 1.2.1 Displacement Vectors; 1.2.2 Vector Algebra; 1.3 Cartesian Coordinate Transformations; 1.4 Curves in Space; 1.5 Dynamics of a Mass Particle; 1.6 Scalar Fields and Vector Fields; 2 Dynamics. The Cauchy Stress Tensor; 2.1 Kinematics; 2.1.1 Lagrangian Coordinates and Eulerian Coordinates; 2.1.2 Material Derivative of Intensive Quantities 2.1.3 Material Derivative of Extensive Quantities2.2 Equations of Motion; 2.2.1 Euler's Axioms; 2.2.2 Newton's Third Law of Action and Reaction; 2.2.3 Coordinate Stresses; 2.2.4 Cauchy's Stress Theorem and Cauchy's Stress Tensor; 2.2.5 Cauchy's Equations of Motion; 2.3 Stress Analysis; 2.3.1 Principal Stresses and Principal Stress Directions; 2.3.2 Stress Deviator and Stress Isotrop; 2.3.3 Extreme Values of Normal Stress; 2.3.4 Maximum Shear Stress; 2.3.5 State of Plane Stress; 2.3.6 Mohr-Diagram for State of Plane Stress; Reference; 3 Tensors; 3.1 Definition of Tensors; 3.2 Tensor Algebra 3.2.1 Isotropic Tensors of Fourth Order3.2.2 Tensors as Polyadics; 3.3 Tensors of Second Order; 3.3.1 Symmetric Tensors of Second Order; 3.3.2 Alternative Invariants of Second Order Tensors; 3.3.3 Deviator and Isotrop of Second Order Tensors; 3.4 Tensor Fields; 3.4.1 Gradient, Divergence, and Rotation of Tensor Fields; 3.4.2 Del-Operators; 3.4.3 Directional Derivative of Tensor Fields; 3.4.4 Material Derivative of Tensor Fields; 3.5 Rigid-Body Dynamics. Kinematics; 3.5.1 Pure Rotation About a Fixed Axis; 3.5.2 Pure Rotation About a Fixed Point; 3.5.3 Kinematics of General Rigid-Body Motion 3.6 Rigid-Body Dynamics. Kinetics3.6.1 Rotation About a Fixed Point. The Inertia Tensor; 3.6.2 General Rigid-Body Motion; 3.7 Q-Rotation of Vectors and Tensors of Second Order; 3.8 Polar Decomposition; 3.9 Isotropic Functions of Tensors; References; 4 Deformation Analysis; 4.1 Strain Measures; 4.2 Green's Strain Tensor; 4.3 Small Strains and Small Deformations; 4.3.1 Small Strains; 4.3.2 Small Deformations; 4.3.3 Principal Strains and Principal Directions for Small Deformations; 4.3.4 Strain Deviator and Strain Isotrop for Small Deformations; 4.3.5 Rotation Tensor for Small Deformations 4.3.6 Small Deformations in a Material Surface4.3.7 Mohr-Diagram for Small Deformations in a Surface; 4.4 Rates of Deformation, Strain, and Rotation; 4.5 Large Deformations; 5 Constitutive Equations; 5.1 Introduction; 5.2 Linearly Elastic Materials; 5.2.1 Generalized Hooke's Law; 5.2.2 Some Basic Equations in Linear Elasticity. Navier's Equations; 5.2.3 Stress Waves in Elastic Materials; 5.3 Linearly Viscous Fluids; 5.3.1 Definition of Fluids; 5.3.2 The Continuity Equation; 5.3.3 Constitutive Equations for Linearly Viscous Fluids; 5.3.4 The Navier-Stokes Equations; 5.3.5 Film Flow; References |

Responsibility: | Fridtjov Irgens. |

### Abstract:

This book presents tensors and tensor analysis as primary mathematical tools for engineering and engineering science students and researchers.
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