Nonlinear Finite Elements for Continua and Structures

Detalles Bibliográficos
Autor principal: Belytschko, Ted
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2014.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro
  • Nonlinear Finite Elements for Continua and Structures Second Edition
  • Copyright
  • Contents
  • Foreword
  • Preface
  • List of Boxes
  • 1 Introduction
  • 1.1 Nonlinear Finite Elements in Design
  • 1.2 Related Books and a Brief History of Nonlinear Finite Elements
  • 1.3 Notation
  • 1.3.1 Indicial Notation
  • 1.3.2 Tensor Notation
  • 1.3.3 Functions
  • 1.3.4 Matrix Notation
  • 1.4 Mesh Descriptions
  • 1.5 Classification of Partial Differential Equations
  • 1.6 Exercises
  • 2 Lagrangian and Eulerian Finite Elements in One Dimension
  • 2.1 Introduction
  • 2.2 Governing Equations for Total Lagrangian Formulation
  • 2.2.1 Nomenclature
  • 2.2.2 Motion and Strain Measure
  • 2.2.3 Stress Measure
  • 2.2.4 Governing Equations
  • 2.2.5 Momentum Equation in Terms of Displacements
  • 2.2.6 Continuity of Functions
  • 2.2.7 Fundamental Theorem of Calculus
  • 2.3 Weak Form for Total Lagrangian Formulation
  • 2.3.1 Strong Form to Weak Form
  • 2.3.2 Weak Form to Strong Form
  • 2.3.3 Physical Names of Virtual Work Terms
  • 2.3.4 Principle of Virtual Work
  • 2.4 Finite Element Discretization in Total Lagrangian Formulation
  • 2.4.1 Finite Element Approximations
  • 2.4.2 Nodal Forces
  • 2.4.3 Semidiscrete Equations
  • 2.4.4 Initial Conditions
  • 2.4.5 Least-Square Fit to Initial Conditions
  • 2.4.6 Diagonal Mass Matrix
  • 2.5 Element and Global Matrices
  • 2.6 Governing Equations for Updated Lagrangian Formulation
  • 2.6.1 Boundary and Interior Continuity Conditions
  • 2.6.2 Initial Conditions
  • 2.7 Weak Form for Updated Lagrangian Formulation
  • 2.8 Element Equations for Updated Lagrangian Formulation
  • 2.8.1 Finite Element Approximation
  • 2.8.2 Element Coordinates
  • 2.8.3 Internal and External Nodal Forces
  • 2.8.4 Mass Matrix
  • 2.8.5 Equivalence of Updated and Total Lagrangian Formulations
  • 2.8.6 Assembly, Boundary Conditions and Initial Conditions
  • 2.8.7 Mesh Distortion
  • 2.9 Governing Equations for Eulerian Formulation
  • 2.10 Weak Forms for Eulerian Mesh Equations
  • 2.11 Finite Element Equations
  • 2.11.1 Momentum Equation
  • 2.12 Solution Methods
  • 2.13 Summary
  • 2.14 Exercises
  • 3 Continuum Mechanics
  • 3.1 Introduction
  • 3.2 Deformation and Motion
  • 3.2.1 Definitions
  • 3.2.2 Eulerian and Lagrangian Coordinates
  • 3.2.3 Motion
  • 3.2.4 Eulerian and Lagrangian Descriptions
  • 3.2.5 Displacement, Velocity and Acceleration
  • 3.2.6 Deformation Gradient
  • 3.2.7 Conditions on Motion
  • 3.2.8 Rigid Body Rotation and Coordinate Transformations
  • 3.3 Strain Measures
  • 3.3.1 Green Strain Tensor
  • 3.3.2 Rate-of-Deformation
  • 3.3.3 Rate-of-Deformation in Terms of Rate of Green Strain
  • 3.4 Stress Measures
  • 3.4.1 Definitions of Stresses
  • 3.4.2 Transformation between Stresses
  • 3.4.3 Corotational Stress and Rate-of-Deformation
  • 3.5 Conservation Equations
  • 3.5.1 Conservation Laws
  • 3.5.2 Gauss's Theorem

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