Читать книгу IGA - Robin Bouclier - Страница 4

1 PrefaceFigure P.1. Innovative stiffened structures with curvilinear stiffeners: (a) fro...

2 Chapter 1Figure 1.1. Two simple planar curvesFigure 1.2. Two simple (surface and volume) geometric objectsFigure 1.3. Quadratic B-spline curve with Figure 1.4. Quadratic B-spline curve with a non-uniform knot-vector. The initial...Figure 1.5. Examples of B-spline basis functions of different degrees. The same ...Figure 1.6. Differentiability of cubic B-spline functions in the case of a unifo...Figure 1.7. An example of a NURBS curve: influence of the weights on the basis f...Figure 1.8. Example of bivariate B-spline basis functions. The lower continuity ...Figure 1.9. Example of a free-form surface described with a cubic B-spline surfa...Figure 1.10. Example of a hollow cylinder described with a quadratic NURBS volum...Figure 1.11. Refinement procedures applied to a B-spline curveFigure 1.12. Example of shape modification by altering the spatial location of t...Figure 1.13. The original motivation of IGA is to improve engineering design and...Figure 1.14. Engineering systems: each engineer has their own vision and require...Figure 1.15. Main steps for shape optimization (inspired from Bletzinger (2014))...Figure 1.16. Illustration of the trimming concept on a simple example of a plate...Figure 1.17. B-spline and NURBS modeling generate multipatch geometries where ea...Figure 1.18. Connecting patches that are initially non-matching (a): the basis f...Figure 1.19. Example of a non-conforming multipatch parameterization: the interf...Figure 1.20. The discretization of the plate needs to be updated at each modific...Figure 1.21. The discretization of the panel needs to be updated at each shape m...Figure 1.22. Reference domain coupling problem. For a color version of this figu...

3 Chapter 2Figure 2.1. Example of a global/local problem. The global model over sub-domainΩ...Figure 2.2. The iterative non-invasive exchange procedure. For a color version o...Figure 2.3. Three different strategies may be applied in IGA to numerically solv...Figure 2.4. Principle of the recursive quadrature approach used in FCM (Ruesset ...Figure 2.5. Global/local non-invasive Nitsche analysis of the curved beam proble...Figure 2.6. Convergence of the error in the energy norm for the curved beam prob...Figure 2.7. Infinite plate with a hole: description and data of the problem. For...Figure 2.8. Global/local non-invasive Nitsche analysis of the infinite plate wit...Figure 2.9. Sequence of meshes considered for the convergence study. For a color...Figure 2.10. Convergence curves in energy norm for the infinite plate with a hol...Figure 2.11. Jump of the interface tractions alongΓ (computed as ||σ₁n₁₁ + σ₂n₂|...Figure 2.12. Plate with a central inclusion: description and discretization of t...Figure 2.13. Plate with a central inclusion: von Mises stress distribution. For ...Figure 2.14. Plate with a central inclusion: jump of the interface tractions alo...

4 Chapter 3Figure 3.1. Principle of non-overlapping domain decomposition methods (DDM): (a)...Figure 3.2. Schematic view of a shell body and the associated Kirchhoff–Love mod...Figure 3.3. Kinematic constraints for Kirchhoff–Love shells: at the patch juncti...Figure 3.4. Cantilever beam with end load: the beam is decomposed into two non-m...Figure 3.5. T-Beam non-conforming coupling. (a) Description of the problem: the ...Figure 3.6. Parallel computing: the communication between the sub-domains is per...Figure 3.7. Illustration of the preconditioning step (generalized preconditioner...Figure 3.8. Description and results of the homogeneous 2D cantilever beam proble...Figure 3.9. Description and results of the heterogeneous 2D cantilever beam prob...Figure 3.10. Convergence of the dual DD solver when applied to the heterogeneous...Figure 3.11. Description and results of the bending plate problem. The plate is ...Figure 3.12. Description and results for the Scordelis–Lo roof test case. Two di...Figure 3.13. Description and results for the stiffened panel problem. It consist...Figure 3.14. Convergence plot of the dual DD solver when applied to the stiffene...

5 Chapter 4Figure 4.1. Isogeometric shape optimization flowchart: overview of the main step...Figure 4.2. Multilevel design approach: design and analysis spaces describe the ...Figure 4.3. Shape modification of a hemisphere. The control points move radially...Figure 4.4. Geometric difficulties to impose design modifications to a stiffened...Figure 4.5. Construction of a stiffened structure using embedded surfaces. The f...Figure 4.6. Generating a geometric complex model of a thin structure by using th...Figure 4.7. Using spine compositions offers two possibilities for imposing shape...Figure 4.8. Settings for the shape optimization of an arch under constant vertic...Figure 4.9. Resolution of the arch optimization problem with embedded Kirchhoff–...Figure 4.10. Settings and optimization results for the initial square roof probl...Figure 4.11. Optimal shape of a square roof subjected to an uniform snow load: (...Figure 4.12. The shape update in the case of multipatch models should be aware o...Figure 4.13. Setting up an FFD-like shape parameterization in order to impose sh...Figure 4.14. Optimization history of the FFD shape update approach applied to th...Figure 4.15. Comparison of the results obtained for the shape optimization of th...Figure 4.16. Composition of trivariates for proper complex solid geometriesFigure 4.17. Transforming a non-matching multipatch model into an optimization s...Figure 4.18. Design optimization of a cantilever beam using the FFD-based approa...Figure 4.19. Settings for the stiffened roof problem. The geometric modeling emp...Figure 4.20. Several intermediary shapes obtained during the optimization of the...Figure 4.21. Final design and result for the stiffened roof problem once the alg...Figure 4.22. Problem description and geometric construction of the stiffened cur...Figure 4.23. Optimization histories for the resolution of the curved wall proble...Figure 4.24. Optimal configuration of the stiffened curved wall: (a) final geome...Figure 4.25. Construction of the model of the wingbox by means of the proposed e...Figure 4.26. Focus on step 1: defining the outer skin of the wing from a point c...Figure 4.27. Focus on step 2: the upper and the lower surfaces are used to gener...Figure 4.28. Structural analysis of the CRM wing (global view). For a color vers...Figure 4.29. Structural analysis of the CRM wing (local views). For a color vers...Figure 4.30. Construction of the geometric model of the representative wing (top...Figure 4.31. Optimization histories for the resolution of the wing problem, and ...Figure 4.32. Simple optimization problem: the position of the inclusion (xc, yc)...Figure 4.33. Application of the embedded shape update approach for designing geo...Figure 4.34. Application of the embedded shape update approach for designing geo...