A First Course in the Finite Element Method (Enhanced Edition) 6th edition

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• Chapter 1: Introduction
  • 1.1: Brief History
  • 1.2: Introduction to Matrix Notation
  • 1.3: Role of the Computer
  • 1.4: General Steps of the Finite Element Method
  • 1.5: Applications of the Finite Element Method
  • 1.6: Advantages of the Finite Element Method
  • 1.7: Computer Programs for the Finite Element Method
  • 1: Chapter Quiz
  
  
• Chapter 2: Introduction to the Stiffness (Displacement) Method
  • 2.1: Definition of the Stiffness Matrix
  • 2.2: Derivation of the Stiffness Matrix for a Spring Element
  • 2.3: Example of a Spring Assemblage
  • 2.4: Assembling the Total Stiffness Matrix by Superposition (Direct Stiffness Method)
  • 2.5: Boundary Conditions
  • 2.6: Potential Energy Approach to Derive Spring Element Equations
  • 2: Chapter Quiz
  
  
• Chapter 3: Development of Truss Equations
  • 3.1: Derivation of the Stiffness Matrix for a Bar Element in Local Coordinates
  • 3.2: Selecting a Displacement Function in Step 2 of the Derivation of Stiffness Matrix for One-Dimensional Bar Element
  • 3.3: Transformation of Vectors in Two Dimensions
  • 3.4: Global Stiffness Matrix for Bar Arbitrarily Oriented in the Plane
  • 3.5: Computation for Stress for a Bar in the x–y Plane
  • 3.6: Solution of a Plane Truss
  • 3.7: Transformation Matrix and Stiffness Matrix for a Bar in Three-Dimensional Space
  • 3.8: Use of Symmetry in Structures
  • 3.9: Inclined, or Skewed, Supports
  • 3.10: Potential Energy Approach to Derive Bar Element Equations
  • 3.11: Comparison of Finite Element Solution to Exact Solution for Bar
  • 3.12: Galerkin's Residual Method and Its Use to Derive the One-Dimensional Bar Element Equations
  • 3.13: Other Residual Methods and Their Application to a One-Dimensional Bar Problem
  • 3.14: Flowchart for Solution of Three-Dimensional Truss Problems
  • 3.15: Computer Program Assisted Step-by-Step Solution for Truss Problem
  • 3: Chapter Quiz
  
  
• Chapter 4: Development of Beam Equations
  • 4.1: Beam Stiffness
  • 4.2: Example of Assemblage of Beam Stiffness Matrices
  • 4.3: Examples of Beam Analysis Using the Direct Stiffness Method
  • 4.4: Distributed Loading
  • 4.5: Comparison of the Finite Element Solution to the Exact Solution for a Beam
  • 4.6: Beam Element with Nodal Hinge
  • 4.7: Potential Energy Approach to Derive Beam Element Equations
  • 4.8: Galerkin's Method for Deriving Beam Element Equations
  • 4: Chapter Quiz
  
  
• Chapter 5: Frame and Grid Equations
  • 5.1: Two-Dimensional Arbitrarily Oriented Beam Element
  • 5.2: Rigid Plane Frame Examples
  • 5.3: Inclined or Skewed Supports—Frame Element
  • 5.4: Grid Equations
  • 5.5: Beam Element Arbitrarily Oriented in Space
  • 5.6: Concept of Substructure Analysis
  • 5: Chapter Quiz
  
  
• Chapter 6: Development of the Plane Stress and Plane Strain Stiffness Equations
  • 6.1: Basic Concepts of Plane Stress and Plane Strain
  • 6.2: Derivation of the Constant-Strain Triangular Element Stiffness Matrix and Equations
  • 6.3: Treatment of Body and Surface Forces
  • 6.4: Explicit Expression for the Constant-Strain Triangle Stiffness Matrix
  • 6.5: Finite Element Solution of a Plane Stress Problem
  • 6.6: Rectangular Plane Element (Bilinear Rectangle, Q4)
  • 6: Chapter Quiz
  
  
• Chapter 7: Practical Considerations in Modeling; Interpreting Results; and Examples of Plane Stress/Strain Analysis
  • 7.1: Finite Element Modeling
  • 7.2: Equilibrium and Compatibility of Finite Element Results
  • 7.3: Convergence of Solution and Mesh Refinement
  • 7.4: Interpretation of Stresses
  • 7.5: Flowchart for the Solution of Plane Stress/Strain Problems
  • 7.6: Computer Program-Assisted Step-by-Step Solution, Other Models, and Results for Plane Stress/Strain Problems
  • 7: Chapter Quiz
  
  
• Chapter 8: Development of the Linear-Strain Triangle Equations
  • 8.1: Derivation of the Linear-Strain Triangular Element Stiffness
  • 8.2: Example LST Stiffness Determination
  • 8.3: Comparison of Elements
  • 8: Chapter Quiz
  
  
• Chapter 9: Axisymmetric Elements
  • 9.1: Derivation of the Stiffness Matrix
  • 9.2: Solution of an Axisymmetric Pressure Vessel
  • 9.3: Applications of Axisymmetric Elements
  • 9: Chapter Quiz
  
  
• Chapter 10: Isoparametric Formulation
  • 10.1: Isoparametric Formulation of the Bar Element Stiffness Matrix
  • 10.2: Isoparametric Formulation of the Plane Quadrilateral (Q4) Element Stiffness Matrix
  • 10.3: Newton-Cotes and Gaussian Quadrature
  • 10.4: Evaluation of the Stiffness Matrix and Stress Matrix by Gaussian Quadrature
  • 10.5: Higher-Order Shape Functions (Including Q6, Q8, Q9, and Q12 Elements)
  • 10: Chapter Quiz
  
  
• Chapter 11: Three-Dimensional Stress Analysis
  • 11.1: Three-Dimensional Stress and Strain
  • 11.2: Tetrahedral Element
  • 11.3: Isoparametric Formulation and Hexahedral Element
  • 11: Chapter Quiz
  
  
• Chapter 12: Plate Bending Element
  • 12.1: Basic Concepts of Plate Bending
  • 12.2: Derivation of a Plate Bending Element Stiffness Matrix and Equations
  • 12.3: Some Plate Element Numerical Comparisons
  • 12.4: Computer Solutions for Bending Problems
  • 12: Chapter Quiz
  
  
• Chapter 13: Heat Transfer and Mass Transport
  • 13.1: Derivation of the Basic Differential Equation
  • 13.2: Heat Transfer with Convection
  • 13.3: Typical Units; Thermal Conductivities, K; and Heat Transfer Coefficients, h
  • 13.4: One-Dimensional Finite Element Formulation Using a Variational Method
  • 13.5: Two-Dimensional Finite Element Formulation
  • 13.6: Line or Point Sources
  • 13.7: Three-Dimensional Heat Transfer by the Finite Element Method
  • 13.8: One-Dimensional Heat Transfer with Mass Transport
  • 13.9: Finite Element Formulation of Heat Transfer with Mass Transport by Galerkin's Method
  • 13.10: Flowchart and Examples of a Heat Transfer Program
  • 13: Chapter Quiz
  
  
• Chapter 14: Fluid Flow in Porous Media and through Hydraulic Networks; and Electrical Networks and Electrostatics
  • 14.1: Derivation of the Basic Differential Equations
  • 14.2: One-Dimensional Finite Element Formulation
  • 14.3: Two-Dimensional Finite Element Formulation
  • 14.4: Flowchart and Example of a Fluid-Flow Program
  • 14.5: Electrical Networks
  • 14.6: Electrostatics
  • 14: Chapter Quiz
  
  
• Chapter 15: Thermal Stress
  • 15.1: Formulation of the Thermal Stress Problem and Examples
  • 15: Chapter Quiz
  
  
• Chapter 16: Structural Dynamics and Time-Dependent Heat Transfer
  • 16.1: Dynamics of a Spring-Mass System
  • 16.2: Direct Derivation of the Bar Element Equations
  • 16.3: Numerical Integration in Time
  • 16.4: Natural Frequencies of a One-Dimensional Bar
  • 16.5: Time-Dependent One-Dimensional Bar Analysis
  • 16.6: Beam Element Mass Matrices and Natural Frequencies
  • 16.7: Truss, Plane, Frame, Plane Stress, Plane Strain, Axisymmetric, and Solid Element Mass Matrices
  • 16.8: Time-Dependent Heat Transfer
  • 16.9: Computer Program Example Solutions for Structural Dynamics
  • 16: Chapter Quiz
  
  
• Chapter A: Appendix A: Matrix Algebra
  • Appendix A: Matrix Algebra
  
  
• Chapter B: Appendix B: Methods for Solution of Simultaneous Linear Equations
  • Appendix B: Methods for Solution of Simultaneous Linear Equations
  
  
• Chapter D: Appendix D: Equivalent Nodal Forces
  • Appendix D: Equivalent Nodal Forces