A First Course in the Finite Element Method

Book Details

Author

Language

Pages

Size

Format

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
  • 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

Related Books

Leave a Reply

Your email address will not be published.

What's the problem with this file?

There is a temporary issue with downloading files and we are working on.
In the meantime, we appreciate your patience.