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Isogeometric Analysis Toward Integration of CAD and FEA

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ISBN-10: 0470748737

ISBN-13: 9780470748732

Edition: 2009

Authors: Thomas J. R. Hughes, Yuri Bazilevs, J. Austin Cottrell

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Description:

Despite many attempts to unify the fields of CAD and FEA software have to date represented two different (though interconnected) worlds. Isogeometric Analysis presents a highly original yet viable solution to the integration of the two methodologies. Taking advantage of the increased computational power available today, they propose combining both packages using complex NURBS geometry in the FEA application directly. This will allow models to designed, tested and adjusted in one go and offer a breakthrough that will change greatly the way automobile and aerospace design around the world is handled. Groundbreaking publication from the originators of isogeometric analysis, presenting a viable…    
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Book details

Copyright year: 2009
Publisher: John Wiley & Sons, Limited
Publication date: 8/14/2009
Binding: Hardcover
Pages: 360
Size: 7.00" wide x 9.75" long x 0.75" tall
Weight: 2.046
Language: English

Preface
From CAD and FEA to Isogeometric Analysis: An Historical Perspective
Introduction
The need for isogeometric analysis
Computational geometry
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
Knot vectors
Basis functions
B-spline geometries
Refinement
Non-Uniform Rational B-Splines
The geometric point of view
The algebraic point of view
Multiple patches
Generating a NURBS mesh: a tutorial
Preliminary considerations
Selection of polynomial orders
Selection of knot vectors
Selection of control points
Notation
Data for the bent pipe
Notes
NURBS as a Basis for Analysis: Linear Problems
The isoparametric concept
Defining functions on the domain
Boundary value problems (BVPs)
Numerical methods
Galerkin
Collocation
Least-squares
Meshless methods
Boundary conditions
Dirichlet boundary conditions
Neumann boundary conditions
Robin boundary conditions
Multiple patches revisited
Local refinement
Arbitrary topologies
Comparing isogeometric analysis with classical finite element analysis
Code architecture
Similarities and differences
Shape function routine
Error estimates
Notes
Linear Elasticity
Formulating the equations of elastostatics
Strong form
Weak form
Galerkin's method
Assembly
Infinite plate with circular hole under constant in-plane tension
Thin-walled structures modeled as solids
Thin cylindrical shell with fixed ends subjected to constant internal pressure
The shell obstacle course
Hyperboloidal shell
Hemispherical shell with a stiffener
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
Formulating the problem
Results: NURBS vs. FEA
Analytically computing the discrete spectrum
Lumped mass approaches
Rotation-free analysis of the transverse vibrations of a Bernoulli-Euler beam
Transverse vibrations of an elastic membrane
Linear and nonlinear parameterizations revisited
Formulation and results
Rotation-free analysis of the transverse vibrations of a Poisson-Kirchhoff plate
Vibrations of a clamped thin circular plate using three-dimensional solid elements
Formulating the problem
Results
The NASA aluminum testbed cylinder
Wave propagation
Dispersion analysis
Duality principle
Kolmogorov n-widths
Notes
Time-Dependent Problems
Elastodynamics
Semi-discrete methods
Matrix formulation
Viscous damping
Predictor/multicorrector Newmark algorithms
Space-time finite elements
Nonlinear Isogeometric Analysis
The Newton-Raphson method
Isogeometric analysis of nonlinear differential equations
Nonlinear heat conduction
Applying the Newton-Raphson method
Nonlinear finite element analysis
Nonlinear time integration: The generalized-a method
Note
Nearly Incompressible Solids
B formulation for linear elasticity using NURBS
An intuitive look at mesh locking
Strain projection and the B method
B, the projection operator, and NURBS
Infinite plate with circular hole under in-plane tension
F formulation for nonlinear elasticity
Constitutive equations
Pinched torus
Notes
Fluids
Dispersion analysis
Pure advection: the first-order wave equation
Pure diffusion: the heat equation
The variational multiscale (VMS) method
Numerical example: linear advection-diffusion
The Green's operator
A multiscale decomposition
The variational multiscale formulation
Reconciling Galerkin's method with VMS
Advection-diffusion equation
Formulating the problem
The streamline upwind/Petrov-Galerkin (SUPG) method
Numerical example: advection-diffusion in two dimensions, revisited
Turbulence
Incompressible Navier-Stokes equations
Multiscale residual-based formulation of the incompressible Navier-Stokes equations employing the advective form
Turbulent channel flow
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
Construction of the arterial cross-section
Numerical results
Rotating components
Coupling of the rotating and stationary domains
Numerical example: two propellers spinning in opposite directions
A geometrical template for arterial blood flow modeling
Higher-order Partial Differential Equations
The Cahn-Hilliard equation
The strong form
The dimensionless strong form
The weak form
Numerical results
A two-dimensional example
A three-dimensional example
The continuous/discontinuous Galerkin (CDG) method
Note
Some Additional Geometry
The polar form of polynomials
Bezier curves and the de Casteljau algorithm
Continuity of piecewise curves
The polar form of B-splines
Knot vectors and control points
Knot insertion and the de Boor algorithm
Bezier decomposition and function subdivision
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