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Isogeometric Analysis : Toward Inregration of CAD and FEA
Cottrell, J. Austin Hughes, Thomas J. R. Bazilevs, Yuri
Hardcover:ハードカバー版  |
Preface xi
From CAD and FEA to Isogeometric Analysis: 1 (18)
An Historical Perspective
Introduction 1 (7)
The need for isogeometric analysis 1 (6)
Computational geometry 7 (1)
The evolution of FEA basis functions 8 (4)
The evolution of CAD representations 12 (4)
Things you need to get used to in order 16 (3)
to understand NURBS-based isogeometric
analysis
Notes 18 (1)
NURBS as a Pre-analysis Tool: Geometric 19 (50)
Design and Mesh Generation
B-splines 19 (28)
Knot vectors 19 (2)
Basis functions 21 (7)
B-spline geometries 28 (8)
Refinement 36 (11)
Non-Uniform Rational B-Splines 47 (5)
The geometric point of view 47 (3)
The algebraic point of view 50 (2)
Multiple patches 52 (2)
Generating a NURBS mesh: a tutorial 54 (11)
Preliminary considerations 56 (3)
Selection of polynomial orders 59 (1)
Selection of knot vectors 60 (1)
Selection of control points 61 (4)
Notation 65 (4)
Appendix 2.A: Data for the bent pipe 66 (2)
Notes 68 (1)
NURBS as a Basis for Analysis: Linear 69 (40)
Problems
The isoparametric concept 69 (3)
Defining functions on the domain 71 (1)
Boundary value problems (BVPs) 72 (1)
Numerical methods 72 (12)
Galerkin 73 (5)
Collocation 78 (3)
Least-squares 81 (2)
Meshless methods 83 (1)
Boundary conditions 84 (3)
Dirichlet boundary conditions 84 (2)
Neumann boundary conditions 86 (1)
Robin boundary conditions 86 (1)
Multiple patches revisited 87 (5)
Local refinement 87 (4)
Arbitrary topologies 91 (1)
Comparing isogeometric analysis with 92 (17)
classical finite element analysis
Code architecture 94 (3)
Similarities and differences 97 (1)
Appendix 3.A: Shape function routine 97 (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 116(4)
constant in-plane tension
Thin-walled structures modeled as solids 120(29)
Thin Cylindrical shell with fixed ends 120(3)
subjected to constant internal pressure
The shell obstacle course 123(8)
Hyperboloidal shell 131(5)
Hemispherical shell with a stiffener 136(6)
Appendix 4.A: Geometrical data for the 142(1)
hemispherical shell
Appendix 4.B: Geometrical data for a 142(2)
cylindrical pipe
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 155(4)
spectrum
Lumped mass approaches 159(5)
Rotation-free analysis of the transverse 164(1)
vibrations of a Bernoulli-Euler beam
Transverse vibrations of an elastic 165(3)
membrane
Linear and nonlinear parameterizations 166(1)
revisited
Formulation and results 166(2)
Rotation-free analysis of the transverse 168(1)
vibrations of a Poisson-Kirchhoff plate
Vibrations of a clamped thin circular 169(3)
plate using three-dimensional solid
elements
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 188(3)
algorithms
Space-time finite elements 191(6)
Nonlinear Isogeometric Analysis 197(14)
The Newton-Raphson method 197(1)
Isogemetric analysis of nonlinear 198(4)
differential equations
Nonlinear heat conduction 198(1)
Applying the Newton-Raphson method 199(1)
Nonlinear finite element analysis 200(2)
Nonlinear time integration: The 202(9)
generalized-α method
Note 209(2)
Nearly Incompressible Solids 211(16)
B formulation for linear elasticity using 212(9)
NURBS
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 220(1)
in-plane tension
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 227(3)
equation
Pure diffusion: the heat equation 230(1)
The variational multiscale (VMS) method 231(8)
Numerical example: linear 232(1)
advection-diffusion
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 240(1)
(SUPG) method
Numerical example: advection-diffusion 241(2)
in two dimensions, revisited
Turbulence 243(10)
Incompressible Navier-Stokes equations 245(1)
Multiscale residual-based formulation 246(2)
of the incompressible Navier-Stokes
equations employing the advective form
Turbulent channel flow 248(3)
Notes 251(2)
Fluid-Structure Interation and Fluids on 253(26)
Moving Domains
The arbitrary Lagrangian-Eulerian (ALE) 253(1)
formulation
Inflation of a balloon 254(2)
Flow in a patient-specific abdominal 256(8)
aorta with aneurysm
Construction of the arterial 256(5)
cross-section
Numerical results 261(3)
Rotating components 264(15)
Coupling of the rotating and stationary 266(6)
domains
Numerical example: two propellers 272(3)
spinning in opposite directions
Appendix 10.A: A geometrical template 275(4)
for arterial blood flow modeling
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 283(4)
(CDG) method
Note 285(2)
Some Additional Geometry 287(16)
The polar form of polynomials 287(6)
Bezier curves and the de Casteljau 288(3)
algorithm
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 297(4)
subdivision
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
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