1. Aerospace Structures and Materials: Lamination Theory and Applications
Dr. Tom Dragone
Orbital Sciences Corporation

2. Structure Design / Analysis Process
GLOBAL LOADS
Aerodynamics
Inertial
Applied
GEOMETRY
Planform
Skin Construction
Spar/Rib Layout
MATERIALS
Metal
Composite
SIZING
Thickness
Ply Orientation
SHEAR-MOMENT
DIAGRAM
Section Loads
Structure
Idealization
Stiffness
Lamination Theory
BOX BEAM ANALYSIS
Component Loads
(Cap Forces, Shear Flow)
FAILURE ANALYSIS
JOINT LOADS
Weld , Braze
Bond, Bolt
Metal
Yield
Rupture
Composite
FPF
LPF
Stability
Buckling
Crippling
Fracture
Toughness
Crack Size
Fatigue
Crack Initiation
Crack Growth
MS>0?
Done
Yes No

3. ABD Matrix Coupling: Uniaxial
Example: [06]
In general, diagonal terms will be different
E11>>E22 D11>>D22
NOTE: Isotropic materials would have same terms populated, but
E11=E22 D11=D22

4. ABD Matrix Coupling: Symmetric Balanced
Example: [ ]S [ ]2S [ ]S
Balanced Symmetric laminates have Bend-Twist coupling
In general, the diagonal terms will be different
Quasi-Isotropic laminates have equal inplane moduli, but still have bend-twist coupling (hence, not truly isotropic)

5. ABD Matrix Coupling: Symmetric Unbalanced
Example: [ ]S [303]S
Unbalanced laminates have Stretch-Shear coupling

6. ABD Matrix Coupling: 0/90 Coupling
Example: [0 90] [04 904]
0/90 laminates have Stretch-Bend coupling 0°
90°
0° (Stiff)
90° (Weak)

7. ABD Matrix Coupling Unsymmetric Balanced
Example: [02 ±45 90]3 [ ]
Unsymmetric laminates have Stretch-Twist and Shear Bend coupling

8. ABD Matrix Coupling Unsymmetric Unbalanced
Example: [ ]
Unsymmetric Unbalanced laminates have all coupling including Shear-Twist coupling

9. ABD Matrix Coupling

10. Introduction to COMPFAIL
COMPFAIL (COMPosite FAILure analysis tool) is an Excel spreadsheet-based implementation of Composite Lamination Theory
User enters
Lamina Information
Laminate Information
Loading
Code calculates
ABD Matrix
Equivalent Moduli
Global Strains and Curvatures
Local Ply Stresses and Strains
Failure Indices

11. COMPFAIL Process
Choose Ply Material
Sets E, Vf, X,Y,S,a,t

12. COMPFAIL Coordinate Systemsx y z
Material Coordinate System 2 1 3
Laminate Coordinate System q

13. COMPFAIL Process Choose Ply Material Choose Layup
Sets E, Vf, X,Y,S,a,t
Choose Layup
Ply by Ply definition of material and angle (relative to reference)

14. COMPFAIL Process Choose Ply Material Choose Layup
Sets E, Vf, X,Y,S,a,t
Choose Layup
Ply by Ply definition of material and angle (relative to reference)
Intermediate Calculations
Define Qij, Aij, Bij, Dij

15. COMPFAIL Process Choose Ply Material Choose Layup
Sets E, Vf, X,Y,S,a,t
Choose Layup
Ply by Ply definition of material and angle (relative to reference)
Intermediate Calculations
Define Qij, Aij, Bij, Dij
Define ABD Matrix

16. COMPFAIL Process
Apply Loads
N1, N2, N6, M1, M2, M6

17. COMPFAIL Process Apply Loads N1, N2, N6, M1, M2, M6
Return Strains and Curvatures
e1, e2, e6, k1, k2, k6

18. COMPFAIL Process Apply Loads N1, N2, N6, M1, M2, M6
Return Strains and Curvatures
e1, e2, e6, k1, k2, k6
Return Equivalent Moduli (For Symmetric Laminates ONLY)
EInPlane, EFlexure

19. COMPFAIL Process Apply Loads Return Strains and Curvatures
Return Equivalent Moduli (For Symmetric Laminates ONLY)
Return Ply Strains and Ply Stresses
e1, e2, e6, s1, s2, s6 for Global (Laminate) Coordinate System
ex, ey, es, sx, sy, ss for Local (Material) Coordinate System
Two Values:
Top and Bottom
of Ply

20. COMPFAIL Process Apply Loads Return Strains and Curvatures
Return Equivalent Moduli (For Symmetric Laminates ONLY)
Return Ply Strains and Ply Stresses
Ignore Failure Criteria for Now

21. Satellite Solar Panel Example
INDOSTAR SATELLITE
Solar Array Panel
Spacecraft Bus
Communications
Antennae

22. Solar Panel Example LAMINATE REQUIREMENTS
Light & Heat
Fragment
Connections
Si or GaAs
Solar Cells
Cracks DT
Broken
Connections
Solar Panel
LAMINATE REQUIREMENTS
Stiff Substrate to Minimize Deflections => High Modulus
Equal Stiffness in All Directions => Quasi-Isotropic
Thermal Stability => High Conductivity
Light Weight => Composite

23. Consider an 8-Ply Quasi-Isotropic Sandwich During Cure Process
Laminate Cure Effects
Consider an 8-Ply Quasi-Isotropic Sandwich During Cure Process
Co-Cure
(Both Skins at Same Time)
80+psi Pressure
Cure Pressure on Thin Sandwich Leads to Pillowing
Poor Consolidation
High Void Content
Wavy Surface
IML Skin
Core
OML Skin
Tool

24. Consider Same 8-Ply Quasi-Isotropic Sandwich During Cure Process
Laminate Cure Effects
Consider Same 8-Ply Quasi-Isotropic Sandwich During Cure Process
Separate-Cure (Skins Cured Separately)
Cold Bond (Room Temp)
IML Skin
OML Skin
Adhesive Film
Skins Must be Cured Separately
Uniform DT During Cure is Like Uniform In-Plane Loads (N1, N2)
Uniform Load on Non-Symmetric Laminate Results in Warping
Individual Skins Must be Quasi-Isotropic

25. Flutter Effects Recall that Cp is @ 1/4 MAC for Subsonic Flight
Results in Torsion that leads to Leading Edge Up
LIFT f CP
Elastic Axis
Torsion Axis
f Increases with Span

26. Typical Operating Point
Flutter Effects
Lift
Local AOA (a + f) f
Typical Operating Point
Recall also that Lift Increases with Angle of Attack
Twist Increases the Local Angle of Attack on a Wing Segment
HIGHER AOA
HIGHER LIFT
TWIST
Positive Feedback
System Becomes Unstable at “Divergence Speed”
Subject to Pronounced Vibrations => Flutter

27. X-29 Composite Wing Design
Canards
Forward-Swept
Wings

28. X-29 Composite Wing Design
Forward-swept wings provide enhanced maneuverability
Would be an advantage to close-combat aircraft
Forward-swept wings enhance flutter effects
Wing bending increases local AOA even without torsion
Composites enable weight-efficient forward swept wings for the X-29 aircraft by exploiting negative stretch-twist coupling

29. Flutter Reduction Effect
Wing bending causes tension (top) and compression (bottom) stretching in the skins
Stretch-Twist coupling produces a twisting moment in the skins
Since the wing is thin, this becomes a torque on the whole wing
Upward Bending => LE Down Twist, reducing flutter effects