The Finite Element Method: Its Basis and Fundamentals

7th Edition

Authors: Olek Zienkiewicz Robert Taylor J.Z. Zhu
Hardcover ISBN: 9781856176330
eBook ISBN: 9780080951355
Imprint: Butterworth-Heinemann
Published Date: 22nd August 2013
Page Count: 756
Tax/VAT will be calculated at check-out
Compatible Not compatible
VitalSource PC, Mac, iPhone & iPad Amazon Kindle eReader
ePub & PDF Apple & PC desktop. Mobile devices (Apple & Android) Amazon Kindle eReader
Mobi Amazon Kindle eReader Anything else

Institutional Access

Table of Contents

Author Biography


List of Figures

List of Tables


Chapter 1. The Standard Discrete System and Origins of the Finite Element Method


1.1 Introduction

1.2 The structural element and the structural system

1.3 Assembly and analysis of a structure

1.4 The boundary conditions

1.5 Electrical and fluid networks

1.6 The general pattern

1.7 The standard discrete system

1.8 Transformation of coordinates

1.9 Problems


Chapter 2. Problems in Linear Elasticity and Fields


2.1 Introduction

2.2 Elasticity equations

2.3 General quasi-harmonic equation

2.4 Concluding remarks

2.5 Problems


Chapter 3. Weak Forms and Finite Element Approximation: 1-D Problems


3.1 Weak forms

3.2 One-dimensional form of elasticity

3.3 Approximation to integral and weak forms: The weighted residual (Galerkin) method

3.4 Finite element solution

3.5 Isoparametric form

3.6 Hierarchical interpolation

3.7 Axisymmetric one-dimensional problem

3.8 Transient problems

3.9 Weak form for one-dimensional quasi-harmonic equation

3.10 Concluding remarks

3.11 Problems


Chapter 4. Variational Forms and Finite Element Approximation: 1-D Problems


4.1 Variational principles

4.2 “Natural” variational principles and their relation to governing differential equations

4.3 Establishment of natural variational principles for linear, self-adjoint differential equations

4.4 Maximum, minimum, or a saddle point?

4.5 Constrained variational principles

4.6 Constrained variational principles: Penalty function and perturbed Lagrangian methods

4.7 Least squares approximations<


The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications.

This edition sees a significant rearrangement of the book’s content to enable clearer development of the finite element method, with major new chapters and sections added to cover:

  • Weak forms
  • Variational forms
  • Multi-dimensional field problems
  • Automatic mesh generation
  • Plate bending and shells
  • Developments in meshless techniques

Focusing on the core knowledge, mathematical and analytical tools needed for successful application, The Finite Element Method: Its Basis and Fundamentals is the authoritative resource of choice for graduate level students, researchers and professional engineers involved in finite element-based engineering analysis.

Key Features

  • A proven keystone reference in the library of any engineer needing to understand and apply the finite element method in design and development.
  • Founded by an influential pioneer in the field and updated in this seventh edition by an author team incorporating academic authority and industrial simulation experience.
  • Features reworked and reordered contents for clearer development of the theory, plus new chapters and sections on mesh generation, plate bending, shells, weak forms and variational forms.


Mechanical, Civil and Electrical Engineers, applied mathematicians and computer aided engineering software developers


No. of pages:
© Butterworth-Heinemann 2013
Hardcover ISBN:
eBook ISBN:


"...this is a book that you simply cannot afford to be without."--INTERNATIONAL JOURNAL OF NUMERICAL METHODS IN ENGINEERING

About the Authors

Olek Zienkiewicz Author

O. C. Zienkiewicz was one of the early pioneers of the finite element method and is internationally recognized as a leading figure in its development and wide-ranging application. He was awarded numerous honorary degrees, medals and awards over his career, including the Royal Medal of the Royal Society and Commander of the British Empire (CBE). He was a founding author of The Finite Element Method books and developed them through six editions over 40 years up to his death in 2009.

Affiliations and Expertise

Finite element method pioneer and former UNESCO Professor of Numerical Methods in Engineering, Barcelona, Spain

Robert Taylor Author

R. L. Taylor is Emeritus Professor of Engineering and Professor in the Graduate School, Department of Civil and Environmental Engineering at the University of California, Berkeley.

Affiliations and Expertise

Emeritus Professor of Engineering, University of California, Berkeley, USA.

J.Z. Zhu Author

J. Z. Zhu is a Senior Scientist at ProCAST, ESI Group, USA.

Affiliations and Expertise

Senior Scientist at ProCast Inc., ESI-Group North America, USA