Isogeometric Analysis

Preface 1 From CAD and FEA to Isogeometric Analysis: An HistoricalPerspective 1.1 Introduction 1.2 The evolution of FEA basis functions 1.3 The evolution of CAD representations 1.4 Things you need to get used to in order to understandNURBS-based isogeometric analysis Notes 2 NURBS as a Pre-analysis Tool: Geometric Design and MeshGeneration 2.1 B-splines 2.2 Non-Uniform Rational B-Splines 2.3 Multiple patches 2.4 Generating a NURBS mesh: a tutorial 2.5 Notation Appendix 2.A: Data for the bent pipe Notes 3 NURBS as a Basis for Analysis: Linear Problems 3.1 The isoparametric concept 3.2 Boundary value problems 3.3 Numerical methods 3.4 Boundary conditions 3.5 Multiple patches revisited 3.6 Comparing isogeometric analysis with classical finiteelement analysis Appendix 3.A: Shape function routine Appendix 3.B: Error estimates Notes 4 Linear Elasticity 4.1 Formulating the equations of elastostatics 4.2 Infinite plate with circular hole under constant in-planetension 4.3 Thin-walled structures modeled as solids Appendix 4.A: Geometrical data for the hemispherical shell Appendix 4.B: Geometrical data for a cylindrical pipe Appendix 4.C: Element assembly routine Notes 5 Vibrations and Wave Propagation 5.1 Longitudinal vibrations of an elastic rod 5.2 Rotation-free analysis of the transverse vibrations of aBernoulli-Euler beam 5.3 Transverse vibrations of an elastic membrane 5.4 Rotation-free analysis of the transverse vibrations of aPoisson-Kirchhoff plate 5.5 Vibrations of a clamped thin circular plate usingthree-dimensional solid elements 5.6 The NASA aluminum testbed cylinder 5.7 Wave propagation Appendix 5.A: Kolmogorov n-widths Notes 6 Time-Dependent Problems 6.1 Elastodynamics 6.2 Semi-discrete methods 6.3 Space-time finite elements 7 Nonlinear Isogeometric Analysis 7.1 The Newton-Raphson method 7.2 Isogeometric analysis of nonlinear differentialequations 7.3 Nonlinear time integration: The generalized-alphamethod Note 8 Nearly Incompressible Solids 8.1 B formulation for linear elasticity using NURBS 8.2 F formulation for nonlinear elasticity Notes 9 Fluids 9.1 Dispersion analysis 9.2 The variational multiscale (VMS) method 9.3 Advection-diffusion equation 9.4 Turbulence Notes 10 Fluid-Structure Interaction and Fluids on MovingDomains 10.1 The arbitrary Lagrangian-Eulerian (ALE)formulation 10.2 Inflation of a balloon 10.3 Flow in a patient-specific abdominal aorta withaneurysm 10.4 Rotating components Appendix 10.A: A geometrical template for arterial blood flowmodeling 11 Higher-order Partial Differential Equations 11.1 The Cahn-Hilliard equation 11.2 Numerical results 11.3 The continuous/discontinuous Galerkin (CDG) method Note 12 Some Additional Geometry 12.1 The polar form of polynomials 12.2 The polar form of B-splines Note 13 State-of-the-Art and Future Directions 13.1 State-of-the-art 13.2 Future directions Appendix A: Connectivity Arrays A.1 The INC Array A.2 The IEN array A.3 The ID array A.3.1 The scalar case A.3.2 The vector case A.4 The LM array Note References Index