IGA.

Format:

Book

Author/Creator:

Bouclier, Robin.

Contributor:

Passieux, Jean-Charles.

Language:

English

Subjects (All):

Isogeometric analysis.

Finite element method--Data processing.

Finite element method.

Physical Description:

1 online resource (230 pages)

Edition:

1st ed.

Place of Publication:

Newark : John Wiley & Sons, Incorporated, 2023.

Summary:

Isogeometric analysis (IGA) consists of using the same higher-order and smooth spline functions for the representation of geometry in Computer Aided Design as for the approximation of solution fields in Finite Element Analysis. Now, almost twenty years after its creation, substantial works are being reported in IGA, making it very competitive in scientific computing. This book proposes to use IGA jointly with standard finite element methods (FEM), presenting IGA as a projection of FEM on a more regular reduced basis. By shedding new light on how IGA relates to FEM, we can see how IGA can be implemented on top of an FE code in order to improve the solution of problems that require more regularity. This is illustrated by using IGA with FEM in a non-invasive fashion to perform efficient and robust multiscale global/local simulations in solid mechanics. Furthermore, we show that IGA can regularize the inverse problem of FE digital image correlation in experimental mechanics.

Contents:

Cover

Title Page

Copyright Page

Contents

Preface

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

1.1. Introduction

1.2. Some necessary elements for B-spline andNURBS-based IGA

1.2.1.B-spline andNURBS basics

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

1.2.3. The trimming concept and analysis-suitable model issue

1.3.The link between IGAandFEM

1.3.1.TheBézier extraction

1.3.2.TheLagrangeextraction

1.3.3.The extractionin case ofNURBS

1.4. Non-invasive implementation using a global bridge between IGA andFEM

1.4.1.The commonpractice

1.4.2. A fully non-invasive implementation scheme

1.5.Numerical experiments

1.5.1. Simple but illustrative examples

1.5.2. An example of non-invasive nonlinear isogeometric analysis

1.6.Summaryand discussion

1.7.References

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

2.1. Introduction

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

2.2.1.Several scales of interest

2.2.2. Typical coupling techniques in the industry

2.2.3. A non-invasive approach as a remedy

2.3. General formulation of the coupling and iterative solution

2.3.1.Governingequations

2.3.2.Weak form and monolithic approach

2.3.3.Non-invasiveiterative approach

2.4. Interest for the local enrichment of isogeometric models

2.4.1. General global-IGA/local-FEM modeling

2.4.2.Challenges and implementationissues

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

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

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

2.6.Summaryand discussion

2.7.References

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

3.1. Brief introduction.

3.2. An introduction to the general field of FE-DIC from a numerical point ofview

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

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

3.2.3.SolutionofDIC: descent algorithms

3.2.4.Extensionto stereo-DIC

3.2.5.Standardregularizationin FE-DIC

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

3.3.1. Inspiration: structural shape optimization

3.3.2. The proposed multilevel geometric and non-invasive scheme

3.3.3. Validation through a real example

3.3.4.Summaryand discussion

3.4.AsplineFFD-based regularizationforFE-DIC

3.4.1. The FFD-DIC methodology

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

3.4.3. Application to mesh-based shape measurement

3.4.4.Summaryand discussion

3.5.References

Index

EULA.

Notes:

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Bouclier, Robin IGA: Non-Invasive Coupling with FEM and Regularization of Digital Image Correlation Problems, Volume 2

ISBN:

9781394229635

1394229631

9781394229611

1394229615

OCLC:

1430211424