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Mathematical foundations of elasticity / Jerrold E. Marsden, Thomas J. R. Hughes

Main Author Marsden, Jerrold E. Coauthor Hughes, Thomas J. R. Country Estados Unidos. Publication New York : Dover, 1994 Description XVIII, 556 p. : il. ; 24 cm Series Dover books on advanced mathematics ISBN 0-486-67865-2 CDU 539.31
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Holdings
Item type Current location Call number Status Date due Barcode Item holds
Monografia Biblioteca da UMinho no Campus de Azurém
BPG 539.31 - M Available 140355
Total holds: 0

Enhanced descriptions from Syndetics:

This graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is directed to mathematicians, engineers and physicists who wish to see this classical subject in a modern setting with examples of newer mathematical contributions. Relevant problems appear throughout the text. 1983 edition.

Table of contents provided by Syndetics

  •   Preface
  • Brief glossary of conventions and notations
  • A point of departure
  • 1 Kinematics
  • 2 Balance laws
  • 3 Elastic materials
  • 4 Boundary value problems
  • 5 Constitutive inequalities
  • 6 The role of geometry and functional analysis
  • 1 Geometry and kinematics of bodies
  • 1.1 Motions of simple bodies
  • 1.2 Vector fields, one-forms, and pull-backs
  • 1.3 The deformation gradient
  • 1.4 Tensors, two-point tensors, and the covariant derivative
  • 1.5 Conservation of mass
  • 1.6 Flows and lie derivatives
  • 1.7 Differential forms and the Piola transformation
  • 2 Balance principles
  • 2.1 The master balance law
  • 2.2 The stress tensor and balance of momentum
  • 2.3 Balance of energy
  • 2.4 Classical spacetimes, covariant balance of energy, and the principle of virtual work
  • 2.5 Thermodynamics II; the second law
  • 3 Constitutive theory
  • 3.1 The constitutive hypothesis
  • 3.2 Consequences of thermodynamics, locality, and material frame indifference
  • 3.3 Covariant constitutive theory
  • 3.4 The elasticity tensor and thermoelastic solids
  • 3.5 Material symmetries and isotropic elasticity
  • 4 Linearization
  • 4.1 The implicit function theorem
  • 4.2 Linearization of nonlinear elasticity
  • 4.3 Linear elasticity
  • 4.4 Linearization stability
  • 5 Hamiltonian and variational principles
  • 5.1 The formal variational structure of elasticity
  • 5.2 Linear Hamiltonian systems and classical elasticity
  • 5.3 Abstract Hamiltonian and Lagrangian systems
  • 5.4 Lagrangian field theory and nonlinear elasticity
  • 5.5 Conservation laws
  • 5.6 Reciprocity
  • 5.7 Relativistic elasticity
  • 6 Methods of functional analysis in elasticity
  • 6.1 Elliptic operators and linear elastostatics
  • 6.2 Abstract semigroup theory
  • 6.3 Linear elastodynamics
  • 6.4 Nonlinear elastostatics
  • 6.5 Nonlinear elastodynamics
  • 6.6 The energy criterion
  • 6.7 A control problem for a beam equation
  • 7 Selected topics in bifurcation theory
  • 7.1 Basic ideas of static bifurcation theory
  • 7.2 A survey of some applications to elastostatics
  • 7.3 The traction problem near a natural state (Signorini's problem)
  • 7.4 Basic ideas of dynamic bifurcation theory
  • 7.5 A survey of some applications to elastodynamics
  • 7.6 Bifurcations in the forced oscillations of a beam
  • Bibliography
  • Index

Author notes provided by Syndetics

Jerrold E. Marsden is Professor of Mathematics, University of California, Berkeley. Thomas J. R. Hughes is Professor of Mechanical Engineering, Stanford University.

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