Efnisyfirlit

• Contents
• Preface to the SI Edition
• Preface
• Digital Resources
• Notation
• Chapter 1: Introduction
  • Chapter Objectives
  • Prologue
  • 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
  • References
  • Problems
• Chapter 2: Introduction to the Stiffness (Displacement) Method
  • Chapter Objectives
  • Introduction
  • 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
  • Summary Equations
  • References
  • Problems
• Chapter 3: Development of Truss Equations
  • Chapter Objectives
  • Introduction
  • 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 the One-Di
  • 3.3 Transformation of Vectors in Two Dimensions
  • 3.4 Global Stiffness Matrix for Bar Arbitrarily Oriented in the Plane
  • 3.5 Computation of 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
  • Summary Equations
  • References
  • Problems
• Chapter 4: Development of Beam Equations
  • Chapter Objectives
  • Introduction
  • 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
  • Summary Equations
  • References
  • Problems
• Chapter 5: Frame and Grid Equations
  • Chapter Objectives
  • Introduction
  • 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
  • Summary Equations
  • References
  • Problems
• Chapter 6: Development of the Plane Stress and Plane Strain Stiffness Equations
  • Chapter Objectives
  • Introduction
  • 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)
  • Summary Equations
  • References
  • Problems
• Chapter 7: Practical Considerations in Modeling; Interpreting Results; and Examples of Plane Stress/
  • Chapter Objectives
  • Introduction
  • 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/Stra
  • References
  • Problems
• Chapter 8: Development of the Linear-Strain Triangle Equations
  • Chapter Objectives
  • Introduction
  • 8.1 Derivation of the Linear-Strain Triangular Element Stiffness Matrix and Equations
  • 8.2 Example LST Stiffness Determination
  • 8.3 Comparison of Elements
  • Summary Equations
  • References
  • Problems
• Chapter 9: Axisymmetric Elements
  • Chapter Objectives
  • Introduction
  • 9.1 Derivation of the Stiffness Matrix
  • 9.2 Solution of an Axisymmetric Pressure Vessel
  • 9.3 Applications of Axisymmetric Elements
  • Summary Equations
  • References
  • Problems
• Chapter 10: Isoparametric Formulation
  • Chapter Objectives
  • Introduction
  • 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)
  • Summary Equations
  • References
  • Problems
• Chapter 11: Three-Dimensional Stress Analysis
  • Chapter Objectives
  • Introduction
  • 11.1 Three-Dimensional Stress and Strain
  • 11.2 Tetrahedral Element
  • 11.3 Isoparametric Formulation and Hexahedral Element
  • Summary Equations
  • References
  • Problems
• Chapter 12: Plate Bending Element
  • Chapter Objectives
  • Introduction
  • 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 Plate Bending Problems
  • Summary Equations
  • References
  • Problems
• Chapter 13: Heat Transfer and Mass Transport
  • Chapter Objectives
  • Introduction
  • 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
  • Summary Equations
  • References
  • Problems
• Chapter 14: Fluid Flow in Porous Media and through Hydraulic Networks; and Electrical Networks and E
  • Chapter Objectives
  • Introduction
  • 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
  • Summary Equations
  • References
  • Problems
• Chapter 15: Thermal Stress
  • Chapter Objectives
  • Introduction
  • 15.1 Formulation of the Thermal Stress Problem and Examples
  • Summary Equations
  • Reference
  • Problems
• Chapter 16: Structural Dynamics and Time-Dependent Heat Transfer
  • Chapter Objectives
  • Introduction
  • 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
  • Summary Equations
  • References
  • Problems
• Appendix A: Matrix Algebra
• Appendix B: Methods for Solution of Simultaneous Linear Equations
• Appendix C: Equations from Elasticity Theory
• Appendix D: Equivalent Nodal Forces
• Appendix E: Principle of Virtual Work
• Appendix F: Geometric Properties of Structural Steel Wide-Flange Sections (W Shapes)
• Answers to Selected Problems
• Index

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