IGA

Preface ix

Chapter 1 IGA: A Projection of FEM onto a Powerful Reduced Basis 1

1.1 Introduction 1

1.2 Some necessary elements for B-spline and NURBS-based IGA 4

1.2.1 B-spline and NURBS basics 4

1.2.2 k-refinement: increasing both the polynomial degree and the regularity 8

1.2.3 The trimming concept and analysis-suitable model issue 12

1.3 The link between IGA and FEM 14

1.3.1 The B©zier extraction 14

1.3.2 The Lagrange extraction 17

1.3.3 The extraction in case of NURBS 19

1.4 Non-invasive implementation using a global bridge between IGA and FEM 20

1.4.1 The common practice 21

1.4.2 A fully non-invasive implementation scheme 23

1.5 Numerical experiments 31

1.5.1 Simple but illustrative examples 31

1.5.2 An example of non-invasive nonlinear isogeometric analysis 37

1.6 Summary and discussion 41

1.7 References 43

Chapter 2 Non-invasive Global/Local Hybrid IGA/FEM Coupling 53

2.1 Introduction 53

2.2 Origin of non-invasiveness: a need for industry 56

2.2.1 Several scales of interest 56

2.2.2 Typical coupling techniques in the industry 57

2.2.3 A non-invasive approach as a remedy 59

2.3 General formulation of the coupling and iterative solution 60

2.3.1 Governing equations 60

2.3.2 Weak form and monolithic approach 62

2.3.3 Non-invasive iterative approach 65

2.4 Interest for the local enrichment of isogeometric models 71

2.4.1 General global-IGA/local-FEM modeling 71

2.4.2 Challenges and implementation issues 73

2.5 Fully non-invasive global-IGA/local-FEM analysis 76

2.5.1 Foundation: non-invasive, non-conforming global/local FEM 76

2.5.2 Extension for the non-invasive hybrid global-IGA/local-FEM coupling 80

2.6 Summary and discussion 103

2.7 References 105

Chapter 3 Non-invasive Spline-based Regularization of FE Digital Image Correlation Problems 115

3.1 Brief introduction 115

3.2 An introduction to the general field of FE-DIC from a numerical point of view 116

3.2.1 FE-DIC: towards an intimate coupling between measurements and simulations 117

3.2.2 Formulation of DIC: a nonlinear least-squares problem 119

3.2.3 Solution of DIC: descent algorithms 124

3.2.4 Extension to stereo-DIC 133

3.2.5 Standard regularization in FE-DIC 146

3.3 Multilevel and non-invasive CAD-based shape measurement 150

3.3.1 Inspiration: structural shape optimization 150

3.3.2 The proposed multilevel geometric and non-invasive scheme 155

3.3.3 Validation through a real example 161

3.3.4 Summary and discussion 165

3.4 A spline FFD-based regularization for FE-DIC 166

3.4.1 The FFD-DIC methodology 167

3.4.2 Application for the displacement measurement of a 2D beam 177

3.4.3 Application to mesh-based shape measurement 180

3.4.4 Summary and discussion 189

3.5 References 191

Index 205