Efnisyfirlit

• Half-title page
• Title page
• Copyright page
• Contents
• Preface
• 1 Finite Element Concepts
  • Chapter Roadmap
  • 1.1 General Solution of Continuum Problems
  • 1.2 What is the Finite Element Method?
  • 1.3 Basic Concepts and Definitions
  • 1.4 Element Types and Degrees of Freedom (DOFs)
    • 1.4.1 Truss Elements
    • 1.4.2 Beam Elements
    • 1.4.3 Two-Dimensional Elements
    • 1.4.4 Three-Dimensional Shell Elements
    • 1.4.5 Three-Dimensional Solid Elements
  • 1.5 General Procedures for Finite Element Analysis
    • 1.5.1 Basic Procedures in Finite Element Analysis
    • 1.5.2 Phases of Finite Element Analysis in Commercial Programs
  • 1.6 Brief History of the Development of the FE Method
    • 1.6.1 Ancient Roots of the FE Method
    • 1.6.2 History of the Development of the FE Method
    • 1.6.3 History of the Development of Computers and FE Software Programs
      • Early Software Development
      • The Law-of-the-Land (Moore's)
      • The Pre-Personal-Computer Era
      • 64 Bits and Parallelization
    • 1.6.4 Future Outlook and What's Next?
  • 1.7 Finite Element Applications
    • 1.7.1 Various Types of Application
• 2 Detailed Procedures
  • Chapter Roadmap
  • 2.1 Element Characteristic Equations for Simple Elements
    • 2.1.1 Simple Truss Element – One DOF per node
    • 2.1.2 One-Dimensional Heat Transfer Element
    • 2.1.3 Pipe Flow Element
    • 2.1.4 Direct Current Flow Element
    • 2.1.5 Torsional Element
  • 2.2 Simple Beam Element
  • 2.3 Assembling of Global Equations
  • 2.4 Application of Boundary Conditions
    • 2.4.1 Rigid Body Motion
    • 2.4.2 Applying Boundary Conditions
    • 2.4.3 Application Example: Beam Element with a Hinge
  • 2.5 Coordinate Transformations and More Element Equations
    • 2.5.1 Coordinate Transformation
    • 2.5.2 General Two-Dimensional Truss Element
    • 2.5.3 General Two-Dimensional Beam Element
    • 2.5.4 Three-Dimensional Truss Element
    • 2.5.5 Three-Dimensional Beam Element
  • Problems
• 3 Modeling Aspects
  • Chapter Roadmap
  • 3.1 The Modeling Process
  • 3.2 Geometric Modeling
    • Problems
    • Key Points
    • Line or Line Segment
    • Area or Patch
    • Volume or Hyperpatch
    • Boolean Operations
    • Theory of Parametric Cubic Geometry
  • 3.3 Discrete Element Types in FE Programs
    • 3.3.1 Concentrated Mass–Inertia Elements
    • 3.3.2 Spring and Damper Elements
  • 3.4 Problem Classification and Element Choice
    • 3.4.1 Truss and Beam Problems
    • 3.4.2 Two-Dimensional Problems
      • (i) 2D Plane Stress Problems
      • (ii) 2D Plane Strain Problems
      • (iii) 2D Axisymmetric Problems
    • 3.4.3 Shell Problems
    • 3.4.4 Three-Dimensional Solid Problems
  • 3.5 Synopsis of Problem Classification and Element Choice
  • 3.6 Symmetry Considerations
    • 3.6.1 Planar Symmetry
    • 3.6.2 Axial Symmetry
    • 3.6.3 Cyclic Symmetry
    • 3.6.4 Symmetric Structure with Non-Symmetric Loading
  • 3.7 Boundary Conditions
    • 3.7.1 Eliminating Rigid Body Motion
    • 3.7.2 Modeling Supports
  • 3.8 Mesh Intensity and Transition
  • 3.9 Modeling with Different Element Types
  • 3.10 Lumped Load Vectors
    • 3.10.1 Lumped Load Methods
    • 3.10.2 Node-by-Node Lumping
    • 3.10.3 Element-by-Element Lumping
  • 3.11 Model Checking
    • 3.11.1 Checks Initiated by the Program
    • 3.11.2 Checks Performed by the User
  • 3.12 General Modeling Hints
  • Problems
• 4 Linear Static Analysis Using Ansys/Workbench
  • Chapter Roadmap
  • 4.1 Introduction to the Ansys Program
    • 4.1.1 Operation Modes in Ansys
    • 4.1.2 Starting up Ansys
    • 4.1.3 Windows in Ansys
    • 4.1.4 Ansys Structure and Files
  • 4.2 Ansys Project 1: Analysis of a 2D Support Bracket
    • 4.2.1 Problem Description
    • 4.2.2 Create the Model Geometry
    • 4.2.3 Generate the FE Model
    • 4.2.4 Solution Operation
    • 4.2.5 Displaying the Results and Exiting Ansys
    • 4.2.6 Batch Type Solution
    • 4.2.7 Mesh Sensitivity Analysis
  • 4.3 Introduction to Workbench
    • 4.3.1 Layout of Program Menus
    • 4.3.2 Overview of the Geometry and the DesignModeler Capabilities
  • 4.4 Workbench Project 1: 2D Cantilever Bracket
    • 4.4.1 Create the Model Geometry
    • 4.4.2 Generate the FE Model
    • 4.4.3 Solution, Results and Mesh Refinement
  • 4.5 Workbench Project 2: 3D T-Junction Analysis
    • 4.5.1 Problem Description
    • 4.5.2 Creating the Geometry
    • 4.5.3 T-Junction FE Model and Solution
• 5 Finite Element Formulations
  • Chapter Roadmap
  • 5.1 Overview
  • 5.2 Strong and Weak Forms of the Problem
  • 5.3 FE Virtual Work Formulations
  • 5.4 Principle of Minimum Potential Energy and the Rayleigh–Ritz Method
  • 5.5 Linear Elastic FE Analysis Using Virtual Work Principle
  • 5.6 Heat Conduction Analysis Using Virtual Work Principle
  • 5.7 Method of Weighted Residuals (MWRs)
    • 5.7.1 Overview of MWRs
    • 5.7.2 Various Weighted Residual Methods
      • Continuous Least Squares Method
      • Least Squares Collocation Method
      • Galerkin Methods
  • 5.8 Galerkin Formulation of 2D Linear Elasticity Problems
  • 5.9 Formulation of Heat Conduction Analysis
    • 5.9.1 Heat Conduction Analysis Using Variational Principles
    • 5.9.2 3D Heat Conduction Analysis Using the Galerkin Formulation
  • Problems
  • Project Type Problems
• 6 Linear Static Analysis
  • Chapter Roadmap
  • 6.1 Linear Elastic Analysis Formulation
    • 6.1.1 Problem Formulation by the Virtual Work and Galerkin Principles
    • 6.1.2 Specialization to Two-Dimensional Problems
  • 6.2 Application to General Three-Dimensional Solid Elements
  • 6.3 Development of Simple Beam Element
  • 6.4 Development of Two-Dimensional Elements
    • 6.4.1 Plane Stress or Strain Triangular Element with Three Nodes
    • 6.4.2 Plane Stress or Strain Rectangular Element with Four Nodes
    • 6.4.3 Axisymmetric Triangular Ring Element with Three Nodes
  • 6.5 Development of Three-Dimensional Solid Elements
    • 6.5.1 Tetrahedron Element with Four Nodes
  • 6.6 Thermal Stresses
    • 6.6.1 Constitutive Equations with Thermal Effect
    • 6.6.2 Element Equations with Thermal Effect
  • 6.7 Isoparametric Elements
    • 6.7.1 General Concepts and the Need for Isoparametric Elements
    • 6.7.2 Development of 1D Truss Element
    • 6.7.3 Development of 2D Quadrilateral Element with Four to Nine Nodes
    • 6.7.4 Development of 2D Triangular Element with Three to Six Nodes
    • 6.7.5 Development of 3D Hexahedral or Cubical Element with Eight to 20 Nodes
    • 6.7.6 Development of 3D Tetrahedral Elements
  • 6.8 Application of Multi-Point Linear Constraint Equations (MPCs)
    • 6.8.1 Types of Constraint
    • 6.8.2 Method of Substitution
    • 6.8.3 Lagrange Multiplier Method
    • 6.8.4 Penalty Method
  • Problems
  • Multiple Choice Questions
• 7 Conduction Heat Transfer Analysis
  • Chapter Roadmap
  • 7.1 General Background
    • 7.1.1 Basic Modes of Heat Transfer
      • (i) Conduction
      • (ii) Convection
      • (iii) Radiation
    • 7.1.2 The One-Dimensional Heat Conduction Equation
    • 7.1.3 Boundary Conditions
    • 7.1.4 Sources of Nonlinearity
  • 7.2 FE Formulation of the Heat Conduction Problem
  • 7.3 Solution of the Transient Heat Transfer Equations
    • 7.3.1 General Considerations
    • 7.3.2 Direction Integration Method
      • (i) Linearization of the General Equation
      • (ii) The α-Method
      • (iii) General Solution Steps
      • (iv) Stability and Accuracy Considerations
      • (v) Accuracy of the α-Method
  • 7.4 Element Equations for Heat Transfer Analysis
    • 7.4.1 One-Dimensional Elements
    • 7.4.2 Two-Dimensional Elements
      • (i) Three-Node Plane Triangular Elements
      • (ii) Three-Node Axisymmetric Elements
      • (iii) Isoparametric Elements
  • 7.5 Ansys/Workbench Project: Square Plate with Prescribed Temperature Boundary Conditions
    • Problem Statement
    • Approach and Assumptions
    • Solution Steps
      • (1) Specifying the Physics Problem
      • (2) Engineering Data
      • (3) Ansys Design Modeler
      • (4) Ansys Workbench Modeling
      • (5) Ansys Workbench Solver
      • (6) Ansys Workbench PostProcessor
      • (7) Comparison (Figure P1-13)
  • Problems
  • Project Type Problems
• Appendix A Matrices and Systems of Linear Equations
• Appendix B Vectors and Tensors
• References
• Index

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