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 | |
Table of Contents provided by Publisher. All Rights Reserved. |
The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.