1 Introduction
2 Problem formulation
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Layout of the internal structure?
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Placement of actuators?
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Definition of actuation schemes?
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Definition of actuation strength?
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Stiffness distribution over the outer skin?
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Aerodynamic quality of the morphed airfoil shapes?
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Assessment of aerodynamic and structural objectives?
3 Modeling framework
3.1 Aims and scope
3.2 Parameterization
3.2.1 Structural layout
3.2.2 Active linear elements
3.2.3 Structural thicknesses
3.3 Aerostructural evaluation
3.4 Modeling of actuators
3.5 Boundary conditions
4 Optimization framework
4.1 Aerodynamic objectives
4.2 Structural objectives
4.3 Optimization constraints
4.4 Optimization problem
4.5 Evolutionary optimization
Purpose | Number of variables | |
---|---|---|
Integer | Floating point | |
Axiom ω | 3 | - |
Set of rules P | 36 | - |
Number of cellular divisions ndiv | 1 | - |
Minimal inner angle φmin | - | 1 |
Minimal area ratio rA | - | 1 |
Minimal edge length le,min | - | 1 |
Number of MMCs nMMC | 1 | - |
Length of MMCs l | - | nMMC |
Width of MMCs w | - | nMMC |
Center of MMCs \(\left (x_{0},y_{0}\right )\) | - | 2nMMC |
Rotation angle of MMCs Θ | - | nMMC |
Actuation degrees Tj,i | - | \(\left (n_{FC} - 1 \right ) n_{MMC}\) |
Contour thicknesses tk | - | 12 |
Internal thickness tinternal | - | 1 |
Total | 41 | \(\mathbf {16+\left (4+n_{FC}\right ) n_{MMC}}\) |
Algorithm | Description | Value |
---|---|---|
All | Population size | 255 |
GA | Number of crossover points | 3 |
Mutation probability | 0.01 | |
ES | Standard deviation | 0.2 |
DE | Mutation rate | 0.9 |
Number of difference vectors used | 1 | |
Crossover constant | 0.5 |
5 Example
Description | Variable | Value | Unit |
---|---|---|---|
Mean aerodynamic chord | lμ | 2.8012 | m |
Take-off mass | mTO | 62,731.8 | kg |
Operating empty weight | mOE | 37,058.5 | kg |
Cruise Mach number | Mac | 0.7 | - |
Wing area | S | 137.23 | m2 |
Description | Variable | Value | Unit |
---|---|---|---|
Young’s modulus | E | 73,773 | MPa |
Shear modulus | G | 27,734 | MPa |
Poisson’s ratio | ν | 0.33 | - |
Density | ρ | 2.77 | g/cm3 |
Artificial thermal expansion | αT | 1 | K-1 |
i | \(u_{\infty } / \frac {\mathrm {m}}{\mathrm {s}}\) | H/km | \(\rho _{ISA} / \frac {\text {kg}}{\mathrm {m^{3}}}\) | \(\eta / \frac {\text {kg}}{\mathrm {m \cdot s}}\) | Re/ − | Ma/ − | mac/kg | cl/ − |
---|---|---|---|---|---|---|---|---|
1 | 206.55 | 11.5 | 0.34 | 1.48 ⋅ 10− 5 | 1.31 ⋅ 107 | 0.70 | 40,119 | 0.40 |
2 | 206.55 | 11.5 | 0.34 | 1.48 ⋅ 10− 5 | 1.31 ⋅ 107 | 0.70 | 61,552 | 0.61 |
3 | 78.11 | 0 | 1.23 | 1.87 ⋅ 10− 5 | 1.44 ⋅ 107 | 0.23 | 62,732 | 1.20 |
5.1 Base airfoil
5.2 Convergence
5.3 Resulting structures
Individual | μ/(kg/m) | cd/ − | σd/ − | HKmax/ − |
---|---|---|---|---|
1 | 7.84552 | 0.00519 | 0.00037 | 3.77533 |
2 | 15.1462 | 0.00435 | 0.00113 | 4.19502 |
3 | 20.5862 | 0.00365 | 0.00178 | 9.65291 |
4 | 5.69445 | 0.01451 | 0.00820 | 27.5551 |