**PDF Free Download | A First Course in the Finite Element Method by Fifth Edition by Daryl L. Logan**

## Contents of First Course in the Finite Element Method

**Chapter 1. Objectives**- Prologue
- Brief History
- Introduction to Matrix Notation
- Role of the Computer
- General Steps of the Finite Element Method
- Applications of the Finite Element Method
- Advantages of the Finite Element Method
- Computer Programs for the Finite Element Method
- Introduction to the Stiffness (Displacement) Method
**Chapter 2. Objectives**- Example of a Spring Assemblage
- Assembling the Total Stiness Matrix by Superposition (Direct Stiness Method)
- Boundary Conditions
- Potential Energy Approach to Derive Spring Element Equations
- Development of Truss Equations
**Chapter 3. Objectives**- Derivation of the Sti¤ness Matrix for a Bar Element in Local Coordinates
- Selecting Approximation Functions for Displacements
- Transformation of Vectors in Two Dimensions
- Global Sti¤ness Matrix for Bar Arbitrarily Oriented in the Plane
- Computation of Stress for a Bar in the x-y Plane
- Solution of a Plane Truss
- Transformation Matrix and Sti¤ness Matrix for a Bar in Three-Dimensional Space
- Use of Symmetry in Structure
- Inclined, or Skewed, Supports
- Potential Energy Approach to Derive Bar Element Equations
- Comparison of Finite Element Solution to Exact Solution for Bar
- Galerkin’s Residual Method and Its Use to Derive the One-Dimensional
- Bar Element Equations
- Other Residual Methods and Their Application to a One-Dimensional
- Bar Problem
- Flowchart for Solution of Three-Dimensional Truss Problems
- Computer Program Assisted Step-by-Step Solution for Truss Problem
- Summary Equations
- Development of Beam Equations
**Chapter 4. Objectives**- Beam Stiness
- Example of Assemblage of Beam Sti¤ness Matrices
- Examples of Beam Analysis Using the Direct Sti¤ness Method
- Distributed Loading
- Comparison of the Finite Element Solution to the Exact Solution for a Beam
- Beam Element with Nodal Hinge
- Potential Energy Approach to Derive Beam Element Equations
- Galerkin’s Method for Deriving Beam
- Element Equations
- Summary Equations
- Frame and Grid Equations
**Chapter 5. Objectives**- Two-Dimensional Arbitrarily Oriented Beam Element
- Rigid Plane Frame Examples
- Inclined or Skewed Supports—Frame Element
- Grid Equations
- Beam Element Arbitrarily Oriented in Space
- Concept of Substructure Analysis
- Summary Equations
- Development of the Plane Stress and Plane Strain Stiffness Equations
**Chapter 6. Objectives**- Basic Concepts of Plane Stress and Plane Strain
- Derivation of the Constant-Strain Triangular Element
- Stiness Matrix and Equations
- Treatment of Body and Surface Forces
- Explicit Expression for the Constant-Strain
- Triangle Stiness Matrix
- Finite Element Solution of a Plane Stress Problem
- Rectangular Plane Element (Bilinear Rectangle, Q )
- Summary Equations
- Practical Considerations in Modeling;
- Interpreting Results; and Examples of Plane Stress–Strain Analysis
**Chapter 7. Objectives**- Finite Element Modeling
- Equilibrium and Compatibility of Finite Element Results
- Convergence of Solution
- Interpretation of Stresses
- Static Condensation
- Flowchart for the Solution of Plane Stress–Strain Problems
- Computer Program-Assisted Step-by-Step Solution, Other Models, and Results for Plane Stress–Strain Problems
- Development of the Linear-Strain Triangle Equations
**Chapter 8. Objectives**- Derivation of the Linear-Strain Triangular Element
- Sti¤ness Matrix and Equations
- Example LST Sti¤ness Determination
- Comparison of Elements
- Summary Equations
- Axisymmetric Elements
**Chapter 9. Objectives**- Derivation of the Sti¤ness Matrix
- Solution of an Axisymmetric Pressure Vessel
- Applications of Axisymmetric Elements
- Summary Equations
- Isoparametric Formulation
**Chapter 10. Objectives**- Isoparametric Formulation of the Bar Element Stiness Matrix
- Isoparametric Formulation of the Plane Quadrilateral Element Stiness Matrix
- Newton-Cotes and Gaussian Quadrature
- Evaluation of the Stiness Matrix and Stress Matrix
- by Gaussian Quadrature
- Higher-Order Shape Functions
- Summary Equations
- Three-Dimensional Stress Analysis
**Chapter 11. Objectives**- Three-Dimensional Stress and Strain
- Tetrahedral Element
- Isoparametric Formulation
- Summary Equations
- Problems
- Plate Bending Element
**Chapter 12. Objectives**- Basic Concepts of Plate Bending
- Derivation of a Plate Bending Element Sti¤ness Matrixand Equations
- Some Plate Element Numerical Comparisons
- Computer Solutions for Plate Bending Problems
- Summary Equations
- Heat Transfer and Mass Transport
**Chapter 13. Objectives**- Heat Transfer with Convection
- Typical Units; Thermal Conductivities, K; and Heat-Transfer
- One-Dimensional Finite Element Formulation Using a Variational Method
- Two-Dimensional Finite Element Formulation
- Line or Point Sources
- Three-Dimensional Heat Transfer by the Finite
- Element Method
- One-Dimensional Heat Transfer with Mass Transport
- Finite Element Formulation of Heat Transfer with Mass Transport by Galerkin’s Method
- Flowchart and Examples of a Heat-Transfer Program
- Fluid Flow in Porous Media and Through
- Hydraulic Networks; and Electrical Networks and Electrostatics
**Chapter 14. Objectives**- Derivation of the Basic Di¤erential Equations
- One-Dimensional Finite Element Formulation
- Two-Dimensional Finite Element Formulation
- Flowchart and Example of a Fluid-Flow Program
- Electrical Networks
- Electrostatics
- Summary Equations
- Thermal Stress
**Chapter 15. Objectives**- Formulation of the Thermal Stress Problem and Examples
- Summary Equations
- Structural Dynamics and Time-Dependent Heat Transfer
**Chapter 16. Objectives**- Dynamics of a Spring-Mass System
- Direct Derivation of the Bar Element Equations
- Numerical Integration in Time
- Natural Frequencies of a One-Dimensional Bar
- Time-Dependent One-Dimensional Bar Analysis
- Beam Element Mass Matrices and Natural Frequencies
- Truss, Plane Frame, Plane Stress, Plane Strain, Axisymmetric, and Solid Element Mass Matrices
- Time-Dependent Heat Transfer
- Computer Program Example Solutions for Structural Dynamics
- Summary Equations
- A Definition of a Matrix
- A Matrix Operations
- A Cofactor or Adjoint Method to Determine the Inverse of a Matrix
- A Inverse of a Matrix by Row Reduction