Finite Element Analysis : A Primer.

Format:

Book

Author/Creator:

Musa, Sarhan M.

Language:

English

Physical Description:

1 online resource (613 pages)

Edition:

2nd ed.

Place of Publication:

Bloomfield : Mercury Learning & Information, 2023.

Summary:

Finite Element Analysis, 2/E is a comprehensive guide that explores the versatility and affordability of the finite element method (FEM) as a powerful tool for solving engineering problems across various industries. This book provides a practical introduction to FEM analysis, covering applications in mechanical engineering, civil engineering, electrical engineering, and physics. It presents a balanced blend of theory and applications, catering to both beginners and those seeking to enhance their FEM skills. The book emphasizes a comparative approach by presenting solutions to problems through three different methods: analytical, FEM hand calculations, and software-based methods. This enables readers to grasp the strengths and limitations of each approach, enhancing their understanding of FEM techniques.

Contents:

Cover

Half-Title

Title

Copyright

Dedication

Contents

Preface

Chapter 1: Mathematical Preliminaries

1.1 Introduction

1.2 Matrix Definition

1.3 Types of Matrices

1.4 Addition or Subtraction of Matrices

1.5 Multiplication of a Matrix by Scalar

1.6 Multiplication of a Matrix by Another Matrix

1.7 Rules of Matrix Multiplications

1.8 Transpose of a Matrix Multiplication

1.9 Trace of a Matrix

1.10 Differentiation of a Matrix

1.11 Integration of a Matrix

1.12 Equality of Matrices

1.13 Determinant of a Matrix

1.14 Direct Methods for Linear Systems

1.15 Gaussian Elimination Method

1.16 Cramer's Rule

1.17 Inverse of a Matrix

1.18 Vector Analysis

1.19 Eigenvalues and Eigenvectors

1.20 Using Matlab

Exercises

References

Chapter 2: Introduction to the Finite Element Method

2.1 Introduction

2.2 Methods of Solving Engineering Problems

2.2.1 Experimental Method

2.2.2 Analytical Method

2.2.3 Numerical Method

2.3 Procedure of Finite Element Analysis (Related to Structural Problems)

2.4 Methods of Prescribing Boundary Conditions

2.4.1 Elimination Method

2.4.2 Penalty Method

2.4.3 Multipoint Constrains Method

2.5 Practical Applications of Finite Element Analysis

2.6 Finite Element Analysis Software Package

2.7 Finite Element Analysis for Structure

2.8 Types of Elements

2.9 Direct Method for Linear Spring

Chapter 3: Finite Element Analysis of Axially Loaded Members

3.1 Introduction

3.1.1 Two-Node Bar Element

3.1.2 Three-Node Bar Element

3.2 Bars of Constant Cross-Section Area

3.3 Bars of Varying Cross-Section Area

3.4 Stepped Bar

Chapter 4: Finite Element Analysis Trusses

4.1 Introduction

4.2 Truss

References.

Chapter 5: Finite Element Analysis of Beams

5.1 Introduction

5.2 Simply Supported Beams

5.3 Cantilever Beams

Chapter 6: Stress Analysis of a Rectangular Plate With a Circular Hole

6.1 Introduction

6.2 A Rectangular Plate with a Circular Hole

Chapter 7: Thermal Analysis

7.1 Introduction

7.2 Procedure of Finite Element Analysis (Related to Thermal Problems)

7.3 One-Dimensional Heat Conduction

7.4 Two-Dimensional Problem with Conduction and with Convection Boundary Conditions

Chapter 8: Fluid Flow Analysis

8.1 Introduction

8.2 Procedure of Finite Element Analysis (Related to Fluid Flow Problems)

8.3 Potential Flow Over a Cylinder

8.4 Potential Flow Around an Airfoil

Chapter 9: Dynamic Analysis

9.1 Introduction

9.2 Procedure of Finite Element Analysis (Related to Dynamic Problems)

9.3 Fixed-Fixed Beam for Natural Frequency Determination

9.4 Transverse Vibrations of a Cantilever Beam

9.5 Fixed-Fixed Beam Subjected to Forcing Function

9.6 Axial Vibrations of a Bar

9.7 Bar Subjected to Forcing Function

Chapter 10: Engineering Electromagnetics Analysis

10.1 Introduction to Electromagnetics

10.2 Maxwell's Equations and Continuity Equation

10.2.1 Maxwell's Equations and Continuity Equation in Differential Form

10.2.2 Maxwell's Equations and Continuity Equation in Integral Form

10.2.3 Divergence and Stokes Theorems

10.2.4 Maxwell's Equations and Continuity Equation in Quasi-Statics Case

10.2.5 Maxwell's Equations and Continuity Equation in Statics Case

10.2.6 Maxwell's Equations and Continuity Equation in Source-Free Regions of Space Case

10.2.7 Maxwell's Equations and Continuity Equation in Time-Harmonic Fields Case.

10.3 Lorentz Force Law and Continuity Equation

10.4 Constitutive Relations

10.5 Potential Equations

10.6 Boundary Conditions

10.7 Laws for Static Fields in Unbounded Regions

10.7.1 Coulomb's Law and Field Intensity

10.7.2 Bio-Savart's Law and Field Intensity

10.8 Electromagnetic Energy and Power Flow

10.9 Loss in Medium

10.10 Skin Depth

10.11 Poisson's and Laplace's Equations

10.12 Wave Equations

10.13 Electromagnetic Analysis

10.13.1 One-Dimensional Elements

10.13.1.1 The Approach to FEM Standard Steps Procedure

10.13.1.2 Application to Poisson's Equation in One-Dimension

10.13.1.3 Natural Coordinates in One Dimension

10.13.2 Two-Dimensional Elements

10.13.2.1 Applications of FEM to Electrostatic Problems

10.14 Automatic Mesh Generation

10.14.1 Rectangular Domains

10.14.2 Arbitrary Domains

10.15 Higher-Order Elements

10.15.1 Pascal Triangle

10.15.2 Local Coordinates

10.15.3 Shape Functions

10.15.4 Fundamental Matrices

10.16 Three-Dimensional Element

10.17 Finite Element Methods for External Problems

10.17.1 Infinite Element Method

10.17.2 Boundary Element Method

10.17.3 Absorbing Boundary Conditions

10.18 Modeling and Simulation of Shielded Microstrip Lines with COMSOL Multiphysics

10.18.1 Rectangular Cross-Section Transmission Line

10.18.2 Square Cross-Section Transmission Line

10.18.3 Rectangular Line with Diamondwise Structure

10.18.4 A Single-Strip Shielded Transmission Line

10.19 Multistrip Transmission Lines

10.19.1 Double-Strip Shielded Transmission Line

10.19.2 Three-Strip Line

10.19.3 Six-Strip Line

10.19.4 Eight-Strip Line

10.20 Solenoid Actuator Analysis with Ansys

Appendix A: Ansys

Appendix B: Matlab

Appendix C: Comsol Multiphysics.

Appendix D: 4-COlor Figures From the Text (On the companion files)

Index.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9781683924173

1683924177

9781683924166

1683924169

OCLC:

1425556148