The Finite Element Method: Its Basis and Fundamentals - 6th Edition

The Finite Element Method: Its Basis and Fundamentals

6th Edition

Authors: Olek Zienkiewicz Robert Taylor J.Z. Zhu
Imprint: Butterworth-Heinemann
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The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians. Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms.

• The classic FEM text, written by the subject's leading authors
• Enhancements include more worked examples and exercises
• With a new chapter on automatic mesh generation and added materials on shape function development and the use of higher order elements in solving elasticity and field problems

Active research has shaped The Finite Element Method into the pre-eminent tool for the modelling of physical systems. It maintains the comprehensive style of earlier editions, while presenting the systematic development for the solution of problems modelled by linear differential equations.

Together with the second and third self-contained volumes (0750663219 and 0750663227), The Finite Element Method Set (0750664312) provides a formidable resource covering the theory and the application of FEM, including the basis of the method, its application to advanced solid and structural mechanics and to computational fluid dynamics.

Key Features

  • The classic introduction to the finite element method, by two of the subject's leading authors
  • Any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in this key text


Senior students, researchers and practicing engineers in mechanical, automotive, aeronautical and civil engineering. Key topic for applied mathematicians and engineering software developers.

Table of Contents

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: A direct physical approach to problems in elasticity: plane stress 2.1 Introduction 2.2 Direct formulation of finite element characteristics 2.3 Generalization to the whole region ¨C internal nodal force concept abandoned 2.4 Displacement approach as a Minimization of total potential energy 2.5 Convergence criteria 2.6 Discretization error and convergence rate 2.7 Displacement functions with discontinuity between elements ¨C non-conforming elements and the patch test 2.8 Finite element solution process 2.9 Numerical examples 2.10 Concluding remarks 2.11 Problems

Chapter 3: Generalization of finite element concepts 3.1 Introduction 3.2 Integral or ¡®weak¡¯ statements equivalent to the differential equations 3.3 Approximation to integral formulations: the weighted residual-Galerkin method 3.4 Virtual work as the ¡®weak form¡¯ of equilibrium equations for analysis of solids or fluids 3.5 Partial discretization 3.6 Convergence 3.7 What are ¡®variational principles¡¯? 3.8 ¡®Natural¡¯ variational principles and their relation to governing differential equations 3.9 Establishment of natural variational principles for linear, self-adjoint


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About the Author

Olek Zienkiewicz

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

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

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


It is very difficult to write a book which covers the entire finite element field. ..The authors have made a splendid attempt at a very difficult task. The books remain a tremendous bargain...and are an invaluable guide to the entire field of finite elements. If you are serious about working on finite elements you cannot do without this book. Mathematics Today, August 2001. "...the publication of the first edition was an epoch making is written by...the greatest theorist of the subject. If you are serious about finite elements, this is a book that you simply cannot afford to be without." International Journal of Numerical Methods in Engineering. "..the pre-eminent reference work on finite element analysis." Applied Mechanical Review "...a very good book...presentation is first class...will be of great assistance to all engineers and scientists interested in the method...a very commendable piece of work." Journal of the British Society for Strain Measurement