The Finite Element Method

The Finite Element Method

A Practical Course

2nd Edition - August 7, 2013

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  • Authors: G.R. Liu, S. S. Quek
  • eBook ISBN: 9780080994413
  • Paperback ISBN: 9780080983561

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Written for practicing engineers and students alike, this book emphasizes the role of finite element modeling and simulation in the engineering design process. It provides the necessary theories and techniques of the FEM in a concise and easy-to-understand format and applies the techniques to civil, mechanical, and aerospace problems. Updated throughout for current developments in FEM and FEM software, the book also includes case studies, diagrams, illustrations, and tables to help demonstrate the material.

Key Features

  • Plentiful diagrams, illustrations and tables demonstrate the material
  • Covers modeling techniques that predict how components will operate and tolerate loads, stresses and strains in reality
  • Full set of PowerPoint presentation slides that illustrate and support the book, available on a companion website


Civil, Mechanical, Structural, Aeronautical, Automotive and Marine engineers all benefit from the techniques outlined. The number of engineers working in industries that would require this modeling and simulation of engineering systems is well over half a million.

Table of Contents

  • Dedication


    Preface to the First Edition

    Chapter 1. Computational Modeling

    1.1 Introduction

    1.2 Physical problems in engineering

    1.3 Computational modeling using FEM

    1.4 Solution procedure

    1.5 Results visualization


    Chapter 2. Briefing on Mechanics for Solids and Structures

    2.1 Introduction

    2.2 Equations for three-dimensional solids

    2.3 Equations for two-dimensional solids

    2.4 Equations for truss members

    2.5 Equations for beams

    2.6 Equations for plates

    2.7 Remarks

    2.8 Review questions


    Chapter 3. Fundamentals for Finite Element Method

    3.1 Introduction

    3.2 Strong and weak forms: problem formulation

    3.3 Hamilton’s principle: A weak formulation

    3.4 FEM procedure

    3.5 Static analysis

    3.6 Analysis of free vibration (eigenvalue analysis)

    3.7 Transient response

    3.8 Remarks

    3.9 Review questions


    Chapter 4. FEM for Trusses

    4.1 Introduction

    4.2 FEM equations

    4.3 Worked examples

    4.4 High order one-dimensional elements

    4.5 Review questions


    Chapter 5. FEM for Beams

    5.1 Introduction

    5.2 FEM equations

    5.3 Remarks

    5.4 Worked examples

    5.5 Case study: resonant frequencies of micro-resonant transducer

    5.6 Review questions


    Chapter 6. FEM for Frames

    6.1 Introduction

    6.2 FEM equations for planar frames

    6.3 FEM equations for space frames

    6.4 Remarks

    6.5 Case study: finite element analysis of a bicycle frame

    6.6 Review questions


    Chapter 7. FEM for Two-Dimensional Solids

    7.1 Introduction

    7.2 Linear triangular elements

    7.3 Linear rectangular elements

    7.4 Linear quadrilateral elements

    7.5 Elements for axisymmetric structures

    7.6 Higher order elements—triangular element family

    7.7 Rectangular Elements

    7.8 Elements with curved edges

    7.9 Comments on Gauss integration

    7.10 Case study: Side drive micro-motor

    7.11 Review questions


    Chapter 8. FEM for Plates and Shells

    8.1 Introduction

    8.2 Plate elements

    8.3 Shell elements

    8.4 Remarks

    8.5 Case study: Natural frequencies of the micro-motor

    8.6 Case study: Transient analysis of a micro-motor

    8.7 Review questions


    Chapter 9. FEM for 3D Solid Elements

    9.1 Introduction

    9.2 Tetrahedron element

    9.3 Hexahedron element

    9.4 Higher order elements

    9.5 Elements with curved surfaces

    9.6 Case study: Stress and strain analysis of a quantum dot heterostructure

    9.7 Review questions


    Chapter 10. Special Purpose Elements

    10.1 Introduction

    10.2 Crack tip elements

    10.3.3 Coupling of FEM and the boundary element method

    10.5 Strip element method

    10.6 Meshfree methods

    10.7 S-FEM


    Chapter 11. Modeling Techniques

    11.1 Introduction

    11.2 CPU time estimation

    11.3 Geometry modeling

    11.4 Meshing

    11.5 Mesh compatibility

    11.6 Use of symmetry

    11.6.4 Repetitive symmetry

    11.7 Modeling of offsets

    11.8 Modeling of supports

    11.9 Modeling of joints

    11.10 Other applications of MPC equations

    11.11 Implementation of MPC equations

    11.12 Review questions


    Chapter 12. FEM for Heat Transfer Problems

    12.1 Field problems

    12.2 Weighted residual approach for FEM

    12.3 1D heat transfer problem

    12.4 2D heat transfer problem

    12.5 Summary

    12.6 Case study: Temperature distribution of heated road surface

    12.7 Review questions


    Chapter 13. Using FEM Software Packages

    13.1 Introduction

    13.2 Basic building block: keywords and data lines

    13.3 Using sets

    13.4 ABAQUS input syntax rules

    13.5 Defining a finite element model in ABAQUS

    13.6 General procedures

    13.7 Remarks (example using a GUI: ANSYS)




Product details

  • No. of pages: 464
  • Language: English
  • Copyright: © Butterworth-Heinemann 2013
  • Published: August 7, 2013
  • Imprint: Butterworth-Heinemann
  • eBook ISBN: 9780080994413
  • Paperback ISBN: 9780080983561

About the Authors

G.R. Liu

Dr. Liu received his PhD from Tohoku University, Japan in 1991. He was a Postdoctoral Fellow at Northwestern University, U.S.A. He is currently the Director of the Centre for Advanced Computations in Engineering Science (ACES), National University of Singapore. He is also an Associate Professor atthe Department of Mechanical Engineering, National University of Singapore. He authored more than 200 technical publications including two books and 130 international journal papers. He is the recipient of the Outstanding University ResearchersAwards (1998), for his development of the Strip Element Method. He is also a recipient of the Defence Technology Prize (National award, 1999) for his contribution to development of underwater shock technology at Singapore. He won the Silver Award at CrayQuest 2000 (Nation wide competition in 2000) (Nationwide competition in 2000) for his development of meshless methods. His research interests include Computational Mechanics, Element Free Methods, Nano-scale Computation, Vibration and Wave Propagation in Composites, Mechanics of Composites and Smart Materials, Inverse Problems and Numerical Analysis.

Affiliations and Expertise

University of Singapore

S. S. Quek

Mr. Quek received his B. Eng. (Hon.) in mechanical engineering from the National University of Singapore in 1999. He did an industrial attachment in the then aeronautics laboratory of DSO National Laboratories, Singapore, gaining much experience in using the finite element method in areas of structural dynamics. He also did research in the areas of wave propagation and infinite domains using the finite element method. In the course of his research, Mr Quek had gained tremendous experience in the applications of the finite element method, especially in using commercially available software like Abaqus. Currently, he is doing research in the field of numerical simulation of quantum dot nanostructures, which will lead to a dissertation for his doctorate degree. To date, he had authored two international journal papers. His research interests include Computational Mechanics, Nano-scale Computation, Vibration and Wave Propagation in Structures and Numerical Analysis.

Affiliations and Expertise

University of Singapore

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