The finite element method in engineering /

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Finite Element Analysis is an analytical engineering tool originated by the Aerospace and nuclear power industries to find usable, approximate solutions to problems with many complex variables. It is an extension of derivative and integral calculus, and uses very large matrix arrays and mesh diagram...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Rao, S. S.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Oxford : Elsevier, Butterworth-Heinemann ; 2010.
Edición:5th ed.
Temas:
Finite element method.
Engineering mathematics.
M�ethode des �el�ements finis.
Math�ematiques de l'ing�enieur.
Engineering mathematics
Finite element method
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Machine generated contents note: pt. 1 Introduction
  • ch. 1 Overview of Finite Element Method
  • 1.1.Basic Concept
  • 1.2.Historical Background
  • 1.3.General Applicability of the Method
  • 1.4.Engineering Applications of the Finite Element Method
  • 1.5.General Description of the Finite Element Method
  • 1.6.One-Dimensional Problems with Linear Interpolation Model
  • 1.7.One-Dimensional Problems with Cubic Interpolation Model
  • 1.8.Derivation of Finite Element Equations Using a Direct Approach
  • 1.9.Commercial Finite Element Program Packages
  • 1.10.Solutions Using Finite Element Software
  • pt. 2 Basic Procedure
  • ch. 2 Discretization of the Domain
  • 2.1.Introduction
  • 2.2.Basic Element Shapes
  • 2.3.Discretization Process
  • 2.4.Node Numbering Scheme
  • 2.5.Automatic Mesh Generation
  • ch. 3 Interpolation Models
  • 3.1.Introduction
  • 3.2.Polynomial Form of Interpolation Functions
  • 3.3.Simplex, Complex, and Multiplex Elements
  • 3.4.Interpolation Polynomial in Terms of Nodal Degrees of Freedom
  • 3.5.Selection of the Order of the Interpolation Polynomial
  • 3.6.Convergence Requirements
  • 3.7.Linear Interpolation Polynomials in Terms of Global Coordinates
  • 3.8.Interpolation Polynomials for Vector Quantities
  • 3.9.Linear Interpolation Polynomials in Terms of Local Coordinates
  • 3.10.Integration of Functions of Natural Coordinates
  • 3.11.Patch Test
  • ch. 4 Higher Order and Isoparametric Elements
  • 4.1.Introduction
  • 4.2.Higher Order One-Dimensional Elements
  • 4.3.Higher Order Elements in Terms of Natural Coordinates
  • 4.4.Higher Order Elements in Terms of Classical Interpolation Polynomials
  • 4.5.One-Dimensional Elements Using Classical Interpolation Polynomials
  • 4.6.Two-Dimensional (Rectangular) Elements Using Classical Interpolation Polynomials
  • 4.7.Continuity Conditions
  • 4.8.Comparative Study of Elements
  • 4.9.Isoparametric Elements
  • 4.10.Numerical Integration
  • ch. 5 Derivation of Element Matrices and Vectors
  • 5.1.Introduction
  • 5.2.Variational Approach
  • 5.3.Solution of Equilibrium Problems Using Variational (Rayleigh-Ritz) Method
  • 5.4.Solution of Eigenvalue Problems Using Variational (Rayleigh-Ritz) Method
  • 5.5.Solution of Propagation Problems Using Variational (Rayleigh-Ritz) Method
  • 5.6.Equivalence of Finite Element and Variational (Rayleigh-Ritz) Methods
  • 5.7.Derivation of Finite Element Equations Using Variational (Rayleigh-Ritz) Approach
  • 5.8.Weighted Residual Approach
  • 5.9.Solution of Eigenvalue Problems Using Weighted Residual Method
  • 5.10.Solution of Propagation Problems Using Weighted Residual Method
  • 5.11.Derivation of Finite Element Equations Using Weighted Residual (Galerkin) Approach
  • 5.12.Derivation of Finite Element Equations Using Weighted Residual (Least Squares) Approach
  • 5.13.Strong and Weak Form Formulations
  • ch. 6 Assembly of Element Matrices and Vectors and Derivation of System Equations
  • 6.1.Coordinate Transformation
  • 6.2.Assemblage of Element Equations
  • 6.3.Incorporation of Boundary Conditions
  • 6.4.Penalty Method
  • 6.5.Multipoint Constraints
  • Penalty Method
  • 6.6.Symmetry Conditions
  • Penalty Method
  • 6.7.Rigid Elements
  • ch. 7 Numerical Solution of Finite Element Equations
  • 7.1.Introduction
  • 7.2.Solution of Equilibrium Problems
  • 7.3.Solution of Eigenvalue Problems
  • 7.4.Solution of Propagation Problems
  • 7.5.Parallel Processing in Finite Element Analysis
  • pt. 3 Application to Solid Mechanics Problems
  • ch. 8 Basic Equations and Solution Procedure
  • 8.1.Introduction
  • 8.2.Basic Equations of Solid Mechanics
  • 8.3.Formulations of Solid and Structural Mechanics
  • 8.4.Formulation of Finite Element Equations (Static Analysis)
  • 8.5.Nature of Finite Element Solutions
  • ch. 9 Analysis of Trusses, Beams, and Frames
  • 9.1.Introduction
  • 9.2.Space Truss Element
  • 9.3.Beam Element
  • 9.4.Space Frame Element
  • 9.5.Characteristics of Stiffness Matrices
  • ch. 10 Analysis of Plates
  • 10.1.Introduction
  • 10.2.Triangular Membrane Element
  • 10.3.Numerical Results with Membrane Element
  • 10.4.Quadratic Triangle Element
  • 10.5.Rectangular Plate Element (In-plane Forces)
  • 10.6.Bending Behavior of Plates
  • 10.7.Finite Element Analysis of Plates in Bending
  • 10.8.Triangular Plate Bending Element
  • 10.9.Numerical Results with Bending Elements
  • 10.10.Analysis of Three-Dimensional Structures Using Plate Elements
  • ch. 11 Analysis of Three-Dimensional Problems
  • 11.1.Introduction
  • 11.2.Tetrahedron Element
  • 11.3.Hexahedron Element
  • 11.4.Analysis of Solids of Revolution
  • ch. 12 Dynamic Analysis
  • 12.1.Dynamic Equations of Motion
  • 12.2.Consistent and Lumped Mass Matrices
  • 12.3.Consistent Mass Matrices in a Global Coordinate System
  • 12.4.Free Vibration Analysis
  • 12.5.Dynamic Response Using Finite Element Method
  • 12.6.Nonconservative Stability and Flutter Problems
  • 12.7.Substructures Method
  • pt. 4 Application to Heat Transfer Problems
  • ch. 13 Formulation and Solution Procedure
  • 13.1.Introduction
  • 13.2.Basic Equations of Heat Transfer
  • 13.3.Governing Equation for Three-Dimensional Bodies
  • 13.4.Statement of the Problem
  • 13.5.Derivation of Finite Element Equations
  • ch. 14 One-Dimensional Problems
  • 14.1.Introduction
  • 14.2.Straight Uniform Fin Analysis
  • 14.3.Convection Loss from End Surface of Fin
  • 14.3.Tapered Fin Analysis
  • 14.4.Analysis of Uniform Fins Using Quadratic Elements
  • 14.5.Unsteady State Problems
  • 14.6.Heat Transfer Problems with Radiation
  • ch. 15 Two-Dimensional Problems
  • 15.1.Introduction
  • 15.2.Solution
  • 15.3.Unsteady State Problems
  • ch. 16 Three-Dimensional Problems
  • 16.1.Introduction
  • 16.2.Axisymmetric Problems
  • 16.3.Three-Dimensional Heat Transfer Problems
  • 16.4.Unsteady State Problems
  • pt. 5 Application to Fluid Mechanics Problems
  • ch. 17 Basic Equations of Fluid Mechanics
  • 17.1.Introduction
  • 17.2.Basic Characteristics of Fluids
  • 17.3.Methods of Describing the Motion of a Fluid
  • 17.4.Continuity Equation
  • 17.5.Equations of Motion or Momentum Equations
  • 17.6.Energy, State, and Viscosity Equations
  • 17.7.Solution Procedure
  • 17.8.Inviscid Fluid Flow
  • 17.9.Irrotational Flow
  • 17.10.Velocity Potential
  • 17.11.Stream Function
  • 17.12.Bernoulli Equation
  • ch. 18 Inviscid and Incompressible Flows
  • 18.1.Introduction
  • 18.2.Potential Function Formulation
  • 18.3.Finite Element Solution Using the Galerkin Approach
  • 18.4.Stream Function Formulation
  • ch. 19 Viscous and Non-Newtonian Flows
  • 19.1.Introduction
  • 19.2.Stream Function Formulation (Using Variational Approach)
  • 19.3.Velocity-Pressure Formulation (Using Galerkin Approach)
  • 19.4.Solution of Navier-Stokes Equations
  • 19.5.Stream Function-Vorticity Formulation
  • 19.6.Flow of Non-Newtonian Fluids
  • 19.7.Other Developments
  • pt. 6 Solution and Applications of Quasi-Harmonic Equations
  • ch. 20 Solution of Quasi-Harmonic Equations
  • 20.1.Introduction
  • 20.2.Finite Element Equations for Steady-State Problems
  • 20.3.Solution of Poisson's Equation
  • 20.4.Transient Field Problems
  • pt. 7 ABAQUS and ANSYS Software and MATLAB� Programs for Finite Element Analysis
  • ch. 21 Finite Element Analysis Using ABAQUS
  • 21.1.Introduction
  • 21.2.Examples
  • ch. 22 Finite Element Analysis Using ANSYS
  • 22.1.Introduction
  • 22.2.GUI Layout in ANSYS
  • 22.3.Terminology
  • 22.4.Finite Element Discretization
  • 22.5.System of Units
  • 22.6.Stages in Solution
  • ch.
  • 23 MATLAB Programs for Finite Element Analysis
  • 23.1.Solution of Linear System of Equations Using Choleski Method
  • 23.2.Incorporation of Boundary Conditions
  • 23.3.Analysis of Space Trusses
  • 23.4.Analysis of Plates Subjected to In-Plane Loads Using CST Elements
  • 23.5.Analysis of Three-Dimensional Structures Using CST Elements
  • 23.6.Temperature Distribution in One-Dimensional Fins
  • 23.7.Temperature Distribution in One-Dimensional Fins Including Radiation Heat Transfer
  • 23.8.Two-Dimensional Heat Transfer Analysis
  • 23.9.Confined Fluid Flow around a Cylinder Using Potential Function Approach
  • 23.10.Torsion Analysis of Shafts.

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