Isogeometric Analysis: Toward Integration of CAD and FEA

by J. Austin Cottrell (Citigroup Inc., USA); Thomas J. R Hughes (University of Texas at Austin, USA); Yuri Bazilevs (University of California, USA)

• ISBN13: 9780470749098
• ISBN10: 0470749091
• Format: eBook
• Copyright: 2009-08-01
• Publisher: Wiley

Summary

"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." - Ren_ 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

Table of Contents

Preface

From CAD and FEA to Isogeometric Analysis: An Historical Perspective

Introduction

The evolution of FEA basis functions

The evolution of CAD representations

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

Notes

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

B-splines

Non-Uniform Rational B-Splines

Multiple patches

Generating a NURBS mesh: a tutorial

Notation

Data for the bent pipe

Notes

NURBS as a Basis for Analysis: Linear Problems

The isoparametric concept

Boundary value problems

Numerical methods

Boundary conditions

Multiple patches revisited

Comparing isogeometric analysis with classical finite element analysis

Shape function routine

Error estimates

Notes

Linear Elasticity

Formulating the equations of elastostatics

Infinite plate with circular hole under constant in-plane tension

Thin-walled structures modeled as solids

Geometrical data for the hemispherical shell

Geometrical data for a cylindrical pipe

Element assembly routine

Notes

Vibrations and Wave Propagation

Longitudinal vibrations of an elastic rod

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

Transverse vibrations of an elastic membrane

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

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

The NASA aluminum testbed cylinder

Wave propagation

Kolmogorov n-widths

Notes

Time-Dependent Problems

Elastodynamics

Semi-discrete methods

Space time finite elements

Nonlinear Isogeometric Analysis

The Newton Raphson method

Isogeometric analysis of nonlinear differential equations

Nonlinear time integration: The generalized-¿ method

Note

Nearly Incompressible Solids

B formulation for linear elasticity using NURBS

F formulation for nonlinear elasticity

Notes

Fluids

Dispersion analysis

The variational multiscale (VMS) method

Advection diffusion equation

Turbulence

Notes

Fluid Structure Interaction and Fluids on Moving Domains

The arbitrary Lagrangian Eulerian (ALE) formulation

Inflation of a balloon

Flow in a patient-specific abdominal aorta with aneurysm

Rotating components

A geometrical template for arterial blood flow modeling

Higher-order Partial Differential Equations

The Cahn Hilliard equation

Numerical results

The continuous/discontinuous Galerkin (CDG) method

Note

Some Additional Geometry

The polar form of polynomials

The polar form of B-splines

Note

State-of-the-Art and Future Directions

State-of-the-art

Future directions

Connectivity Arrays

The INC Array

The IEN array

The ID array

The scalar case

The vector case

The LM array

Note

References

Index

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