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## Details

Genre/Form: | Electronic resource |
---|---|

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Temam, Roger.; Alain Miranville |

OCLC Number: | 741249627 |

Description: | 1 online resource (342) |

Contents: | Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- A few words about notations -- PART I FUNDAMENTAL CONCEPTS IN CONTINUUM MECHANICS -- CHAPTER ONE Describing the motion of a system: geometry and kinematics -- 1.1. Deformations -- 1.2. Motion and its observation (kinematics) -- 1.3. Description of the motion of a system: Eulerian and Lagrangian derivatives -- 1.4. Velocity field of a rigid body: helicoidal vector fields -- 1.5. Differentiation of a volume integral depending on a parameter -- CHAPTER TWO The fundamental law of dynamics -- 2.1. The concept ofmass -- 2.2. Forces -- 2.3. The fundamental law of dynamics and its first consequences -- 2.4. Application to systems ofmaterial points and to rigid bodies -- 2.5. Galilean frames: the fundamental law of dynamics expressed in a non-Galilean frame -- CHAPTER THREE The Cauchy stress tensor and the Piola-Kirchhoff tensor. Applications -- 3.1. Hypotheses on the cohesion forces -- 3.2. The Cauchy stress tensor -- 3.3. General equations ofmotion -- 3.4. Symmetry of the stress tensor -- 3.5. The Piola-Kirchhoff tensor -- CHAPTER FOUR Real and virtual powers -- 4.1. Study of a system of material points -- 4.2. General material systems: rigidifying velocities -- 4.3. Virtual power of the cohesion forces: the general case -- 4.4. Real power: the kinetic energy theorem -- CHAPTER FIVE Deformation tensor, deformation rate tensor, constitutive laws -- 5.1. Further properties of deformations -- 5.2. The deformation rate tensor -- 5.3. Introduction to rheology: the constitutive laws -- 5.4. Appendix. Change of variable in a surface integral -- CHAPTER SIX Energy equations and shock equations -- 6.1. Heat and energy -- 6.2. Shocks and the RankineHugoniot relations -- PART II PHYSICS OF FLUIDS -- CHAPTER SEVEN General properties of Newtonian fluids -- 7.1. General equations of fluids mechanics -- 7.2. Statics of fluids -- 7.3. Remark on the energy of a fluids -- CHAPTER EIGHT Flows of inviscid fluids -- 8.1. General theorems -- 8.2. Plane irrotational flows -- 8.3. Transsonic flows -- 8.4. Linear accoustics -- CHAPTER NINE Viscous fluids and thermohydraulics -- 9.1. Equations ofviscous incompressible fluids -- 9.2. Simple flows of viscous incompressible fluids -- 9.3. Thermohydraulics -- 9.4. Equations in nondimensional form: similarities -- 9.5. Notions of stability and turbulence -- 9.6. Notion of boundary layer -- CHAPTER TEN Magnetohydrodynamics and inertial conflnement of plasmas -- 10.1. The Maxwell equations and electromagnetism -- 10.2. Magnetohydrodynamics -- 10.3. The Tokamak machine -- CHAPTER ELEVEN Combustion -- 11.1. Equations for mixtures of fluids -- 11.2. Equations ofchemical kinetics -- 11.3. The equations of combustion -- 11.4. StefanMaxwell equations -- 11.5. A simplifed problem: the two-species model -- CHAPTER TWELVE Equations of the atmosphere and of the ocean -- 12.1. Preliminaries -- 12.2. Primitive equations of the atmosphere -- 12.3. Primitive equations of the ocean -- 12.4. Chemistry of the atmosphere and the ocean -- Appendix. The differential operators in spherical coordinates -- PART III SOLID MECHANICS -- CHAPTER THIRTEEN The general equations of linear elasticity -- 13.1. Back to the stressstrain law oflinear elasticity: the elasticity coefficients of a material -- 13.2. Boundary value problems in linear elasticity: the li. |

### Abstract:

Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.

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