a beam reduction method for wing aeroelastic design
Post on 16-Oct-2021
2 Views
Preview:
TRANSCRIPT
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
A beam reduction method for
wing aeroelastic design optimisation with
detailed stress constraints
O. Stodieck, J. E. Cooper, S. A. Neild, M. H. LowenbergUniversity of Bristol
N.L. IorgaAirbus Operations Ltd.
29 November 2017
1
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
Overview
• Motivation
• Benefits of analysis-specific structural idealisations (hi-fidelity / low-fidelity)
• Integration of the beam reduction method into an aeroelastic design optimisation
• Beam reduction method description
• Overview
• Stiffness reduction
• Examples
• Rectangular wingbox model
• University of Bristol Ultra-Green (BUG) aircraft wingbox
• Conclusions
2
29 November 2017
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
Motivation
3
29 November 2017
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
Benefits of analysis-specific structural idealisations
4
29 November 2017
Hi-Fidelity = Accuracy
Low-Fidelity = Speed
* Degrees of freedom
** Global finite element model
Why do we use different structural idealisations?
Example:
Flutter analysis
102 DOF*
Beam
model
Wingbox GFEM
detailed
stress
analysis
Example:
GFEM** Internal loads analysis
104 to 106 DOF
DC3 wing section
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
Gra
die
nt
bas
ed
op
tim
izat
ion
alg
ori
thm
,it
era
tes
the
de
sign
var
iab
les u
nti
l co
nve
rge
nce
is r
eac
he
d Update of optimization
variables values
Update of beam model
properties and M
GFEM to Beam model reduction
External loads
Multidisciplinary analysis
Stress analyses
Start
End
Aeroelastic analyses
Aeroelastic constraint
values
Stress constraint values
Total derivatives matrix
Objective and constraint
function values
Aeroelastic design optimisation
5
29 November 2017
How can we do MDO* with high and low fidelity structural idealisations?
*Multidisciplinary
design optimisation
Example:
Automatic beam reduction
integration into a
Multidisciplinary Feasible
(MDF) architecture.
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
Beam reduction method description
6
29 November 2017
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation7
29 November 2017
GFEM with variables 𝑣• Thicknesses
• Ply percentages
• Stringer orientations …
Beam with properties Ω and [𝑀]
0° ply direction in upper and lower skins26°
Front Spar
Rear SparRib
Upper Skin
Lower Skin1 Rib-bay
Stringer (equivalent area and offset shown)
Spar Cap
Beam Node
Multi-point Constraint
Beam reduction method - Overview
CL
GFEM
Beam
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
Τ𝜕𝐶 𝜕𝑣
Beam reduction method - Overview
8
29 November 2017
Definition of a beam
reference axis
Beam element flexibility
matrix [𝐶](numerical)
13 physical isotropic beam
element stiffness parameters Ω
(analytical)
Stiffness
reduction
Mass
reduction
Definition of lumped mass
element groups
Lumped mass and inertia matrix [𝑀]
determination (numerical)
Τ𝜕Ω 𝜕𝐶
Τ𝜕𝑀 𝜕𝑣
Τ𝜕Ω 𝜕𝑣
Manual
input
Manual
input
Auto -
mated
Auto -
mated
Auto -
mated
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
Stiffness reduction
9
29 November 2017
Definition of a beam reference
axis
Beam element flexibility
matrix determination
(numerical)
Calculation of 13 physical
isotropic beam element stiffness
parameters
CL
Stringer datum
Ribdatum
Front Spar
Rear SparRib
Upper Skin
Lower Skin1 Rib-bay
Stringer (equivalent area and offset shown)
Spar Cap
Fuselage/Wing Interface
Beam Element Reference Axis
Beam Node
Multi-point Constraint
x
y
Local beam reference axis coordinate system
Global model analysis coordinate system
Beam Node
Section 1 Section 2 Section 3
Example: BUG wing model GFEM
Straight beam sections
Manual
input
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
Stiffness reduction
10
29 November 2017
Definition of a beam reference
axis
Beam element flexibility
matrix determination
(numerical)
Calculation of 13 physical
isotropic beam element stiffness
parameters
1) GFEM analysis with 6 static tip load cases / section
2) Nodal deflection and rotation output
3) Post-process to find 6x6 [𝐶] matrix /
beam element
Note:
This approach is equivalent to the
‘blade property extraction’ (BPE)
method used for wind-turbine blades:
Malcolm DJ, Laird DL. Extraction of
equivalent beam properties from
blade models. Wind Energy. 2007
Mar 1;10(2):135-57.
Auto -
matedNASTRAN analysis
(1s / straight wing section)
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
Stiffness reduction
11
29 November 2017
Definition of a beam reference
axis
Beam element flexibility
matrix determination
(numerical)
Calculation of 13 physical
isotropic beam element stiffness
parameters
defines the properties of an isotropic
Timoschenko theory beam element. is calculated analytically from 𝐶 and assumed
isotropic material properties 𝐸 and 𝐺. Non-dimensional bend-twist coupling parameters
Ψ = 𝐾/ 𝐸𝐼. 𝐺𝐽 can be derived as functions of .
Effective shear centre offsets at nodes A and B= elastic axis definition
Bending and Torsion Stiffness parameters
Section centroid offsets from the elastic axis
Section Area Timoschenkoshear coefficients
Node A
Node B
Shear Centre in yz-plane @ Node B (SCB)
Shear Centre in yz-plane @ Node A (SCA)
SCAY SCAZSCBY
SCBZ
Elastic axis
Beam element reference axis
y
x
z
y
x
z
Bend-twist coupling exists for any 𝑆𝐶𝐴 ≠ 𝑆𝐶𝐵
Auto -
mated
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
Examples
12
29 November 2017
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
Rectangular wingbox model
13
29 November 2017
1.0
0m
Upper skin
Lower skin Rib Stringers, Spar caps
Beam Node
Front spar
Multi-point Constraint
Baseline model stiffness, with
• 𝑆𝐶𝐴 = 𝑆𝐶𝐵 = 0• 𝑁𝑦 = 𝑁𝑍 = 0
• Stiffness increase at the root (Y=0m) >> boundary constraint effect• Stiffness reduction at the tip (Y=16.8m) >> load introduction effect
due to the multipoint constraint (RBE3) assumption here resulting in equally distributed skin forces, not taking into account the section stiffness distribution or the skin/stiffener offsets
Constant-section rectangular wing-box GFEM: 16.8m span (28 rib bays), 1.68m chord and 1.0m height
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
Rectangular wingbox model
14
29 November 2017
+Thicker front spar + Unbalanced skin laminate + Rotated ribBaseline
Effect of incremental stiffness changes on the elastic axis (locus of shear centres).
Model 1 Model 2 Model 3
𝑆𝐶𝐴 = 0𝑆𝐶𝐵 = 0
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
Gradients of the rectangular wingbox model
15
29 November 2017
Stiffness parameter
sensitivities to changes in
the +45º fibre percentage
in the upper skin.
Gradients are captured accurately.
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
University of Bristol Ultra-Green (BUG) aircraft
wingbox (static & dynamic)
16
29 November 2017
0° ply direction in upper and lower skins26°
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
University of Bristol Ultra-Green (BUG) aircraft
wingbox (static & dynamic)
17
29 November 2017
Static deflections captured accurately (tip displacements within 5% error).
Comparison of the GFEM and equivalent beam displacements and rotations for an applied tip force (linear analysis).
Up-
bendingWing
Twist*
*Twist due to wing sweep + bend-twist coupling
GFEMbeam
Z-disp.X-rot.
Y-rot.
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
University of Bristol Ultra-Green (BUG) aircraft
wingbox (static & dynamic)
18
29 November 2017
Dynamic behaviour captured accurately (first 10 modes natural frequencies within 2.1% error).
Frequency response
plots at the wing tip,
for an applied
wing tip excitation
force of 104N in the
Global Z-direction.
1.26 Hz (-0.1% Freq. error)
First up/down bending mode
14.78 Hz (0.5% Freq. error)
Mode 8
16.3 Hz (2.1% Freq. error)
Mode 9
3.18 Hz (0.1% Freq. error)
First FWD/AFT bending mode
Mode 8 Mode 9
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
Conclusions
19
29 November 2017
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
Summary:✓ Developed a numerical method for efficiently and accurately reducing a high-fidelity GFEM to a
Timoschenko beam theory model with lumped masses.
✓ Suggested an approach for integrating the beam reduction method into a gradient-based aeroelastic design optimisation architecture.
Advantages:
• physical insight into the GFEM design optimization results (e.g. quantify bend-twist coupling in terms of elastic axis rotation or Ψ values)
• information about the effects of design changes on the overall wing stiffness and mass properties, in the vicinity of the current design
20
29 November 2017
➢ faster aeroelastic
optimisation
➢ more aeroelastic load cases
➢ large deflection cases
➢ more refined GFEM
Speed or Scope
DiPaRT 2017 - O. Stodieck, Beam Reduction
Method for Wing Aeroelastic Design Optimisation
• Publication:• O. Stodieck, J. E. Cooper, S. A. Neild, M. H. Lowenberg and N. L. Iorga , “Beam
reduction method for wing aeroelastic design optimization with detailed stress constraints”, submitted to the AIAA Journal in Nov. 2017
• Contact:• Dr Olivia Stodieck (olivia.stodieck@bristol.ac.uk)
• Acknowledgements• Airbus and Innovate UK (AWI project)
21
29 November 2017
top related