Variational Methods in Theoretical Mechanics

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Variational Methods in Theoretical Mechanics

PDF Free Download | Variational Methods in Theoretical Mechanics by J. T. Oden and J. N. Reddy

Contents of Variational Methods in Theoretical Mechanics

  • INTRODUCTION
  • The Role of Variational Theory in Mechanics
  • Some Historical Comments Plan of Study
  • MATHEMATICAL FOUNDATIONS OF CLASSICAL VARIATIONAL THEORY
  • Introduction Nonlinear Operators Differentiation of Operators
  • Mean Value Theorems Taylor Formulas Gradients of Functionals Minimization of Functionals
  • Convex Functionals Potential Operators and the Inverse Problem
  • Sobo ev Spaces
  • MECHANICS OF CONTINUA- A BRIEF REVIEW
  • Introduction
  • Kinematics Stress and the Mechanical Laws of Balance
  • The Principle of Conservation of Mass The Principle of Balance of Linear Momentum
  • The Principle of Balance of Angular Momentum
  • Thermodynamic Principles
  • The Principle of Conservation of Energy
  • The Clausius-Duhem Inequality
  • Constitutive Theory
  • Rules of Constitutive Theory Special Forms of Constitutive Equations
  • Jump Conditions for Discontinuous Fields
  • COMPLEMENTARY AND DUAL VARIATIONAL PRINCIPLES IN MECHANICS
  • Introduction Boundary Conditions and Green’s Formulas
  • Examples from Mechanics and Physics The Fourteen Fundamental Complementary-Dual Principles Some Complementary-Dual Variational Principles of
  • Mechanics and Physics Legendre Transformations
  • Generalized Hamiltonian Theory Upper and Lower Bounds and Existence Theory Lagrange Multipliers
  • VARIATIONAL PRINCIPLES IN CONTINUUM MECHANICS
  • Introduction Some Preliminary Properties and Lemmas
  • General Variational Principles for Linear Theory
  • of Dynamic Viscoelasticity
  • Gurtin’s Variational Principles for the Linear
  • Theory of Dynamic Viscoelasticity
  • Variational Principles for Linear Coupled
  • Dynamic Thermoviscoelasticity
  • Linear (coupled) Thermoe asticity
  • Variational Principles in Linear Eastodynamics Variational Principles for Linear Piezoelectric
  • E astodynamic Problems
  • Variational Principles for Hypereastic Materials
  • Finite Elasticity Quasi-Static Problems
  • Variational Principles in the Flow Theory of
  • Plasticity
  • Variational Principles for a” Large Displacement
  • Theory of E astop asticity
  • Variational Principles in Heat Conduction
  • Biot’s Quasi-Variational Principle in Heat Transfer
  • Some Variational Principles in Fluid Mechanics and
  • Magnetohydrodynamics
  • Non-Newtonian Fluids Perfect Fluids An Alternate Principle for
  • Magnetohydrodynamics
  • Invicid Flow
  • Variational Principles for Discontinuous Fields
  • VARIATIONAL BOUNDARY-VALUE PROBLEMS, MONOTONE OPERATORS, AND VARIATIONAL INEQUALITIES
  • Direct Variational Methods
  • Linear Elliptic Variational Boundary-Value Problems
  • Regularity
  • The Lax-Milgram-Babuska Theorem
  • Existence Theory in Linear Incompressible Elasticity
  • Monotone Operators
  • Existence Theory in Nonlinear Elasticity
  • Variational Inequalities
  • Applications in Mechanics “
  • VARIATIONAL METHODS OF APPROXIMATION
  • Introduction
  • Several Variational Methods of Approximation
  • The Rayleigh-Ritz Method Semidiscrete Galerkin Methods
  • Methods of Weighted Residuals
  • Least Square Methods
  • Collocation Methods
  • Finite-Element Approximations
  • Finite-Element Interpolation Theory
  • Existence and Uniqueness of Galerkin Approximations
  • Convergence and Accuracy of Finite-Element Galerkin
  • Approximations

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