This document describes research on isogeometric analysis of lightweight structures using multipatch surfaces. It discusses the development and application of isogeometric membrane analysis, Kirchhoff-Love shell analysis, and fluid-structure interaction simulations using multipatch surfaces. It also describes work on stochastic optimization of wind turbine tower designs using isogeometric analysis and exact CAD geometry.

1. Dr.-Ing. Andreas Apostolatos
Technical University of Munich
Department of Civil, Geo and Environmental Engineering
Chair of Structural Analysis
Isogeometric Analysis of Lightweight Structures
with application to Fluid-Structure Interaction and
Stochastic Optimization

2. Motivation
Isogeometric Analysis on Multipatch Surfaces
Isogeometric Membrane Analysis on Multipatches
Isogeometric Kirchhoff-Love Shell Analysis on Multipatches
Fluid-Structure Interaction
Stochastic Optimization
Conclusions & Outlook

3. a) Roof of the olympia stadion in Munich
b) Inflatable hangar
c) NREL phase VI wind turbine
http://www.cimne.com/websasp/ulites/
1
Simms, D., Schreck, S., Hand, M., Fingersh, L.J.: Nrel unsteady aerodynamics experiment in the nasa-ames wind tunnel:
a comparison of predictions to measurements. National Renewable Energy Laboratory Colorado, USA (2001)
2
Motivation
1
2

4. b) Pneumatic roof
a) NREL phase VI wind turbine
Motivation

5. Motivation
Isogeometric Analysis on Multipatch Surfaces
Isogeometric Membrane Analysis on Multipatches
Isogeometric Kirchhoff-Love Shell Analysis on Multipatches
Fluid-Structure Interaction
Stochastic Optimization
Conclusions & Outlook

6. Isogeometric Analysis on Multipatch Surfaces

7. Isogeometric Analysis on Multipatch Surfaces

8. Method
Positive
definiteness
Variational
consistency
Implementation
complexity
Additional
Unknowns
Penalty
Lagrange
Multipliers
Augmented
Lagrange
Multipliers
Nitsche-type
Yes No Easy No
No Yes Moderate Yes
No Yes Moderate Yes
Yes Yes Hard No
Isogeometric Analysis on Surface Multipatches

9. Motivation
Isogeometric Analysis on Multipatch Surfaces
Isogeometric Membrane Analysis on Multipatches
Isogeometric Kirchhoff-Love Shell Analysis on Multipatches
Fluid-Structure Interaction
Stochastic Optimization
Conclusions & Outlook

10. Isogeometric Membrane Analysis on Multipatches
A. Apostolatos, K.-U. Bletzinger, R. Wüchner (in press). “Weak imposition of constraints for membrane structures in transient geome-
trically nonlinear multipatch isogeometric analysis.” Computer Methods in Applied Mechanics and Engineering (2019)

11. Isogeometric Membrane Analysis on Multipatches
Fig. Form-finding for structural membranes
a. Reference geometry b. Form-found shape

12. Fig. Middle sail of the olympic stadium roof in Munich (form-found shape)
Isogeometric Membrane Analysis on Multipatches
Fig. Middle sail of the olympic stadium roof in Munich (form-finding)

13. Isogeometric Membrane Analysis on Multipatches
Fig. Middle sail of the roof of the Olympic stadium in Munich (mode shapes)

14. Motivation
Isogeometric Analysis on Multipatch Surfaces
Isogeometric Membrane Analysis on Multipatches
Isogeometric Kirchhoff-Love Shell Analysis on Multipatches
Fluid-Structure Interaction
Stochastic Optimization
Conclusions & Outlook

15. Isogeometric Kirchhoff-Love Shell Analysis on Multipatches
A. Apostolatos, M. Breitenberger, K.-U. Bletzinger, R. Wüchner: Domain Decomposition Methods and Kirchhoff-Love Shell Multipatch
Coupling in Isogeometric Analysis. Isogeometric Analysis and Applications 2014. Springer, Cham, 2015. 73-101

16. Isogeometric Kirchhoff-Love Shell Analysis on Multipatches
Fig. NREL phase VI wind turbine

17. Isogeometric Kirchhoff-Love Shell Analysis on Multipatches
Fig. NREL phase VI wind turbine (computational models)

18. Isogeometric Kirchhoff-Love Shell Analysis on Multipatches
Fig. NREL phase VI wind turbine (linear static analysis)

19. Isogeometric Kirchhoff-Love Shell Analysis on Multipatches
Fig. NREL phase VI wind turbine (linear static analysis)

20. Isogeometric Kirchhoff-Love Shell Analysis on Multipatches
Fig. NREL phase VI wind turbine (modal analysis)

21. Motivation
Isogeometric Analysis on Multipatch Surfaces
Isogeometric Membrane Analysis on Multipatches
Isogeometric Kirchhoff-Love Shell Analysis on Multipatches
Fluid-Structure Interaction
Stochastic Optimization
Conclusions & Outlook

22. Fluid-Structure Interaction
A. Apostolatos, G. De Nayer, K.-U. Bletzinger, M. Breuer, R. Wüchner (in press). “Systematic evaluation of the interface description for
fluid-structure interaction simulations using the isogeometric mortar-based mapping”. Journal of Fluids and Structures (2019)

23. Fluid-Structure Interaction
Fig. NREL phase VI wind turbine with flexible blades

24. Fluid-Structure Interaction
Fig. NREL phase VI wind turbine with flexible blades

25. Motivation
Isogeometric Analysis on Multipatch Surfaces
Isogeometric Membrane Analysis on Multipatches
Isogeometric Kirchhoff-Love Shell Analysis on Multipatches
Fluid-Structure Interaction
Stochastic Optimization
Conclusions & Outlook

26. Stochastic optimization
Fig. Stochastic inlet
Fig. Problem setup

27. Stochastic optimization
Optimization for the conditional value at risk: CVaR𝛽 𝑋 =
1
1−𝛽
VaR𝛽 𝑋 ‫׬‬
𝛽
1
𝑑𝛼
Fig. Design variables based on CAD

28. Stochastic optimization
Fig. Turbulent inlet

29. Stochastic optimization
Fig. Embedded tower in turbulent flow (meshes) Fig. Optimized geometry

30. Motivation
Isogeometric Analysis on Multipatch Surfaces
Isogeometric Membrane Analysis on Multipatches
Isogeometric Kirchhoff-Love Shell Analysis on Multipatches
Fluid-Structure Interaction
Conclusions & Outlook

31. Conclusions & Outlook
Achievements
• Constraint enforcement methods for the multipatch coupling in IGA
• Penalty
• Lagrange Multipliers
• Augmented Lagrange Multipliers
• Nitsche-type
• Isogeometric membrane analysis on multipatches
• Form-finding analysis using the URS
• Geometrically nonlinear, modal and transient analysis
• Isogeometric Kirchhoff-Love shell analysis on multipatches
• Shell obstacle course
• Geometrically nonlinear, modal and transient analysis
• Development of an isogeometric mortar-based surface mapping method
• Development of a stochastic optimization framework based on the exact CAD geometry

32. • A. Apostolatos, R. Schmidt, R. Wüchner, K.-U. Bletzinger. „A Nitsche-type formulation and comparison of the most
common domain decomposition methods in isogeometric analysis.“ In: International Journal for Numerical Methods in
Engineering 97.7 (2014) pp. 473-504.
• A. Apostolatos, M. Breitenberger, R. Wüchner, K.-U. Bletzinger. „Domain Decomposition Methods and Kirchhoff-
Love Shell Multipatch Coupling in Isogeometric Analysis“. In: Isogeometric analysis and applications 2014. Ed. by B.
Simeon. Vol. 107. Lecture Notes in Computational science and Engineering. Cham, Heildelberg and New York:
Springer, 2015, pp. 73-101. ISBN:978-3-319-23314-7.
• M. Breitenberger, A. Apostolatos, B. Philipp, R. Wüchner, K.-U. Bletzinger. „Analysis in computer aided design:
Nonlinear isogeometric B-Rep analysis of shell structures“. In: Computer Methods in Applied Mechanics and
Engineering 284 (2015), pp. 401-457.
• A. Apostolatos, R. Wüchner, K.U. Bletzinger (in press). „Weak enforcement of constraints for membrane structures
in transient geometrically nonlinear multipatch isogeometric analysis“. In: Computer Methods in Applied Mechanics
and Engineering (2019).
• G. de Nayer, A. Apostolatos, J.N. Wood, K.-U. Bletzinger, R. Wüchner, M. Breuer.. „Numerical studies on the fluid-
structure interaction of an air-inflated flexible hemisphere in turbulent flows.“ In: Journal of Fluids and Structures 82
(2018) pp. 577-609.
• A. Apostolatos, G. de Nayer, K.-U. Bletzinger, M. Breuer, R. Wüchner (in press). „Systematic evaluation of the
interface description for fluid-structure interaction simulations using the isogeometric mortar-based mapping.“ In:
Journal of Fluids and Structures (2019).
Literature