The Finite Element Method

2nd Edition

A Practical Course

Authors: G.R. Liu S. S. Quek
Paperback ISBN: 9780080983561
eBook ISBN: 9780080994413
Imprint: Butterworth-Heinemann
Published Date: 7th August 2013
Page Count: 464
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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



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 Line


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About the Author

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