Mathematical modeling in continuum mechanics

著者

書誌事項

Mathematical modeling in continuum mechanics

Roger Temam, Alain Miranville

Cambridge University Press, 2000

大学図書館所蔵 件 / 全21件

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

Continuum mechanics is widely taught to graduate students in applied mathematics, physics, and engineering, providing the basis for further study in fluid and solid mechanics. Presentations of the subject, however, vary greatly in their level of formalism, being either engineering and example oriented or mathematically over-sophisticated. Temam and Miranville provide a rigorous presentation of the underlying mathematics and physics of the problem, avoiding unnecessary use of function spaces. The authors then build on this base to 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 Schroedinger equation. This original text should 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.

目次

  • Part I. Fundamental Concepts in Continuum Mechanics: 1. Describing the motion of a system: geometry and kinematics
  • 2. The fundamental law of dynamics
  • 3. The Cauchy stress-tensor. Applications
  • 4. Real and virtual powers
  • 5. Deformation tensor. Deformation rate tensor. Constitutive laws
  • 6. Energy equations. Shock equations
  • Part II. Physics of Fluids: 7. General properties of Newtonian fluids
  • 8. Flows of perfect fluids
  • 9. Viscous fluids and thermohydraulics
  • 10. Magnetohydrodynamics and inertial confinement of plasmas
  • 11. Combustion
  • 12. Equations of the atmosphere and of the ocean
  • Part III. Solid Mechanics: 13. The general equations of linear elasticity
  • 14. Classical problems of elastostatics
  • 15. Energy theorems. Duality. Variational formulations
  • 16. Introduction to nonlinear constitutive laws and to homogenization
  • Part IV. Introduction to Wave Phenomena: 17. Linear wave equations in mechanics
  • 18. The soliton equation: the Korteweg-de Vries equations
  • 19. The nonlinear Schrodinger equation
  • Appendix A.

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