Klienditugi: 7440010 (E-R 10-18)

E-raamat: Isogeometric Analysis - Toward Integration of CAD and FEA: Toward Integration of CAD and FEA [Wiley Online]

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

Formaat: 360 pages
Ilmumisaeg: 14-Aug-2009
Kirjastus: John Wiley & Sons Inc
ISBN-10: 470749083
ISBN-13: 9780470749081

Teised raamatud teemal:

Electronics & communications engineering

Wiley Online
Hind: 158,59 €*
* hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks

Formaat: 360 pages
Ilmumisaeg: 14-Aug-2009
Kirjastus: John Wiley & Sons Inc
ISBN-10: 470749083
ISBN-13: 9780470749081

Teised raamatud teemal:

Electronics & communications engineering

Rohkem infot Wiley Online kohta

Raamatu kodulehekülg: https://onlinelibrary.wiley.com/doi/book/10.1002/9780470749081

Some engineers conduct isogeometric analysis with finite element analysis and some with computer-aided design, and the FEA folks and the CAD folks tend to sit on opposite sides of the cafeteria without acknowledging each other. US banker Cottrell, Thomas J. R. Hughes (computational engineering and sciences, U. of Texas-Austin) and Yuri Bazilevs (structural engineering, U. of California-San Diego) are FEAs but have crossed the line and fraternized with the CADs enough to believe they can effect a reconciliation. Among their topics are non-uniform rational B-splines and their use is analyzing linear problems, vibrations and wave propagation, nonlinear isogeometric analysis, fluids, higher-order partial differential equations, and some additional geometry. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)

“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

Preface

From CAD and FEA to Isogeometric Analysis: An Historical Perspective

(18)

Introduction

(7)

The need for isogeometric analysis

(6)

Computational geometry

(1)

The evolution of FEA basis functions

(4)

The evolution of CAD representations

(4)

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

(3)

Notes

(1)

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

(50)

B-splines

(28)

Knot vectors

(2)

Basis functions

(7)

B-spline geometries

(8)

Refinement

(11)

Non-Uniform Rational B-Splines

(5)

The geometric point of view

(3)

The algebraic point of view

(2)

Multiple patches

(2)

Generating a NURBS mesh: a tutorial

(11)

Preliminary considerations

(3)

Selection of polynomial orders

(1)

Selection of knot vectors

(1)

Selection of control points

(4)

Notation

(4)

Appendix 2.A: Data for the bent pipe

(2)

Notes

(1)

NURBS as a Basis for Analysis: Linear Problems

(40)

The isoparametric concept

(3)

Defining functions on the domain

(1)

Boundary value problems (BVPs)

(1)

Numerical methods

(12)

Galerkin

(5)

Collocation

(3)

Least-squares

(2)

Meshless methods

(1)

Boundary conditions

(3)

Dirichlet boundary conditions

(2)

Neumann boundary conditions

(1)

Robin boundary conditions

(1)

Multiple patches revisited

(5)

Local refinement

(4)

Arbitrary topologies

(1)

Comparing isogeometric analysis with classical finite element analysis

(17)

Code architecture

(3)

Similarities and differences

(1)

Appendix 3.A: Shape function routine

(6)

Appendix 3.B: Error estimates

103

(3)

Notes

106

(3)

Linear Elasticity

109

(40)

Formulating the equations of elastostatics

110

(6)

Strong form

111

(1)

Weak form

111

(1)

Galerkin's method

112

(1)

Assembly

113

(3)

Infinite plate with circular hole under constant in-plane tension

116

(4)

Thin-walled structures modeled as solids

120

(29)

Thin Cylindrical shell with fixed ends subjected to constant internal pressure

120

(3)

The shell obstacle course

123

(8)

Hyperboloidal shell

131

(5)

Hemispherical shell with a stiffener

136

(6)

Appendix 4.A: Geometrical data for the hemispherical shell

142

(1)

Appendix 4.B: Geometrical data for a cylindrical pipe

142

(2)

Appendix 4.C: Element assembly routine

144

(3)

Notes

147

(2)

Vibrations and Wave Propagation

149

(36)

Longitudinal vibrations of an elastic rod

149

(15)

Formulating the problem

149

(2)

Results: NURBS vs. FEA

151

(4)

Analytically computing the discrete spectrum

155

(4)

Lumped mass approaches

159

(5)

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

164

(1)

Transverse vibrations of an elastic membrane

165

(3)

Linear and nonlinear parameterizations revisited

166

(1)

Formulation and results

166

(2)

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

168

(1)

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

169

(3)

Formulating the problem

170

(2)

Results

172

(1)

The NASA aluminum testbed cylinder

172

(1)

Wave propagation

173

(12)

Dispersion analysis

178

(1)

Duality principle

179

(1)

Appendix 5.A: Kolmogorov n-widths

180

(4)

Notes

184

(1)

Time-Dependent problems

185

(12)

Elastodynamics

185

(1)

Semi-discrete methods

186

(5)

Matrix fromulation

186

(1)

Viscous damping

187

(1)

Predictor/multicorrector Newmark algorithms

188

(3)

Space-time finite elements

191

(6)

Nonlinear Isogeometric Analysis

197

(14)

The Newton-Raphson method

197

(1)

Isogemetric analysis of nonlinear differential equations

198

(4)

Nonlinear heat conduction

198

(1)

Applying the Newton-Raphson method

199

(1)

Nonlinear finite element analysis

200

(2)

Nonlinear time integration: The generalized-α method

202

(9)

Note

209

(2)

Nearly Incompressible Solids

211

(16)

B formulation for linear elasticity using NURBS

212

(9)

An intuitive look at mesh locking

213

(2)

Strain projection and the B method

215

(1)

B, the projection operator, and NURBS

216

(4)

Infinite plate with circular hole under in-plane tension

220

(1)

F formulation for nonlinear elasticity

221

(6)

Constitutive equations

221

(1)

Pinched torus

222

(3)

Notes

225

(2)

Fluids

227

(26)

Dispersion analysis

227

(4)

Pure advection: the first-order wave equation

227

(3)

Pure diffusion: the heat equation

230

(1)

The variational multiscale (VMS) method

231

(8)

Numerical example: linear advection-diffusion

232

(1)

The Green's operator

233

(2)

A multiscale decomposition

235

(2)

The variational multiscale formulation

237

(1)

Reconciling Galerkin's method with VMS

238

(1)

Advection-diffusion equation

239

(4)

Formulating the problem

240

(1)

The streamline upwind/Petrov-Galerkin (SUPG) method

240

(1)

Numerical example: advection-diffusion in two dimensions, revisited

241

(2)

Turbulence

243

(10)

Incompressible Navier-Stokes equations

245

(1)

Multiscale residual-based formulation of the incompressible Navier-Stokes equations employing the advective form

246

(2)

Turbulent channel flow

248

(3)

Notes

251

(2)

Fluid-Structure Interation and Fluids on Moving Domains

253

(26)

The arbitrary Lagrangian-Eulerian (ALE) formulation

253

(1)

Inflation of a balloon

254

(2)

Flow in a patient-specific abdominal aorta with aneurysm

256

(8)

Construction of the arterial cross-section

256

(5)

Numerical results

261

(3)

Rotating components

264

(15)

Coupling of the rotating and stationary domains

266

(6)

Numerical example: two propellers spinning in opposite directions

272

(3)

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

275

(4)

Higher-order partial Differential Equations

279

(8)

The Cahn-Hilliard equation

279

(3)

The strong form

280

(1)

The dimensionless strong form

281

(1)

The weak form

281

(1)

Numerical results

282

(1)

A two-dimensional example

282

(1)

A three-dimensional example

282

(1)

The continuous/discontinuous Galerkin (CDG) method

283

(4)

Note

285

(2)

Some Additional Geometry

287

(16)

The polar form of polynomials

287

(6)

Bezier curves and the de Casteljau algorithm

288

(3)

Continuity of piecewise curves

291

(2)

The polar form of B-splines

293

(10)

Knot vectors and control points

293

(2)

Knot insertion and the de Boor algorithm

295

(2)

Bezier decomposition and function subdivision

297

(4)

Note

301

(2)

State-of-the-Art and Future Directions

303

(10)

State-of-the-art

303

(2)

Future directions

305

(8)

Appendix A: Connectivity Arrays

313

(10)

The INC Array

313

(2)

The IEN array

315

(3)

The ID array

318

(1)

The scalar case

318

(1)

The vector case

318

(1)

The LM array

319

(4)

Note

321

(2)

References

323

(10)

Index

333

J. Austin Cottrell, Thomas J. R. Hughes & Yuri Basilievs, University of Texas at Austin, USA J. Austin Cottrell is a postdoctoral scholar at the University of Texas at Austin, having received his PhD in Computational and Applied Mathematics in 2007. Isogeometric analysis is a topic pioneered by his graduate research under the supervision of Tom Hughes.

Tom Hughes was a leading professor of mechanical engineering at Stanford University before being lured to join the University of Texas at Austin in 2002 as Professor of Aerospace Engineering and Engineering Mechanics within the Institute for Computational Engineering and Sciences. He is co-editor of the International Journal of Computer Methods in Applied Mechanics and Engineering, a founder and past President of USACM and IACM, and past Chairman of the Applied Mechanics Division of ASME. A world leader in the development of the finite element method, he has received the Walter L. Huber Civil Engineering Research Prize from ASCE, the Melville Medal from ASME, the Computational Mechanics Award from the Japan Society of Mechanical Engineers, the von Neumann Medal from USACM, the Gauss-Newton Medal from IACM, and the Worcester Reed Warner Medal from ASME. Dr. Hughes is a member of the National Academy of Engineering.

Yuri Basilievs also obtained his PhD from the University of Texas at Austin in 2007 under the supervision of Tom Hughes.

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