Main Wing Structure Selection
Geometry and Simplification
The primary structure carries the bending moment from aerodynamic lift. It was modeled as a cantilever beam with a hollow rectangular cross-section (h = b/4), where the wing root acts as the fixed support (fuselage junction). The distributed load along the wing was approximated as a triangular distribution representing the combined effect of lift and self-weight.
Performance Indices
Two mechanical constraints were derived, fatigue resistance and stiffness, leading to two performance indices combined using the AND method with equal weighting (m₁ = ½):
Final Performance Index Expression: Primary Structure
Using the AND method with base b as free variable:
log(σf½ / ρ) = −log(E⅓ / ρ) + 2·log(W*)
Where W₁ = σf½/ρ (fatigue index) and W₂ = E⅓/ρ (stiffness index), combined into the iso-performance line: y = −x + p
Constraint Limits
| Constraint | Limit |
|---|---|
| Maximum thermal expansion α | ≤ 10⁻⁶ µstrain/°C |
| Minimum fracture toughness Kc | ≥ 30 MPa·m½ |
| Minimum service temperature | ≤ −80°C |
CES EduPack Results
Candidate Material Properties
| Property | BMI-CF65 | Cyanate-CF65 | EP-RF50 | EP-CF70 |
|---|---|---|---|---|
| Density (kg/m³) | 1570–1610 | 1620–1670 | 1380 | 1550–1580 |
| Young's Modulus (GPa) | 110–130 | 299–376 | 60–80 | 129–154 |
| Yield Strength (MPa) | 1710–1740 | 1890–2530 | 1100–1380 | 1740–2170 |
| Fatigue Strength 10⁷ cycles (MPa) | 940–1130 | 1040–1650 | 605–897 | 959–1410 |
| Fracture Toughness (MPa·m½) | 56.9–73.9 | 48.3–59 | 56.3–68.8 | 60.2–73.5 |
| Min Service Temp (°C) | −67 to −47 | −51 to −31 | −48 to −28 | −123 to −73 |
| Thermal Expansion (µstrain/°C) | −0.17 | −1.6 | −0.83 | −0.6 |
| Price (EUR/kg) | 89.2–107 | 196–219 | 44.6–73.4 | 34.9–38.8 |
At the B787's maximum cruising altitude of 43,100 ft (~13,137 m), the standard ISA temperature is approximately −56.5°C, but can drop to −70°C or even −80°C in polar/winter conditions. This eliminates BMI-CF65, Cyanate-CF65, and EP-RF50, leaving only EP-CF70.
Selected Material: EP-CF70
| Property | Value |
|---|---|
| Fatigue Strength σf (MPa) | 959–1410 |
| Young's Modulus E (GPa) | 129–154 |
| Yield Strength Re (MPa) | 1740–2170 |
| Price (EUR/kg) | 34.9–38.8 |
| Density ρ (kg/m³) | 1550–1580 |
| Fracture Toughness Kc (MPa·m½) | 60.2–73.5 |
| Thermal Expansion α (µstrain/°C) | −0.6 |
| Min Service Temperature (°C) | −123 to −73 |
| Performance Index P (N·m/kg) | 7.69–7.95 |
| Cost/Performance C/P (EUR/N·m) | 4.38–5.04 |