kiendl - isogeometric analysis and shape optimal design of shell structures
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7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 1/32
Technische Universität München
Technische Universität München
Isogeometric Analysis and Shape Optimal Design
of Shell Structures
Josef Kiendl
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 2/32
Technische Universität München
Technische Universität München
Outline
- NURBS and isogeometric analysis
- The isogeometric Kirchhoff-Love shell
- Integration into CAD
- Isogeometric shape optimization
- Application to FSI simulations of wind turbine blades
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 3/32
Technische Universität München
Technische Universität München
B-Splines
• Piecewise polynomial functions
• Smoothness over element boundaries
• Used for modeling of free form curves and surfaces
NURBS and Isogeometric Analysis
n
i
i pi u N u1
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i pi
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i pi
i pi
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:0
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, otherwise
uuu
u N ii
pi
Cubic B-Spline functionsCubic B-Spline curve
u
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 4/32
Technische Universität MünchenTechnische Universität München
Tensor product of basis functions:
jiq j
m
j
pi
n
i
v M u N vu ,,
1
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B-Spline Surfaces and Solids
k jir k q j
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1
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NURBS and Isogeometric Analysis
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
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Technische Universität MünchenTechnische Universität München
Weighted control points Pi (xi,yi,zi,wi):
=> Exact representation of conic sections
NURBSNon-Uniform Rational B-Splines
jiq j
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NURBS and Isogeometric Analysis
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7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 6/32
Technische Universität MünchenTechnische Universität München
Weighted control points Pi (xi,yi,zi,wi):
=> Exact representation of conic sections
NURBSNon-Uniform Rational B-Splines
Circle Sphere
=> standard in CAD-programs !
NURBS and Isogeometric Analysis
jiq j
m
j
pi
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7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 7/32
Technische Universität MünchenTechnische Universität München
Isogeometric Analysis with NURBS
Idea:
Use functions from CAD (NURBS) as basis functions for FE -> common geometry description
+ No meshing - CAD model implies a NURBS mesh
+ Mesh refinement by NURBS refinement (order elevation and knot insertion)
+ Analysis on exact geometry -> advantage especially for thin shells
+ High-order elements with high continuities between elements
NURBS and Isogeometric Analysis
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 8/32
Technische Universität MünchenTechnische Universität München
Outline
- NURBS and isogeometric analysis
- The isogeometric Kirchhoff-Love shell
- Integration into CAD
- Isogeometric shape optimization
- Application to FSI simulations of wind turbine blades
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 9/32
Technische Universität MünchenTechnische Universität München
Kirchhoff-Love Shell Theory
• Cross sections remain straight
• Cross sections remain normal-> transverse shear strain is neglected
-> no decoupling of rotations and translations
• Valid for thin shells R/t > 20 (e.g. cooling tower R/t > 500)
x
xz x
w
R
t
z
x
Isogeometric Kirchhoff-Love shell
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 10/32
Technische Universität MünchenTechnische Universität München
Governing Equations
Internal virtual work
S - Piola-Kirchhoff 2 stress tensor E - Green-Lagrange strain tensor (large deformations)
=> Separating strain into membrane and bending action
ε - membrane strain
κ - change of curvature
Isogeometric Kirchhoff-Love shell
=> Problem for FE: curvature -> 2nd derivatives -> C1 continuity between elements
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 11/32
Technische Universität MünchenTechnische Universität München
Isogeometric Analysis: NURBS -> C1 continuity
geometrically nonlinear kinematics:
base vectors
unit normal vector
metric tensor
curvature tensor
membrane strain
change of curvature
Degrees of freedom = Control point displacements
No rotations!
Isogeometric Kirchhoff-Love shell
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 12/32
Technische Universität MünchenTechnische Universität München
Scordelis-Lo roof – displacement plot
Isogeometric Kirchhoff-Love shell
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 13/32
Technische Universität MünchenTechnische Universität München
Large deformations and rotations
Benchmark: Straight plate bent to a circle
Moment modeled by a pair of forces perpendicular to the geometry
Isogeometric Kirchhoff-Love shell
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 14/32
Technische Universität MünchenTechnische Universität München
Outline
- NURBS and isogeometric analysis
- The isogeometric Kirchhoff-Love shell
- Integration into CAD
- Isogeometric shape optimization
- Application to FSI simulations of wind turbine blades
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 15/32
Technische Universität MünchenTechnische Universität München
Isogeometric shell analysis integrated into CAD
CAD model of an oil barrel Applying boundary conditions
CAD models are surface-based.
-> For thin-walled structures, CAD and shell model use the same geometry description.
-> Design-through-analysis process inside CAD program (Rhino with IGA-plug-in):
geometric modeling, preprocessing, analysis, postprocessing
Refinement
Integration into CAD
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 16/32
Technische Universität MünchenTechnische Universität München
Isogeometric shell analysis integrated into CAD
Deformation (scaled) Normal forces n1 (circumferential) Normal forces n2 (longitudinal)
Integration into CAD
CAD models are surface-based.
-> For thin-walled structures, CAD and shell model use the same geometry description.
-> Design-through-analysis process inside CAD program (Rhino with IGA-plug-in):
geometric modeling, preprocessing, analysis, postprocessing
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 17/32
Technische Universität MünchenTechnische Universität München
Outline
- NURBS and isogeometric analysis
- The isogeometric Kirchhoff-Love shell
- Integration into CAD
- Isogeometric shape optimization
- Application to FSI simulations of wind turbine blades
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 18/32
Technische Universität MünchenTechnische Universität München
min.dV.50:e.g. σε
0)( sg0sh )( def :masse.g. mm
max:stresse.g. σ σ
.min)( s f
Shape Optimization
• Shape Optimization with FE -> two different geometry descriptions
• Optimization Problem:
objective function:
equality constraints:inequality constraints:
design variables:
initial design objective
sensitivities
• Design Parametrization:
CAD-based: CAD parameters
FE-based: FE nodes
n,...,1s ii iii z y xl, r ,, e.g.variablesshape
meshing
CAD model Analysis model
Isogeometric Shape Optimization
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 19/32
Technische Universität MünchenTechnische Universität München
min.dV.50:e.g. σε
0)( sg0sh )( def :masse.g. mm
max:stresse.g. σ σ
.min)( s f
Shape Optimization
• Shape Optimization with FE -> two different geometry descriptions
• Optimization Problem:
objective function:
equality constraints:inequality constraints:
design variables:
• Design Parametrization:
CAD-based: CAD parameters
FE-based: FE nodes
Isogeometric: Control Points
n,...,1s ii iii z y xl, r ,, e.g.variablesshape
Isogeometric Shape Optimization
initial design objective
sensitivities
meshing
CAD model Analysis model
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 20/32
Technische Universität MünchenTechnische Universität München
Isogeometric Shape Optimization
Design variables: Control points
CAD model Isogeometric analysis model
Isogeometric optimization model
Isogeometric Shape Optimization
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 21/32
Technische Universität MünchenTechnische Universität München
Isogeometric Shape Optimization
Example: Tube under constant internal pressure
Find optimal shape of the section in order to maximize the stiffness
constant pressure
Isogeometric Shape Optimization
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 22/32
Technische Universität MünchenTechnische Universität München
Example: Tube under constant internal pressure
12 design variables:
x, y, w
of the four edge control points
Design Variables
Isogeometric Shape Optimization
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
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Technische Universität MünchenTechnische Universität München
Animation: Optimization steps
Isogeometric Shape Optimization
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 24/32
Technische Universität MünchenTechnische Universität München
Example: Tube under constant internal pressure
Section shape after optimization: circular
Circular section exactly represented by NURBS
constant pressureconstant pressure
Isogeometric Shape Optimization
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 25/32
Technische Universität MünchenTechnische Universität München
Example: Circular Tube under point loads
Isogeometric Shape Optimization
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 26/32
Technische Universität MünchenTechnische Universität München
Example: Circular Tube under point loads
coarse optimization model fine optimization model
Different refinements for optimization model
Isogeometric Shape Optimization
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 27/32
Technische Universität MünchenTechnische Universität München
Example: Circular Tube under point loads
Optimized design model in CAD program
Isogeometric Shape Optimization
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 28/32
Technische Universität MünchenTechnische Universität München
Outline
- NURBS and isogeometric analysis
- The isogeometric Kirchhoff-Love shell
- Integration into CAD
- Isogeometric shape optimization
- Application to FSI simulations of wind turbine blades
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 29/32
Technische Universität MünchenTechnische Universität München
Application: FSI simulation of a Wind Turbine Blade
Cooperation project with Y. Bazilevs, M.-C. Hsu, UCSD:
Fully coupled, 3D FSI simulation of a wind turbine blade rotating in the air flow
Fluid: Isogeometric fluid elements
Structure: Isogeometric K-L shell
-> matching discretization at the interface
Wind turbine blade Fluid mesh
FSI simulation of wind turbine blades
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 30/32
Technische Universität MünchenTechnische Universität München
Application: FSI simulation of a Wind Turbine Blade
Cooperation project with Y. Bazilevs, M.-C. Hsu, UCSD:
Fully coupled, 3D FSI simulation of a wind turbine blade rotating in the air flow
Fluid: Isogeometric fluid elements
Structure: Isogeometric K-L shell
-> matching discretization at the interface
Structural modelFluid mesh
FSI simulation of wind turbine blades
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 31/32
Technische Universität MünchenTechnische Universität München
3D FSI Simulation
Normal forces
FSI simulation of wind turbine blades
7/18/2019 Kiendl - Isogeometric Analysis and Shape Optimal Design of Shell Structures
http://slidepdf.com/reader/full/kiendl-isogeometric-analysis-and-shape-optimal-design-of-shell-structures 32/32
Technische Universität MünchenTechnische Universität München
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