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# A First Course in the Finite Element Method

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
• 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
• Evaluation of the Stiness Matrix and Stress Matrix
• 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

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