# The Finite Element Method

## 7th Edition

**Authors:**Olek Zienkiewicz Robert Taylor

**Hardcover ISBN:**9781856176309

**eBook ISBN:**9780080950976

**Imprint:**Butterworth-Heinemann

**Published Date:**20th November 2013

## Description

The Finite Element Method: Its Basis and Fundamentals, 7th Edition

Table of contents:

Some Preliminaries: The Standard Discrete System; A Direct Physical Approach to Problems in Elasticity; Generalization of the Finite Element Concepts; Galerkin-Weighted Residual and Variational Approaches; 'Standard’ and ‘hierarchical’ Element Shape Functions: Some General Families of Continuity; Mapped Elements and Numerical Integration – ‘Infinite’ and ‘Singularity’ Elements; Two Dimensional Problems in Plane Stress, Plane Strain and Axisymmetric Elasticity; Steady-State Field Problems; Three-Dimensional Elasticity and Field Problems; Mesh Generation; The Patch Test; Mixed Formulation and Constraints – Complete Field Methods; Incompressible Materials; Mixed Formulation and Constraints; Errors, Recovery Processes and Error Estimates; Adaptive Finite Element Refinement; Point-Based Approximations – Meshless Methods; The Time Dimension – Semi-discretization of Field and Dynamic Problems and Analytical Solution Procedures; The Time Dimension – Discrete Approximation in Time; Coupled Systems; Computer Procedures for Finite Element Analysis; Matrix Algebra; Tensor-Indicial Notation in the Approximation of Elasticity Problems; Basic Equations of Displacement Analysis; Some Integration Formulae for a Triangle; Some Integration Formulae for a Tetrahedron; Some Vector Algebra; Integration by Parts in Two and Three Dimensions (Green’s Theorem); Solutions Exact at Nodes; Matrix Diagonalization or Lumping

The Finite Element Method for Solid and Structural Mechanics, 7th Edition

Table of contents:

General problems in solid mechanics and non-linearity; Galerkin method of approximation – irreducible and mixed forms; Solution of non-linear algebraic equations; Inelastic and non-linear materials; Geometrically non-linear problems – finite deformation; Material constitution in finite deformation; Treatment of constraints – contact and tied interfaces; Pseudo-rigid and rigid-flexible bodies; Structural mechanics problems in one dimension – rods; Structural mechanics problems in two dimensions – plates and shells; Structural mechanics problems in two dimensions – linearize theory; Curved rods and axisymmetric shells; Discrete element methods; Multi-scale modelling; Computer procedures

The Finite Element Method for Fluid Dynamics, 7th Edition

Table of contents:

Introduction to the equations of fluid dynamics and the finite element approximation; Convection dominated problems – finite element approximations to the convection–diffusion-reaction equation; The characteristic-based split (CBS) algorithm; Incompressible Newtonian laminar flows; Incompressible non-Newtonian flows; Free surface and buoyancy driven flows; Compressible high-speed gas flow; Turbulent flows; Flow through porous media; Shallow water problems; Long and medium waves; Short waves; Local conservation; Fluid-structure interaction; Biofluid dynamics; Micro-scale fluid dynamics and molecular dynamics; Computer implementation of the CBS algorithm; Appendices

## Key Features

- The Finite Element Method: Its Basis and Fundamentals, 7th Edition
- The Finite Element Method for Solid and Structural Mechanics, 7th Edition
- The Finite Element Method for Fluid Dynamics, 7th Edition

## Readership

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

## Table of Contents

The Finite Element Method: Its Basis and Fundamentals, 7th Edition

Table of contents:

Some Preliminaries: The Standard Discrete System; A Direct Physical Approach to Problems in Elasticity; Generalization of the Finite Element Concepts; Galerkin-Weighted Residual and Variational Approaches; 'Standard’ and ‘hierarchical’ Element Shape Functions: Some General Families of Continuity; Mapped Elements and Numerical Integration – ‘Infinite’ and ‘Singularity’ Elements; Two Dimensional Problems in Plane Stress, Plane Strain and Axisymmetric Elasticity; Steady-State Field Problems; Three-Dimensional Elasticity and Field Problems; Mesh Generation; The Patch Test; Mixed Formulation and Constraints – Complete Field Methods; Incompressible Materials; Mixed Formulation and Constraints; Errors, Recovery Processes and Error Estimates; Adaptive Finite Element Refinement; Point-Based Approximations – Meshless Methods; The Time Dimension – Semi-discretization of Field and Dynamic Problems and Analytical Solution Procedures; The Time Dimension – Discrete Approximation in Time; Coupled Systems; Computer Procedures for Finite Element Analysis; Matrix Algebra; Tensor-Indicial Notation in the Approximation of Elasticity Problems; Basic Equations of Displacement Analysis; Some Integration Formulae for a Triangle; Some Integration Formulae for a Tetrahedron; Some Vector Algebra; Integration by Parts in Two and Three Dimensions (Green’s Theorem); Solutions Exact at Nodes; Matrix Diagonalization or Lumping

The Finite Element Method for Solid and Structural Mechanics, 7th Edition

Table of contents:

General problems in solid mechanics and non-linearity; Galerkin method of approximation – irreducible and mixed forms; Solution of non-linear algebraic equations; Inelastic and non-linear materials; Geometrically non-linear problems – finite deformation; Material constitution in finite deformation; Treatment of constraints – contact and tied interfaces; Pseudo-rigid and rigid-flexible bodies; Structural mechanics problems in one dimension – rods; Structural mechanics problems in two dimensions – plates and shells; Structural mechanics problems in two dimensions – linearize theory; Curved rods and axisymmetric shells; Discrete element methods; Multi-scale modelling; Computer procedures

The Finite Element Method for Fluid Dynamics, 7th Edition

Table of contents:

Introduction to the equations of fluid dynamics and the finite element approximation; Convection dominated problems – finite element approximations to the convection–diffusion-reaction equation; The characteristic-based split (CBS) algorithm; Incompressible Newtonian laminar flows; Incompressible non-Newtonian flows; Free surface and buoyancy driven flows; Compressible high-speed gas flow; Turbulent flows; Flow through porous media; Shallow water problems; Long and medium waves; Short waves; Local conservation; Fluid-structure interaction; Biofluid dynamics; Micro-scale fluid dynamics and molecular dynamics; Computer implementation of the CBS algorithm; Appendices

## Details

- Language:
- English

- Copyright:
- © Butterworth-Heinemann 2014

- Published:
- 20th November 2013

- Imprint:
- Butterworth-Heinemann

- Hardcover ISBN:
- 9781856176309

- eBook ISBN:
- 9780080950976

## 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.