Оглавление
Robin Bouclier. IGA
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
IGA: Non-conforming Coupling and Shape Optimization of Complex Multipatch Structures
Preface. P.1. The book series
P.2. The present volume
P.2.1. Intended audience
P.2.2. Organization of the text
P.3. Acknowledgments
1. Introduction to IGA: Key Ingredients for the Analysis and Optimization of Complex Structures. 1.1. Brief introduction
1.2. Geometric modeling and simulation with splines
1.2.1. Parametric representation of geometries
1.2.2. B-spline and NURBS technologies
1.2.2.1. B-spline curves
1.2.2.2. B-spline basis functions
1.2.2.3. NURBS curves
1.2.2.4. Surfaces and volumes
1.2.3. Design features and shape parameterization
1.2.3.1. Refinement
1.2.3.2. Geometric modification
1.2.4. Spline-based finite element analysis: isogeometric principle. 1.2.4.1. General idea
1.2.4.2. Performance
1.3. Improved CAD-CAE integration for robust optimization
1.3.1. Returning to the original motivations behind IGA
1.3.2. An ideal framework for parametric shape optimization
1.4. The analysis-suitable model issue
1.4.1. The trimming concept
1.4.2. Non-conforming multipatch parameterization
1.4.3. Imposing shape variation
1.5. Computation of non-conforming interfaces: a brief overview of usual weak coupling methods
1.5.1. Governing equations
1.5.2. Penalty coupling
1.5.3. Mortar coupling
1.5.4. Nitsche coupling
2. Non-invasive Coupling for Flexible Global/Local IGA. 2.1. Brief introduction
2.2. The standard non-invasive strategy
2.2.1. Origin
2.2.2. Non-invasive resolution of the coupling problem
2.2.2.1. The global/local problem
2.2.2.2. Monolithic resolution
2.2.2.3. Non-invasive iterative resolution
2.3. Interest in the field of IGA
2.3.1. Global/local modeling in IGA
2.3.1.1. Spline re-parameterization
2.3.1.2. Treatment of an unfitted spline domain
2.3.1.3. Non-invasive strategy
2.3.2. Challenges
2.4. A robust algorithm for non-conforming global/local IGA
2.4.1. Reference formulation: non-symmetric Nitsche coupling
2.4.1.1. Motivation
2.4.1.2. Theory
2.4.2. A Nitsche-based non-invasive algorithm
2.4.2.1. Monolithic resolution
2.4.2.2. Making the Nitsche method non-invasive
2.4.2.3. Incremental formulation and mechanical interpretation
2.4.3. Validation
2.4.3.1. Curved beam subjected to end shear
2.4.3.2. Infinite plate with a circular hole
2.4.3.3. Plate with a central inclusion
2.5. Summary and discussion
3. Domain Decomposition Solvers for Efficient Multipatch IGA. 3.1. Introduction
3.2. Benefiting from the additional Lagrange multiplier field for multipatch analysis
3.3. Case of multipatch Kirchhoff–Love shell analysis
3.3.1. Kirchhoff–Love shell formulation: basics. 3.3.1.1. Kinematics
3.3.1.2. Continuum mechanics
3.3.1.3. Element formulation
3.3.2. Formulation of the coupled problem
3.3.2.1. Kinematic coupling conditions
3.3.2.2. Weak coupling with a Mortar approach
3.3.3. Preliminary results: monolithic resolution
3.3.3.1. Bending and shear of a simple beam
3.3.3.2. T-shape beam
3.4. On the construction of dual domain decomposition solvers
3.4.1. Formulation of the interface problem
3.4.1.1. Equilibrium of floating sub-domains
3.4.1.2. Substitution
3.4.2. Solving the interface problem
3.4.2.1. Projection
3.4.2.2. Parallel computing
3.4.3. Null space and pseudo-inverse
3.4.4. Preconditioning
3.4.4.1. Dirichlet preconditioner
3.4.4.2. Generalized preconditioner
3.5. Numerical investigation of the developed algorithms
3.5.1. Standard solid elasticity
3.5.1.1. Homogeneous 2D cantilever beam
3.5.1.2. Heterogeneous 2D cantilever beam
3.5.2. Heterogeneous plate bending
3.5.3. Scordelis–Lo roof
3.5.4. Stiffened panel
3.6. Summary and discussion
4. Isogeometric Shape Optimization of Multipatch and Complex Structures. 4.1. Introduction
4.2. Isogeometric shape optimization framework
4.2.1. Optimization flowchart
4.2.2. Multilevel design
4.2.3. Design variables
4.2.4. Formulation and resolution. 4.2.4.1. A constrained optimization problem
4.2.4.2. Gradient-based optimization algorithm
4.2.4.3. Sensitivity analysis
4.3. Unify the DD approach and multipatch optimization: towards ultimate efficiency
4.3.1. DD computation of the response functions
4.3.2. DD computation of the sensitivities
4.3.3. Non-design parts
4.3.4. Fast re-analysis
4.3.5. Optimization algorithm
4.4. Innovative design of multipatch structures: focus on aeronautical stiffened panels
4.4.1. Geometric modeling: embedded entities
4.4.1.1. Geometric challenges
4.4.1.2. Using spline compositions for shape updating. 4.4.1.2.1. Embedded entities
4.4.1.2.2. Mathematical description
4.4.1.2.3. Potential for shape optimization
4.4.2. Analysis: an embedded Kirchhoff–Love shell element
4.4.2.1. Mid-surface defined by spline composition
4.4.2.2. Approximation space for the displacement field
4.4.3. Two preliminary examples to illustrate the design capabilities
4.4.3.1. FFD versus embedded shape updates. 4.4.3.1.1. Arch under constant vertical load
4.4.3.1.2. Resolution with the two variants of the embedded strategy
4.4.3.2. Optimizing the global shape of a multipatch structure. 4.4.3.2.1. Initial square roof problem
4.4.3.2.2. The multipatch version solved with the FFD shape update approach
4.5. Application to solid structures and first interests
4.5.1. Simple extension of the method
4.5.2. A test case in 2D
4.6. Advanced numerical optimization examples
4.6.1. Global shell optimization: stiffened roof. 4.6.1.1. Settings and geometric modeling
4.6.1.2. Results and discussion
4.6.2. Local shell optimization: curved wall
4.6.2.1. Settings and geometric modeling
4.6.2.2. Results and discussion
4.6.3. Designing an aircraft wing-box
4.6.3.1. Versatile construction of an aircraft wingbox
4.6.3.2. Structural analysis
4.6.3.3. Shape optimization
4.7. Towards the optimal design of structural details within isogeometric patches
4.7.1. A simple but instructive test case
4.7.2. Unify the non-invasive global/local approach and the optimization of local details
4.7.3. Preliminary results and perspectives
4.8. Summary and discussion
References
Index. A, B
C, D
E, F
G, I
K, L
M, N
P
S, T
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