An introduction to nonlinear finite element analysis /

Reddy presents the theory and computer implementation of the finite element method as applied to nonlinear problems of heat transfer and similar field problems, fluid mechanics (flows of incompressible fluids), and solid mechanics (elasticity, beams and plates).

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Reddy, J. N. (Junuthula Narasimha), 1945- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Oxford ; New York : Oxford University Press, 2004.
Temas:
Finite element method.
Nonlinear mechanics.
Méthode des éléments finis.
Mécanique non linéaire.
MATHEMATICS > Numerical Analysis.
Finite element method
Nonlinear mechanics
Método dos elementos finitos.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Preface
  • 1 Introduction
  • 1.1 Mathematical Models
  • 1.2 Numerical Simulations
  • 1.3 The Finite Element Method
  • 1.4 Nonlinear Analysis
  • 1.4.1 Introduction
  • 1.4.2 Classification of Nonlinearities
  • 1.5 The Big Picture
  • References
  • 2 The Finite Element Method: A Review
  • 2.1 Introduction
  • 2.2 One-Dimensional Problems
  • 2.2.1 Governing Differential Equation
  • 2.2.2 Finite Element Approximation
  • 2.2.3 Derivation of the Weak Form
  • 2.2.4 Interpolation Functions
  • 2.2.5 Finite Element Model
  • 2.3 Two-Dimensional Problems
  • 2.3.1 Governing Differential Equation.
  • 2.3.2 Finite Element Approximation
  • 2.3.3 Weak Formulation
  • 2.3.4 Finite Element Model
  • 2.3.5 Interpolation Functions
  • 2.3.6 Assembly of Elements
  • 2.4 Library of Two-Dimensional Finite Elements
  • 2.4.1 Introduction
  • 2.4.2 Triangular Elements
  • 2.4.3 Rectangular Elements
  • 2.5 Numerical Integration
  • 2.5.1 Preliminary Comments
  • 2.5.2 Coordinate Transformations
  • 2.5.3 Integration Over a Master Rectangular Element
  • 2.5.4 Integration Over a Master Triangular Element
  • 2.6 Computer Implementation
  • 2.6.1 General Comments
  • 2.6.2 One-Dimensional Problems.
  • 2.6.3 Two-Dimensional Problems
  • 2.7 Closure
  • Problems
  • References
  • 3 Heat Transfer and Other Field Problems in One Dimension
  • 3.1 Model Differential Equation
  • 3.2 Weak Formulation
  • 3.3 Finite Element Model
  • 3.4 Solution Procedures
  • 3.4.1 General Comments
  • 3.4.2 Direct Iteration Procedure
  • 3.4.3 Newton's Iteration Procedure
  • 3.5 Computer Implementation
  • 3.5.1 Introduction
  • 3.5.2 Preprocessor Unit
  • 3.5.3 Processor Unit
  • 3.6 Closing Remarks
  • Problems
  • References
  • 4 Nonlinear Bending of Straight Beams
  • 4.1 Introduction
  • 4.2 Euler-Bernoulli Beams.
  • 4.2.1 Basic Assumptions
  • 4.2.2 Displacement Field and Strains
  • 4.2.3 Weak Forms
  • 4.2.4 Finite Element Model
  • 4.2.5 Iterative Solutions of Nonlinear Equations
  • 4.2.6 Load Increments
  • 4.2.7 Membrane Locking
  • 4.2.8 Computer Implementation
  • 4.3 Timoshenko Beams
  • 4.3.1 Displacement Field and Strains
  • 4.3.2 Weak Forms
  • 4.3.3 General Finite Element Model
  • 4.3.4 Shear and Membrane Locking
  • 4.3.5 Tangent Stiffness Matrix
  • Problems
  • References
  • 5 Heat Transfer and Other Fields Problems in Two Dimensions
  • 5.1 Model Equation
  • 5.2 Weak Form
  • 5.3 Finite Element Model.
  • 5.4 Solution Procedures
  • 5.4.1 Direct Iteration
  • 5.4.2 Newton-Raphson Iteration
  • 5.5 Computer Implementation
  • 5.5.1 Introduction
  • 5.5.2 Numerical Integration
  • 5.5.3 Element Calculations
  • Problems
  • References
  • 6 Nonlinear Bending of Elastic Plates
  • 6.1 Introduction
  • 6.2 Classical Plate Theory
  • 6.2.1 Assumptions of the Kinematics
  • 6.2.2 Displacement Field and Strains
  • 6.3 Variational Formulation of CPT
  • 6.3.1 Virtual Work
  • 6.3.2 Weak Forms
  • 6.3.3 Equilibrium Equations
  • 6.3.4 Boundary Conditions
  • 6.3.5 Stress Resultant-Deflection Relations.

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