UID:
almahu_9947366456002882
Format:
1 online resource (279 p.)
ISBN:
1-282-03469-3
,
9786612034695
,
0-08-091849-2
Series Statement:
Mathematics in science and engineering ; v. 158
Content:
This book presents an introduction to the classical theories of continuum mechanics; in particular, to the theories of ideal, compressible, and viscous fluids, and to the linear and nonlinear theories of elasticity. These theories are important, not only because they are applicable to a majority of the problems in continuum mechanics arising in practice, but because they form a solid base upon which one can readily construct more complex theories of material behavior. Further, although attention is limited to the classical theories, the treatment is modern with a major emphasis on foundations
Note:
Includes index.
,
Front Cover; An Introduction to Continuum Mechanics; Copyright Page; Contents; Preface; Acknowledgments; Chapter I. Tensor Algebra; 1. Points. Vectors. Tensors; 2. Spectral Theorem. Cayley-Hamilton Theorem. Polar Decomposition Theorem; Selected References; Chapter II. Tensor Analysis; 3. Differentiation; 4. Gradient. Divergence. Curl; 5. The Divergence Theorem. Stokes' Theorem; Selected References; Chapter III. Kinematics; 6. Bodies. Deformations. Strain; 7. Small Deformations; 8. Motions; 9. Types of Motions. Spin. Rate of Stretching; 10. Transport Theorems. Volume. Isochoric Motions
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11. Spin. Circulation. VorticitySelected References; Chapter IV. Mass. Momentum; 12. Conservation of Mass; 13. Linear and Angular Momentum. Center of Mass; Selected Reference; Chapter V. Force; 14. Force. Stress. Balance of Momentum; 15. Consequences of Momentum Balance; Selected References; Chapter VI. Constitutive Assumptions. Inviscid Fluids; 16. Constitutive Assumptions; 17. Ideal Fluids; 18. Steady, Plane, Irrotational Flow of an Ideal Fluid; 19. Elastic Fluids; Selected References; Chapter VII. Change in Observer. Invariance of Material Response; 20. Change in Observer
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21. Invariance under a Change in ObserverSelected References; Chapter VIII. Newtonian Fluids. The Navier-Stokes Equations; 22. Newtonian Fluids; 23. Some Simple Solutions for Plane Steady Flow; 24. Uniqueness and Stability; Selected References; Chapter IX. Finite Elasticity; 25. Elastic Bodies; 26. Simple Shear of a Homogeneous and Isotropic Elastic Body; 27. The Piola-Kirchhoff Stress; 28. Hyperelastic Bodies; 29. The Elasticity Tensor; Selected References; Chapter X. Linear Elasticity; 30. Derivation of the Linear Theory; 31. Some Simple Solutions; 32. Linear Elastostatics
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33. Bending and Torsion34. Linear Elastodynamics; 35. Progressive Waves; Selected References; Appendix; 36. The Exponential Function; 37. Isotropic Functions; 38. General Scheme of Notation; References; Hints for Selected Exercises; Index
,
English
Additional Edition:
ISBN 0-12-309750-9
Language:
English
