Essentials of the Finite Element Method - 1st Edition - ISBN: 9780128023860, 9780128026069

Essentials of the Finite Element Method

1st Edition

For Mechanical and Structural Engineers

Authors: Dimitrios Pavlou
eBook ISBN: 9780128026069
Paperback ISBN: 9780128023860
Imprint: Academic Press
Published Date: 14th July 2015
Page Count: 500
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Description

Fundamental coverage, analytic mathematics, and up-to-date software applications are hard to find in a single text on the finite element method (FEM). Dimitrios Pavlou’s Essentials of the Finite Element Method: For Structural and Mechanical Engineers makes the search easier by providing a comprehensive but concise text for those new to FEM, or just in need of a refresher on the essentials.

Essentials of the Finite Element Method explains the basics of FEM, then relates these basics to a number of practical engineering applications. Specific topics covered include linear spring elements, bar elements, trusses, beams and frames, heat transfer, and structural dynamics. Throughout the text, readers are shown step-by-step detailed analyses for finite element equations development. The text also demonstrates how FEM is programmed, with examples in MATLAB, CALFEM, and ANSYS allowing readers to learn how to develop their own computer code.

Suitable for everyone from first-time BSc/MSc students to practicing mechanical/structural engineers, Essentials of the Finite Element Method presents a complete reference text for the modern engineer.

Key Features

  • Provides complete and unified coverage of the fundamentals of finite element analysis
  • Covers stiffness matrices for widely used elements in mechanical and civil engineering practice
  • Offers detailed and integrated solutions of engineering examples and computer algorithms in ANSYS, CALFEM, and MATLAB

Readership

Mechanical and Structural Engineers.  Undergrad/grad students in mechanical and civil engineering.

Table of Contents

  • Dedication
  • Preface
  • Acknowledgments
  • Chapter 1: An Overview of the Finite Element Method
    • Abstract
    • 1.1 What Are Finite Elements?
    • 1.2 Why Finite Element Method Is Very 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
  • Chapter 2: Mathematical Background
    • Abstract
    • 2.1 Vectors
    • 2.2 Coordinate Systems
    • 2.3 Elements of Matrix Algebra
    • 2.4 Variational Formulation of Elasticity Problems
  • Chapter 3: Linear Spring Elements
    • Abstract
    • 3.1 The Element Equation
    • 3.2 The Stiffness Matrix of a System of Springs
  • Chapter 4: Bar Elements and Hydraulic Networks
    • Abstract
    • 4.1 Displacement Interpolation Functions
    • 4.2 Alternative Procedure Based On the Principle of Direct Equilibrium
    • 4.3 Finite Element Method Modeling of a System of Bars
    • 4.4 Finite Elements Method Modeling of a Piping Network
  • Chapter 5: Trusses
    • Abstract
    • 5.1 The Element Equation for Plane Truss Members
    • 5.2 The Element Equation for 3D Trusses
    • 5.3 Calculation of the Bar’s Axial Forces (Internal Forces)
  • Chapter 6: Beams
    • Abstract
    • 6.1 Element Equation of a Two-Dimensional Beam Subjected to Nodal Forces
    • 6.2 Two-Dimensional Element Equation of a Beam Subjected to a Uniform Loading
    • 6.3 Two-Dimensional Element Equation of a Beam Subjected to an Arbitrary Varying Loading
    • 6.4 Two-Dimensional Element Equation of a Beam on Elastic Foundation Subjected to Uniform Loading
    • 6.5 Engineering Applications of the Element Equation of the Beam on Elastic Foundation
    • 6.6 Element Equation for a Beam Subjected to Torsion
    • 6.7 Two-Dimensional Element Equation For a Beam Subjected To Nodal Axial Forces, Shear Forces, Bending Moments, and Torsional Moments
    • 6.8 Three-Dimensional Element Equation for a Beam Subjected to Nodal Axial Forces, Shear Forces, Bending Moments, and Torsional Moments
  • Chapter 7: Frames
    • Abstract
    • 7.1 Framed Structures
    • 7.2 Two-Dimensional Frame Element Equation Subjected to Nodal Forces
    • 7.3 Two-Dimensional Frame Element Equation Subjected to Arbitrary Varying Loading
    • 7.4 Three-Dimensional Beam Element Equation Subjected to Nodal Forces
    • 7.5 Distribution of Bending Moments, Shear Forces, Axial Forces, and Torsional Moments of Each Element
  • Chapter 8: The Principle of Minimum Potential Energy for One-Dimensional Elements
    • Abstract
    • 8.1 The Basic Concept
    • 8.2 Application of the MPE Principle on Systems of Spring Elements
    • 8.3 Application of the MPE Principle on Systems of Bar Elements
    • 8.4 Application of the MPE Principle on Trusses
    • 8.5 Application of the MPE Principle on Beams
  • Chapter 9: From “Isotropic” to “Orthotropic” Plane Elements: Elasticity Equations for Two-Dimensional Solids
    • Abstract
    • 9.1 The Generalized Hooke’s Law
    • 9.2 From “Isotropic” to “Orthotropic” Plane Elements
    • 9.3 Hooke’s Law of an Orthotropic Two-Dimensional Element, with Respect to the Global Coordinate System
    • 9.4 Transformation of Engineering Properties
    • 9.5 Elasticity Equations for Isotropic Solids
  • Chapter 10: The Principle of Minimum Potential Energy for Two-Dimensional and Three-Dimensional Elements
    • Abstract
    • 10.1 Interpolation and Shape Functions
    • 10.2 Isoparametric Elements
    • 10.3 Derivation of Stiffness Matrices
  • Chapter 11: Structural Dynamics
    • Abstract
    • 11.1 The Dynamic Equation
    • 11.2 Mass Matrix
    • 11.3 Solution Methodology for the Dynamic Equation
    • 11.4 Free Vibration—Natural Frequencies
  • Chapter 12: Heat Transfer
    • Abstract
    • 12.1 Conduction Heat Transfer
    • 12.2 Convection Heat Transfer
    • 12.3 Finite Element Formulation
  • Index

Details

No. of pages:
500
Language:
English
Copyright:
© Academic Press 2015
Published:
Imprint:
Academic Press
eBook ISBN:
9780128026069
Paperback ISBN:
9780128023860

About the Author

Dimitrios Pavlou

Dimitrios Pavlou is a Professor in the Department of Mechanical and Structural Engineering and Materials Science at the University of Stavanger in Norway. In 2014 he was elected a full member of the Norwegian Academy of Technological Sciences. He has had twenty years of teaching and research experience in the fields of finite elements, boundary elements, mechanics of solids, and fracture mechanics. Prof. Pavlou has published many research publications and authored/edited five books and conference proceedings. He is a reviewer in more than 18 international journals and has participated as a plenary speaker and session chair in many international conferences. Today he is a Research Group Leader (Faggruppeleder) of the Mechanical Engineering and Materials Science Group

Affiliations and Expertise

Department of Mechanical and Structural Engineering and Materials Science, Faculty of Science and Technology, University of Stavanger, Stavanger, Norway