Essentials of the Finite Element Method
- 2nd Edition - September 4, 2026
- Latest edition
- Author: Dimitrios G. Pavlou
- Language: English
Essentials of the Finite Element Method, Second Edition aims to simplify search by offering a comprehensive yet concise resource suitable for newcomers to FEM or those in need o… Read more
Description
Description
Essentials of the Finite Element Method, Second Edition aims to simplify search by offering a comprehensive yet concise resource suitable for newcomers to FEM or those in need of a refresher. This edition begins by explaining the basics of FEM and gradually introduces advanced topics, while also illustrating the practical applications of the theory in engineering. The book covers various specific subjects, including linear spring elements, bar elements, trusses, beams and frames, plates, heat transfer, structural dynamics, and buckling. Throughout the text, readers are provided with step-by-step detailed analyses for the development of finite element equations.
Moreover, the book demonstrates the programming aspect of FEM, offering examples in MATLAB, EXCEL, CALFEM, and ANSYS. This allows readers to gain insights into developing their own computer code. Designed for a wide range of readers, from first-time BSc/MSc students to experienced researchers and practicing mechanical/structural engineers, the book serves as a comprehensive reference text suitable for modern engineers.
Moreover, the book demonstrates the programming aspect of FEM, offering examples in MATLAB, EXCEL, CALFEM, and ANSYS. This allows readers to gain insights into developing their own computer code. Designed for a wide range of readers, from first-time BSc/MSc students to experienced researchers and practicing mechanical/structural engineers, the book serves as a comprehensive reference text suitable for modern engineers.
Key features
Key features
- Includes step-by-step instructions for developing finite element equations with detailed analysis procedures
- Presents Excel exercises with dynamic inputs and static tests, allowing for innumerable exercise possibilities
- Contains comprehensive coverage of Higher-order beam models in Finite Element Analysis that are often absent in classical textbooks
- Covers stiffness matrices that are provided for commonly used engineering elements in practice
- Provides theoretical resources for conducting FE analysis on isotropic and orthotropic materials
Readership
Readership
BSc and MSc students, Professional engineers
Table of contents
Table of contents
1. An Overview of the Finite Element Method
1.1. What Are Finite Elements?
1.2. Why Finite Element Method Is Popular
1.3. Main Advantages of Finite Element Method
1.4. Main Disadvantages of Finite Element Method
1.5. What Is Structural Matrix?
1.6. What Are the Steps to be Followed for Finite Element Method Analysis of Structure?
1.7. What About the Available Software Packages?
1.8. Physical Principles in the Finite Element Method
1.9. From the Element Equation to the Structure Equation
1.10. Computer-Aided Learning of the Finite Element Method
1.11. Introduction to Excel
1.12. Merging dynamic equations and static text: a powerful learning tool
1.13. Basic knowledge required to write a personal calculation code
1.14. Introductory examples
1.15. Introduction to CALFEM
2. Mathematical Background
2.1. Vectors
2.2. Coordinate Systems
2.3. Elements of Matrix Algebra
2.4. Variational Formulation of Elasticity Problems
2.5. Excel Exercise
3. Bar, Spring, Hydraulic Elements, and Corresponding Networks
3.1. Displacement Interpolation Functions
3.1.1. Functional Form of Displacement Distribution
3.1.2. Derivation of the Element Equation
3.2. Alternative Procedure Based on the Principle of Direct Equilibrium
3.3. Finite Element Method Modeling of a System of Bars
3.3.1. Derivation of Element Matrices
3.3.2. Expansion of Element Equations to the Degrees of Freedom of the Structure
3.3.3. Assembly of Element Equations
3.3.4. Derivation of the Field Values
3.3.5. Linear Spring Elements
3.4. Finite Elements Method Modeling of a Piping Network
3.5. The Element Equation for Plane Truss Members
3.6. The Element Equation for 3D Trusses
3.7. Excel Examples
4. Euler-Bernoulli, Ehrenfest-Timoshenko and Reddy Beam Models
4.1. Bernoulli beam model
4.2. Timoshenko beam model
4.3. Reddy beam model
4.4. Element Equation for a Beam Subjected to Torsion
4.5. Three-Dimensional Element Equation for a Beam Subjected to Nodal Axial Forces, Shear Forces, Bending Moments, and Torsional Moments
4.6. Functionally Graded Beams
4.7. Excel Examples
5. Frames
5.1. Framed Structures
5.2. Two-Dimensional Frame Element Equation Subjected to Nodal Forces
5.3. Two-Dimensional Frame Element Equation Subjected to Arbitrary Varying Loading
5.4. Three-Dimensional Beam Element Equation Subjected to Nodal Forces
5.5. Distribution of Bending Moments, Shear Forces, Axial Forces, and Torsional Moments of Each Element
5.6. Excel Examples
6. Kirchhoff, Mindlin and Reddy Plate Models
6.1. Kirchhoff plate model
6.2. Mindlin plate model
6.3. Reddy plate model
7. The Principle of Minimum Potential Energy
7.1. The Basic Concept
7.2. Application of the MPE Principle on Systems of Spring Elements
7.3. Application of the MPE Principle on Systems of Bar Elements
7.4. Application of the MPE Principle on Trusses
7.5. Application of the MPE Principle on Euler-Bernoulli Beams
7.6. Application of the MPE Principle on Ehrenfest-Timoshenko Beams
7.7. Application of the MPE Principle on Reddy Beams
7.8. Application of the MPE Principle on Kirchhoff Plates
7.9. Application of the MPE Principle on Mindlin Plates
7.10. Application of the MPE Principle on Reddy Plates
7.11. Excel Examples
8. From "Isotropic" to "Orthotropic" Plane Elements: Elasticity Equations for Two-Dimensional Solids
8.1. The Generalized Hooke's Law
8.2. From "Isotropic" to "Orthotropic" Plane Elements
8.3. Hooke's Law of an Orthotropic Two-Dimensional Element, with Respect to the Global Coordinate System
8.4. Transformation of Engineering Properties
8.5. Elasticity Equations for Isotropic Solids
8.6. Excel Examples
9. The Principle of Minimum Potential Energy for Two-Dimensional and Three-Dimensional Elements
9.1. Interpolation and Shape Functions
9.2. Isoparametric Elements
9.3. Derivation of Stiffness Matrices
9.4. Excel Examples
10. Structural Dynamics and Elastic Stability
10.1. The Dynamic Equation
10.2. Mass Matrix
10.2.1. Definition of Isoparametric Elements
10.2.2. Lagrange Polynomials
10.2.3. The Bilinear Quadrilateral Element
10.3. Solution Methodology for the Dynamic Equation
10.4. Free Vibration—Natural Frequencies
10.5. Elastic Buckling of Euler-Bernoulli beams
10.6. Excel Examples
11. Heat Transfer
11.1. Conduction Heat Transfer
11.2. Convection Heat Transfer
11.3. Finite Element Formulation
11.3.1. Central Difference Method
11.3.2. Newmark-Beta Method
1.1. What Are Finite Elements?
1.2. Why Finite Element Method Is Popular
1.3. Main Advantages of Finite Element Method
1.4. Main Disadvantages of Finite Element Method
1.5. What Is Structural Matrix?
1.6. What Are the Steps to be Followed for Finite Element Method Analysis of Structure?
1.7. What About the Available Software Packages?
1.8. Physical Principles in the Finite Element Method
1.9. From the Element Equation to the Structure Equation
1.10. Computer-Aided Learning of the Finite Element Method
1.11. Introduction to Excel
1.12. Merging dynamic equations and static text: a powerful learning tool
1.13. Basic knowledge required to write a personal calculation code
1.14. Introductory examples
1.15. Introduction to CALFEM
2. Mathematical Background
2.1. Vectors
2.2. Coordinate Systems
2.3. Elements of Matrix Algebra
2.4. Variational Formulation of Elasticity Problems
2.5. Excel Exercise
3. Bar, Spring, Hydraulic Elements, and Corresponding Networks
3.1. Displacement Interpolation Functions
3.1.1. Functional Form of Displacement Distribution
3.1.2. Derivation of the Element Equation
3.2. Alternative Procedure Based on the Principle of Direct Equilibrium
3.3. Finite Element Method Modeling of a System of Bars
3.3.1. Derivation of Element Matrices
3.3.2. Expansion of Element Equations to the Degrees of Freedom of the Structure
3.3.3. Assembly of Element Equations
3.3.4. Derivation of the Field Values
3.3.5. Linear Spring Elements
3.4. Finite Elements Method Modeling of a Piping Network
3.5. The Element Equation for Plane Truss Members
3.6. The Element Equation for 3D Trusses
3.7. Excel Examples
4. Euler-Bernoulli, Ehrenfest-Timoshenko and Reddy Beam Models
4.1. Bernoulli beam model
4.2. Timoshenko beam model
4.3. Reddy beam model
4.4. Element Equation for a Beam Subjected to Torsion
4.5. Three-Dimensional Element Equation for a Beam Subjected to Nodal Axial Forces, Shear Forces, Bending Moments, and Torsional Moments
4.6. Functionally Graded Beams
4.7. Excel Examples
5. Frames
5.1. Framed Structures
5.2. Two-Dimensional Frame Element Equation Subjected to Nodal Forces
5.3. Two-Dimensional Frame Element Equation Subjected to Arbitrary Varying Loading
5.4. Three-Dimensional Beam Element Equation Subjected to Nodal Forces
5.5. Distribution of Bending Moments, Shear Forces, Axial Forces, and Torsional Moments of Each Element
5.6. Excel Examples
6. Kirchhoff, Mindlin and Reddy Plate Models
6.1. Kirchhoff plate model
6.2. Mindlin plate model
6.3. Reddy plate model
7. The Principle of Minimum Potential Energy
7.1. The Basic Concept
7.2. Application of the MPE Principle on Systems of Spring Elements
7.3. Application of the MPE Principle on Systems of Bar Elements
7.4. Application of the MPE Principle on Trusses
7.5. Application of the MPE Principle on Euler-Bernoulli Beams
7.6. Application of the MPE Principle on Ehrenfest-Timoshenko Beams
7.7. Application of the MPE Principle on Reddy Beams
7.8. Application of the MPE Principle on Kirchhoff Plates
7.9. Application of the MPE Principle on Mindlin Plates
7.10. Application of the MPE Principle on Reddy Plates
7.11. Excel Examples
8. From "Isotropic" to "Orthotropic" Plane Elements: Elasticity Equations for Two-Dimensional Solids
8.1. The Generalized Hooke's Law
8.2. From "Isotropic" to "Orthotropic" Plane Elements
8.3. Hooke's Law of an Orthotropic Two-Dimensional Element, with Respect to the Global Coordinate System
8.4. Transformation of Engineering Properties
8.5. Elasticity Equations for Isotropic Solids
8.6. Excel Examples
9. The Principle of Minimum Potential Energy for Two-Dimensional and Three-Dimensional Elements
9.1. Interpolation and Shape Functions
9.2. Isoparametric Elements
9.3. Derivation of Stiffness Matrices
9.4. Excel Examples
10. Structural Dynamics and Elastic Stability
10.1. The Dynamic Equation
10.2. Mass Matrix
10.2.1. Definition of Isoparametric Elements
10.2.2. Lagrange Polynomials
10.2.3. The Bilinear Quadrilateral Element
10.3. Solution Methodology for the Dynamic Equation
10.4. Free Vibration—Natural Frequencies
10.5. Elastic Buckling of Euler-Bernoulli beams
10.6. Excel Examples
11. Heat Transfer
11.1. Conduction Heat Transfer
11.2. Convection Heat Transfer
11.3. Finite Element Formulation
11.3.1. Central Difference Method
11.3.2. Newmark-Beta Method
Product details
Product details
- Edition: 2
- Latest edition
- Published: September 10, 2026
- Language: English
About the author
About the author
DP
Dimitrios G. Pavlou
Dimitrios Pavlou is Professor of Mechanics at University of Stavanger in Norway, and Elected Academician of the Norwegian Academy of Technological Sciences. He has had over twenty-five years of teaching and research experience in the fields of Theoretical and Applied Mechanics, Fracture Mechanics, Finite and Boundary Elements, Structural Dynamics, Anisotropic Materials, and their applications in Engineering Structures.
Professor Pavlou is the author of titles, "Essentials of the Finite Element Method" (Elsevier) and "Composite Materials in Piping Applications" (Destech Publications), and guest co-editor of several international journal Special Issues and conference proceedings.
His research portfolio includes over 120 publications in the areas of Applied Mechanics and Engineering Mathematics (majority as single or first author). Since January 2020, Professor Pavlou joined the Editorial Board of the journal "Computer-Aided Civil and Infrastructure Engineering" (IF=11.775, 1st of 134 journals in Civil Engineering – 2020 Journal Citation Reports).
He works as Editor for the journals “Maritime Engineering” (IF=5.952); “Nondestructive Testing and Evaluation” (IF=2.098); “Advances in Civil Engineering” (IF= 1.843); “Aerospace Technology and Management” (IF= 0.713);
“Dynamics”; “Aeronautics and Aerospace Open Access Journal” and “Journal of Materials Science and Research”.
He is also an Editorial Board Member for the “International Journal of Structural Integrity,” the “International Journal of Ocean Systems Management” and “Journal of Materials Science and Research”.
Affiliations and expertise
Professor, University of Stavanger, Stavanger, NorwayView book on ScienceDirect
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