IGA: Non-Conforming Coupling and Shape Optimization of Complex Multipatch Structures

ISBN-13: 9781786308245 / Angielski / Twarda / 2022 / 256 str.

Bouclier

Spis treści

ContentsPreface ixChapter 1: Introduction to IGA: Key Ingredients for the Analysis and Optimization of Complex Structures 11.1 Brief introduction 11.2 Geometric modeling and simulation with splines 21.2.1.Parametric representationof geometries 21.2.2 B-spline and NURBS technologies 51.2.3 Design features and shape parameterization 151.2.4 Spline-based finite element analysis: isogeometric principle 211.3 Improved CAD-CAE integration for robust optimization 231.3.1 Returning to the original motivations behind IGA 231.3.2 An ideal framework for parametric shape optimization 251.4.The analysis-suitablemodel issue 271.4.1.The trimmingconcept 281.4.2 Non-conformingmultipatch parameterization 301.4.3 Imposingshape variation 331.5 Computation of non-conforming interfaces: a brief overview of usual weak coupling methods 351.5.1.Governingequations 361.5.2.Penalty coupling 381.5.3.Mortar coupling 391.5.4.Nitsche coupling 41Chapter 2: Non-invasive Coupling for Flexible Global/Local IGA 452.1 Brief introduction 452.2 The standard non-invasive strategy 462.2.1.Origin 462.2.2 Non-invasive resolution of the coupling problem 472.3 Interest in the field of IGA 542.3.1 Global/local modeling in IGA 552.3.2.Challenges 572.4 A robust algorithm for non-conforming global/local IGA 592.4.1 Reference formulation: non-symmetric Nitsche coupling 592.4.2 A Nitsche-based non-invasive algorithm 642.4.3.Validation 722.5.Summaryand discussion 84Chapter 3: Domain Decomposition Solvers for Efficient Multipatch IGA 873.1 Introduction 873.2 Benefiting from the additional Lagrange multiplier field for multipatch analysis 893.3 Case of multipatch Kirchhoff-Love shell analysis 913.3.1 Kirchhoff-Love shell formulation: basics 923.3.2 Formulation of the coupled problem 973.3.3 Preliminary results: monolithic resolution 1003.4 On the construction of dual domain decomposition solvers 1033.4.1 Formulation of the interface problem 1043.4.2.Solvingthe interfaceproblem 1063.4.3 Null space and pseudo-inverse 1103.4.4.Preconditioning 1113.5 Numerical investigation of the developed algorithms 1153.5.1.Standardsolid elasticity 1163.5.2 Heterogeneous plate bending 1213.5.3.Scordelis-Loroof 1233.5.4.Stiffenedpanel 1253.6.Summaryand discussion 128Chapter 4: Isogeometric Shape Optimization of Multipatch and Complex Structures 1314.1 Introduction 1314.2 Isogeometric shape optimization framework 1334.2.1.Optimizationflowchart 1334.2.2 Multilevel design 1334.2.3.Design variables 1354.2.4.Formulationandresolution 1364.3 Unify the DD approach and multipatch optimization: towards ultimate efficiency 1454.3.1 DD computation of the response functions 1454.3.2 DD computation of the sensitivities 1464.3.3.Non-designparts 1474.3.4.Fast re-analysis 1484.3.5.Optimizationalgorithm 1494.4 Innovative design of multipatch structures: focus on aeronautical stiffenedpanels 1494.4.1 Geometric modeling: embedded entities 1504.4.2 Analysis: an embedded Kirchhoff-Love shell element 1564.4.3.Two preliminary examples to illustrate the design capabilities 1594.5 Application to solid structures and first interests 1684.5.1.Simple extensionof themethod 1694.5.2.Atest case in 2D 1714.6 Advanced numerical optimization examples 1754.6.1 Global shell optimization: stiffened roof 1764.6.2.Local shell optimization: curvedwall 1794.6.3.Designingan aircraftwing-box 1854.7 Towards the optimal design of structural details within isogeometric patches 1924.7.1.Asimple but instructive test case 1924.7.2 Unify the non-invasive global/local approach and the optimizationof local details 1934.7.3.Preliminaryresults and perspectives 1974.8.Summaryand discussion 198References 201Index 229

O autorze

Robin Bouclier is Associate Professor at INSA-Toulouse, France. His work on isogeometric analysis started during his PhD in Lyon. He has since brought this technology to the scientific landscape of Toulouse, focusing on its development for image registration and shape optimization.Thibaut Hirschler is a post-doctoral researcher at École Polytechnique Fédérale de Lausanne, Switzerland. His research mainly focuses on the development of isogeometric modeling approaches that are suitable for designing new and innovative structures.