The Finite Element Method: Its Basis and Fundamentals

Front Cover
Butterworth-Heinemann, Aug 31, 2013 - Technology & Engineering - 756 pages

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.

  • 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


1 The Standard Discrete System and Origins of the Finite Element Method
2 Problems in Linear Elasticity and Fields
1D Problems
1D Problems
A Multidimensional Finite Element Method
6 Shape Functions Derivatives and Integration
Two and ThreeDimensional Finite Elements
8 The Patch Test Reduced Integration and Nonconforming Elements
16 Adaptive Finite Element Refinement
17 Automatic Mesh Generation
18 Computer Procedures for Finite Element Analysis
Matrix Algebra
Some Vector Algebra
TensorIndicial Notation in the Approximation of Elasticity Problems
Solution of Simultaneous Linear Algebraic Equations
Triangle and Tetrahedron Integrals

Complete Field Methods
10 Incompressible Problems Mixed Methods and Other Procedures of Solution
11 Multidomain Mixed Approximations
SemiDiscretization of Field and Dynamic Problems
Thin and Thick Plates
14 Shells as a Special Case of ThreeDimensional Analysis
15 Errors Recovery Processes and Error Estimates
Integration by Parts in Two or Three Dimensions Greens Theorem
Solutions Exact at Nodes
1 Matrix Diagonalization or Lumping
Author Index
Subject Index

Other editions - View all

Common terms and phrases

About the author (2013)

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. Previous positions held by O.C. Zienkiewicz include UNESCO Professor of Numerical Methods in Engineering at the International Centre for Numerical Methods in Engineering, Barcelona, Director of the Institute for Numerical Methods in Engineering at the University of Wales, Swansea, U.K.

R.L Taylor is Professor of the Graduate School at the Department of Civil and Environmental Engineering, University of California at Berkeley, USA. Awarded the Daniel C. Drucker Medal by the American Society of Mechanical Engineering in 2005, the Gauss-Newton Award and Congress Medal by the International Association for Computational Mechanics in 2002, and the Von Neumann Medal by the US Association for Computational Mechanics in 1999.

Bibliographic information