# Isogeometric Analysis: Toward Integration of CAD and FEA

ISBN: 978-0-470-74873-2
360 pages
September 2009

## Description

“The authors are the originators of isogeometric analysis, are excellent scientists and good educators. It is very original. There is no other book on this topic.”
René de Borst, Eindhoven University of Technology

Written by leading experts in the field and featuring fully integrated colour throughout, Isogeometric Analysis provides a groundbreaking solution for the integration of CAD and FEA technologies. Tom Hughes and his researchers, Austin Cottrell and Yuri Bazilevs, present their pioneering isogeometric approach, which aims to integrate the two techniques of CAD and FEA using precise NURBS geometry in the FEA application. This technology offers the potential to revolutionise automobile, ship and airplane design and analysis by allowing models to be designed, tested and adjusted in one integrative stage.

Providing a systematic approach to the topic, the authors begin with a tutorial introducing the foundations of Isogeometric Analysis, before advancing to a comprehensive coverage of the most recent developments in the technique. The authors offer a clear explanation as to how to add isogeometric capabilities to existing finite element computer programs, demonstrating how to implement and use the technology. Detailed programming examples and datasets are included to impart a thorough knowledge and understanding of the material.

• Provides examples of different applications, showing the reader how to implement isogeometric models
• Addresses readers on both sides of the CAD/FEA divide
• Describes Non-Uniform Rational B-Splines (NURBS) basis functions
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## Table of Contents

Preface

1 From CAD and FEA to Isogeometric Analysis: An Historical Perspective

1.1 Introduction

1.2 The evolution of FEA basis functions

1.3 The evolution of CAD representations

1.4 Things you need to get used to in order to understand NURBS-based isogeometric analysis

Notes

2 NURBS as a Pre-analysis Tool: Geometric Design and Mesh Generation

2.1 B-splines

2.2 Non-Uniform Rational B-Splines

2.3 Multiple patches

2.4 Generating a NURBS mesh: a tutorial

2.5 Notation

Appendix 2.A: Data for the bent pipe

Notes

3 NURBS as a Basis for Analysis: Linear Problems

3.1 The isoparametric concept

3.2 Boundary value problems

3.3 Numerical methods

3.4 Boundary conditions

3.5 Multiple patches revisited

3.6 Comparing isogeometric analysis with classical finite element analysis

Appendix 3.A: Shape function routine

Appendix 3.B: Error estimates

Notes

4 Linear Elasticity

4.1 Formulating the equations of elastostatics

4.2 Infinite plate with circular hole under constant in-plane tension

4.3 Thin-walled structures modeled as solids

Appendix 4.A: Geometrical data for the hemispherical shell

Appendix 4.B: Geometrical data for a cylindrical pipe

Appendix 4.C: Element assembly routine

Notes

5 Vibrations and Wave Propagation

5.1 Longitudinal vibrations of an elastic rod

5.2 Rotation-free analysis of the transverse vibrations of a Bernoulli–Euler beam

5.3 Transverse vibrations of an elastic membrane

5.4 Rotation-free analysis of the transverse vibrations of a Poisson–Kirchhoff plate

5.5 Vibrations of a clamped thin circular plate using three-dimensional solid elements

5.6 The NASA aluminum testbed cylinder

5.7 Wave propagation

Appendix 5.A: Kolmogorov n-widths

Notes

6 Time-Dependent Problems

6.1 Elastodynamics

6.2 Semi-discrete methods

6.3 Space–time finite elements

7 Nonlinear Isogeometric Analysis

7.1 The Newton–Raphson method

7.2 Isogeometric analysis of nonlinear differential equations

7.3 Nonlinear time integration: The generalized-α method

Note

8 Nearly Incompressible Solids

8.1 B formulation for linear elasticity using NURBS

8.2 F formulation for nonlinear elasticity

Notes

9 Fluids

9.1 Dispersion analysis

9.2 The variational multiscale (VMS) method

9.3 Advection–diffusion equation

9.4 Turbulence

Notes

10 Fluid–Structure Interaction and Fluids on Moving Domains

10.1 The arbitrary Lagrangian–Eulerian (ALE) formulation

10.2 Inflation of a balloon

10.3 Flow in a patient-specific abdominal aorta with aneurysm

10.4 Rotating components

Appendix 10.A: A geometrical template for arterial blood flow modeling

11 Higher-order Partial Differential Equations

11.1 The Cahn–Hilliard equation

11.2 Numerical results

11.3 The continuous/discontinuous Galerkin (CDG) method

Note

12 Some Additional Geometry

12.1 The polar form of polynomials

12.2 The polar form of B-splines

Note

13 State-of-the-Art and Future Directions

13.1 State-of-the-art

13.2 Future directions

Appendix A: Connectivity Arrays

A.1 The INC Array

A.2 The IEN array

A.3 The ID array

A.3.1 The scalar case

A.3.2 The vector case

A.4 The LM array

Note

References

Index

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## Reviews

"This is the most beautiful scientific book that I have ever seen. (I am excluding popular science books from this statement; this book matches some of them in its beauty.) The authors, editors and publishers should be congratulated for giving so much attention not just to the content but also to the way the book looks. It is extremely inviting to read." (Iacm Expressions, 1 October 2010)
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