topology and parametric optimisation of a lattice composite fuselage structure
DESCRIPTION
Topology and Parametric Optimisation of a Lattice Composite Fuselage Structure. Dianzi Liu, V assili V. Toropov , Osvaldo M. Querin University of Leeds. Content. Introduction Topology Optimisation Parametric Optimisation Conclusion. - PowerPoint PPT PresentationTRANSCRIPT
Topology and Parametric Optimisation of a Lattice Composite Fuselage Structure
Dianzi Liu, Vassili V. Toropov, Osvaldo M. Querin University of Leeds
Content
Introduction
Topology Optimisation
Parametric Optimisation
Conclusion
Topology OptimisationMethod
Topology Optimisation is a computational means of determining the physical domain for a structure subject to applied loads and constraints.
The method used in this research is the Solid Isotropic Material with Penalization (SIMP).
It works by minimising the compliance (maximising global stiffness) of the structure by solving the following optimization problem:
for a single load case,
or by minimising the weighted compliance for multiple (N) load cases:
eVd
pEE
FuEKtsuFC
ee
pee
e
T
,10,
,1,
:..min
0
N
LoadLoadLoadTot cc
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• Topology Optimisation: minimizing the compliance of the structure for 3 load cases
• Load cases consist of distributed loads over the length and loads at the barrel end(shear forces, bending moments and torque)
• Question: what are the appropriate weight coefficient values?
Topology OptimisationLoad Cases
Topology OptimisationMethod for weight allocation
The following strategy was used:• Do topology optimization separately for each load case, obtain the
corresponding compliance values• Allocate the weights to the individual compliance components (that correspond
to the individual load cases) in the same proportion• The logic behind this is as follows: if for a particular load case topology
optimization produced a relatively high compliance value, then this load case is a critical one and hence it should be taken with a higher weight in the total weighted compliance optimization problem
Topology Optimisation Results for 3 load cases
Topology OptimisationModel and Results
BendingTorsion
Transverse bending
Topology OptimisationResults
Iso view: optimization of the barrel for weighted compliance
Optimization of the barrel without windows (Top) and with windows (Bottom)
Two backbones on top and bottom of the barrelNearly +-45° stiffening on the side panel
Result: beam structure for the barrel
Note: SIMP approach does not consider buckling
Topology OptimisationPresence of window openings
Development of the Design Concept by DLR• Reflection on the layout of the “ideal” structure from the
topology optimization it in the aircraft design context• Consideration of airworthiness and manufacturing
requirements• Fuselage design concept developed by DLR• High potential for weight savings achievable due to new
material for stiffeners and non-rectangular skin bays• Due to large number of parameters in the obtained
concept a multi-variable optimisation should be performed
Bearing Skin Stiffener grid
Frame
Aerodynamic skin
Foam core
Bearing Skin Stiffener grid
Frame
Aerodynamic skin
Foam core
Multi-parametric OptimisationMethod: the multi-parameter global approximation-based approach used to solve the optimization problem
Problem: optimize an anisogrid composite fuselage barrel with respect to weight and stability, strength, and stiffness using 7 geometric design variables, one of which is an integer variable.
Procedure:• develop a set of numerical experiments (FEA runs) where each corresponds to a
different combinations of the design variables. The concept of a uniform Latin hypercube Design of Experiments (DOE) with 101 experiments (points in the variable space) was used.
• FE analysis of these 101 fuselage geometries was performed• global approximations built as explicit expressions of the design variables using
Genetic Programming (GP)• parametric optimisation of the fuselage barrel by a Genetic Algorithm (GA) • verification of the optimal solution by FE simulation
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Design of ExperimentsIn order to generate the sampling points for approximation building, a uniform DOE (optimal Latin hypercube design) is proposed. The main principles in this approach are as follows:
• The number of levels of factors (same for each factor) is equal to the number of experiments and for each level there is only one experiment;
• The points of experiments are distributed as uniformly as possible in the domain of factors, which are achieved by minimizing the equation:
where Lpq is the distance between the points p and q (p≠q) in the system.
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min1
1 12
p
p
p
pq pqLU
Example: A 100-point DOE generatedby an optimal Latin hypercube technique
Genetic ProgrammingGenetic Programming (GP) is a symbolic regression technique, it produces an analytical expression that provides the best fit of the approximation into the data from the FE runs. Example: a approximation for the shear strain obtained from the 101 FE responses:
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where Z1, Z2, …, Z7 are the design variables.
0.975381 )Z Z Z Z/(Z Z Z 15.5318
)Z Z Z Z/(Z 660.152 -)Z Z/(Z Z Z 0.202164 +
)Z Z/(Z Z 163.814 +)Z Z Z/(Z 4143.98-
Z Z Z Z 06045610.00000000+ Z/Z 603.316+ Z/Z 2.93847+
Z Z 0.00132105+Z 1.76206-Z 1.26902= )Z;Z;Z;Z;Z;Z;f(Z
542
34
24
762
1
742
323
12
7562
42
5243642
22
1
72
5315323
53317654321
Indications of the quality of fit of the obtained expression into the data:
FEM Modeling and Simulation
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Automated Multiparametric Global Barrel FEA Tool: Modeling, Analysis, and Result Summary
Displacement Skin Strains Beam Strains BucklingResults:
Results of all analyzed models are summarized in a separate file
Session file: List of Models to be Analyzed
Modeling and Analysis
PCL Function
Post-processing PCL Function
User Defined Parameters: -Geometry -Loads -Materials -Mesh seed
MSC PatranMSC Nastran
PCL
xy
z Qz
Optimisation of the Fuselage Barrel
Composite skin and stiffeners
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An upward gust load case at low altitude and cruise speed
Undisturbed anisogrid fuselage barrelEarly design stage
Variables and Constraints
Design variables Lower bound Upper bound Skin thickness (h) 0.6 (mm) 4.0 (mm)Number of helix rib pairs around the circumference, (n) 50 150
Helix rib thickness, (th) 0.6 (mm) 3.0 (mm)Helix rib height, (Hh) 15.0 (mm) 30.0 (mm)Frame pitch, (d) 500.0 (mm) 650.0 (mm)Frame thickness, (tf) 1.0 (mm) 4.0 (mm)Frame height, (Hf) 50.0 (mm) 150.0 (mm)
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Hf
tf
Wf =20mm
Wf =20mm
Hh
Wh=20mm
dh=8mm dh=8mm
th
Circumferential Frames Helix Ribs
Frame Pitch, d
Circumf. Helix Rib Pitch, dep. on n
2φ
Fuselage Geometry
Radius2m h
Barrel Cross Section
Constraints:• Strength: strains in the skin and in the stiffeners• Stiffness: bending and torsional stiffness• Stability: buckling
Normalization• Normalized mass against largest mass• Margin of safety ≥0
• Strain• Stiffness• Buckling
Variables:
Results: Summary of parametric optimisation
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Model Tensile Strain (MS)
Compressive Strain (MS)
Shear Strain (MS)
Buckling (MS)
Torsional Stiffness
(MS)
Bending Stiffness
(MS)
Normalized mass
Prediction I 0.02 0.00 1.42 --- --- --- 0.10Optimum I 0.36 -0.09 1.21 --- --- --- 0.11Prediction II 0.03 0.01 1.64 --- --- --- 0.11Optimum II 0.54 0.04 1.54 --- --- --- 0.12Prediction III 0.20 0.23 1.27 0.00 1.21 0.89 0.29Optimum III 0.62 0.08 1.09 -0.07 1.21 0.89 0.29Comp. Des. 1.15 0.19 1.31 -0.04 1.25 0.81 0.29
DesignSkin
thickness (h), mm
Nr. of helix rib pairs, (n)
Helix rib thickness, (th), mm
Helix rib height,
(Hh), mm
Frame pitch,
(d), mm
Frame thickness,
(tf), mm
Frame height,
(Hf), mmOptimum I 2.08 60.00 0.60 27.90 627.70 1.00 50.00Optimum II 2.28 60.00 0.66 27.90 627.70 1.00 50.00Optimum III 1.71 150.00 0.61 27.80 501.70 1.00 50.00
Strength Contraint
Stability, Strength,
and Stiffness
ContraintsOptimum III geometry with realistic ply layup:
Helical ribs: tall and slender Frames: thin and small
209 mm
628 mm
18.94 °
Optimum II84 mm
502 mm
9.55 °
Optimum III and Comp. Design
(±45,0,45,0,-45,90)s, 14 plies, total thickness = 1.75 mm
Results: Interpretation of the skin as a laminate, 14 plies
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Stacking sequence Buckling (MS)
Torsional Stiffness
Bending Stiffness
Normalized mass
(±45,0,45,0,-45,90)s -0.04 1.25 0.81 0.29
(±45,0,45,90,-45,0)s 0.04 1.25 0.81 0.29
(±45,90,45,0,-45,0)s 0.13 1.25 0.81 0.29
% of 0° plies % of +/-45° plies % of 90° plies
28.6% 57.1% 14.3%
Results: Interpretation of the skin as a laminate, 15 plies
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Stacking sequence Buckling (MS)
Torsional Stiffness
Bending Stiffness
Normalized mass
(±45,0,45,0,-45,90)s ,0 0.12 1.26 0.92 0.30
(±45,0,45,90,-45,0)s ,0 0.20 1.26 0.92 0.30
(±45,90,45,0,-45,0)s ,0 0.28 1.26 0.92 0.30
% of 0° plies % of +/-45° plies % of 90° plies
33.3% 53.3% 13.3%
ConclusionMulti-parameter global metamodel-based optimization was used for:
• Optimization of a composite anisogrid fuselage barrel with respect to weight, stability, strength, stiffness using 7 design variables, 1 being an integer
• 101-point uniform design of numerical experiments, i.e. 101 designs analysed• Automated Multiparametric Global Barrel FEA Tool generates responses• global approximations built using Genetic Programming (GP) • parametric optimization on global approximations• optimal solution verified via FE
Overall, the use of the global metamodel-based approach has allowed to solve this optimization problem with reasonable accuracy as well as provided information on the structural behavior of the anisogrid design of a composite fuselage.
There is a good correspondence of the obtained results with the analytical estimates of DLR, e.g. the angle of the optimised triangular grid cell is 9.55° whereas the DLR value is 12°
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