Introduction to Finite Element Methods 1st ediion by Niels Ottosen ISBN 0134738772 9780134738772

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ISBN 10:       0134738772
ISBN 13: 978-0134738772
Author:         Niels Ottosen

Introduction to Finite Element Methods 1st Table of contents:

1. Introduction to Finite Element Methods
1–1 Overview of Finite Element Analysis (FEA)
1–2 Historical Development of Finite Element Methods
1–3 Applications of FEA in Engineering
1–4 Advantages and Limitations of FEA
1–5 Basic Concepts of Discretization and Approximation
1–6 The Role of FEA in Problem Solving

2. Mathematical Background
2–1 Linear Algebra Fundamentals
2–2 Matrix Operations and Notation
2–3 Systems of Linear Equations
2–4 Eigenvalues and Eigenvectors
2–5 Introduction to Differential Equations
2–6 Variational Formulation of Problems

3. Governing Equations for Structural Problems
3–1 Equilibrium Equations in Structural Mechanics
3–2 Constitutive Relations (Stress-Strain Relationships)
3–3 Strain-Displacement Relations
3–4 Boundary Conditions in Structural Problems
3–5 The Principle of Virtual Work
3–6 Variational Formulation for Structural Analysis

4. Discretization of the Domain
4–1 Introduction to Meshing
4–2 Types of Elements (1D, 2D, 3D)
4–3 Types of Nodes and Degrees of Freedom
4–4 Element Types and Their Properties
4–5 Mesh Generation Techniques
4–6 Mesh Quality and Refinement

5. The Finite Element Method for One-Dimensional Problems
5–1 Introduction to 1D Problems
5–2 Linear Shape Functions
5–3 The Stiffness Matrix for 1D Elements
5–4 Assembly of Global Stiffness Matrix
5–5 Application of Boundary Conditions
5–6 Solution of the System of Equations
5–7 Example of a Simple 1D Problem (Axial Deformation)

6. The Finite Element Method for Two-Dimensional Problems
6–1 Introduction to 2D Problems
6–2 Triangular and Quadrilateral Elements
6–3 Shape Functions for 2D Elements
6–4 Derivation of Stiffness Matrix for 2D Elements
6–5 Global Assembly of Stiffness Matrices
6–6 Boundary Conditions in 2D Problems
6–7 Example of a Simple 2D Problem (Plane Stress)

7. The Finite Element Method for Three-Dimensional Problems
7–1 Introduction to 3D Problems
7–2 Tetrahedral and Hexahedral Elements
7–3 Shape Functions for 3D Elements
7–4 Derivation of Stiffness Matrix for 3D Elements
7–5 Global Assembly for 3D Problems
7–6 Example of a Simple 3D Problem (Stress Analysis)

8. Solution Techniques for Finite Element Problems
8–1 Direct Solution Methods (Gauss Elimination, LU Decomposition)
8–2 Iterative Solution Methods (Conjugate Gradient, GMRES)
8–3 Preconditioning Techniques
8–4 Handling Nonlinear Problems in FEA
8–5 Time Stepping Methods for Dynamic Problems
8–6 Convergence and Stability in Solution Methods

9. Error Analysis and Convergence
9–1 Sources of Error in FEA
9–2 Approximation Errors (Element Size, Shape Functions)
9–3 Convergence Criteria for FEA
9–4 Refinement Techniques and Adaptive Meshes
9–5 Error Estimation and Validation of Results
9–6 Practical Guidelines for Improving Accuracy

10. Nonlinear Finite Element Analysis
10–1 Introduction to Nonlinear Problems
10–2 Material Nonlinearities (Plasticity, Hyperelasticity)
10–3 Geometrical Nonlinearities (Large Deformations)
10–4 Contact Problems in FEA
10–5 Solution Strategies for Nonlinear FEA
10–6 Example of Nonlinear Structural Analysis

11. Dynamic Analysis and Modal Analysis
11–1 Introduction to Dynamics in FEA
11–2 Transient Analysis and Time Stepping Methods
11–3 Modal Analysis and Eigenvalue Problems
11–4 Natural Frequencies and Mode Shapes
11–5 Damped Vibrations and Forced Response
11–6 Example of a Dynamic Problem (Vibration Analysis)

12. Thermal and Fluid Problems in FEA
12–1 Introduction to Thermal Analysis
12–2 Heat Transfer Analysis (Conduction, Convection, Radiation)
12–3 Thermal Stress Analysis
12–4 Fluid Flow Problems and CFD Coupling
12–5 Example of Thermal or Fluid Problem in FEA

13. Multiphysics Problems and Coupling
13–1 Introduction to Multiphysics Analysis
13–2 Thermal-Structural Coupling
13–3 Electromagnetic-Structural Coupling
13–4 Fluid-Structure Interaction
13–5 Multiphysics Applications in FEA

14. Advanced Topics in Finite Element Methods
14–1 Isogeometric Analysis (IGA)
14–2 Meshless Methods in FEA
14–3 Finite Element Analysis for Composite Materials
14–4 Adaptive Finite Element Methods
14–5 Parallel Computing in FEA
14–6 High-Performance FEA Software

15. Applications of Finite Element Analysis
15–1 Structural Applications (Stress, Strain, Deformation)
15–2 Thermal Applications (Heat Transfer Analysis)
15–3 Fluid Mechanics and CFD Applications
15–4 Electromagnetic Applications
15–5 Coupled Multiphysics Applications
15–6 Case Studies and Real-World Applications

16. Conclusion and Future Trends in FEA
16–1 Summary of Key Concepts in FEA
16–2 Limitations and Challenges of FEA
16–3 Future Developments in FEA Technology
16–4 The Role of FEA in Modern Engineering

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