1. Design of Structural Elements

2. Composite panel design
Laminate analysis gives the fundamental information on stiffness, elastic constants and uniaxial strengths.
For structural analysis, we need in-plane stiffness [A] and flexural rigidity [D].

3. A11
D66
D22
D12
A12
D11
A22
Remember that these values depend on laminate thickness.

4. Composite panel design
For convenience, D1 = D11, D2 = D22, D3 = D D66
For a homogeneous orthotropic plate, thickness h: D1 = Ex h3 / 12m D2 = Ey h3 / 12m D66 = Gxy h3 / 12 where m = 1 - nxy nyx = 1 - nxy2 Ey / Ex

5. Composite panel design
For in-plane loads, the elastic constants are used in the normal way.
Under uniaxial compression, a plate is likely to buckle at some critical load Nx’.
Buckling loads depend on geometry, edge conditions and flexural properties.
Thin plates may fail by shear buckling before shear failure load.

6. Buckling of Composite Panels
For small aspect ratios (0.5 < a/b < 2):
For long, simply-supported plates with a/b > 2, buckling is independent of length: where

7. Transverse Loading of Composite Panels
Transverse point load P, or uniform pressure p, so that P = p a b:
Maximum transverse panel deflection is: with max bending moments and a b

8. Transverse Loading of Composite Panels
The design parameters a, b1 and b2 depend on plate aspect ratio, flexural stiffness, edge conditions and load:
Hollaway (ed), Handbook of Polymer Composites for Engineers

9. Thin walled beam design
Standard isotropic design formulae for deflections may be used, but check whether a shear correction is required: where D is the flexural rigidity and Q is the shear stiffness.

10. Hollaway (ed), Handbook of Polymer Composites for Engineers

11. Thin walled beam design
In torsion, wall buckling may be a critical condition.
In general, several failure modes are possible - a systematic design procedure is required.
Laminates may have different tensile and compressive strengths.
Powell, Engineering with Fibre-Polymer Laminates

12. Sandwich Construction
Thin composite skins bonded to thicker, lightweight core.
Large increase in second moment of area without weight penalty.
Core needs good shear stiffness and strength.
Skins carry tension and compression loads.

13. Sandwich panels are a very efficient way of providing high bending stiffness at low weight. The stiff, strong facing skins carry the bending loads, while the core resists shear loads. The principle is the same as a traditional ‘I’ beam:

14. Bending stiffness is increased by making beams or panel thicker - with sandwich construction this can be achieved with very little increase in weight:

15. The stiff, strong facing skins carry the bending loads, while the core resists shear loads.
Total deflection = bending + shear
Bending depends on the skin properties; shear depends on the core

16. Foam core comparison
PVC (closed cell) - ‘linear’ – high ductility, low properties - ‘cross-linked’ – high strength and stiffness, but brittle - ~ 50% reduction of properties at 40-60oC - chemical breakdown (HCl vapour) at 200oC

17. Foam core comparison
PU - inferior to PVC at ambient temperatures - better property retention (max. 100oC)
Phenolic - poor mechanical properties - good fire resistance - strength retention to 150oC

18. Foam core comparison
Syntactic foam - glass or polymer microspheres - used as sandwich core or buoyant filler - high compressive strength
Balsa - efficient and low cost - absorbs water (swelling and rot) - not advisable for primary hull and deck structures; OK for internal bulkheads, etc?

19. Both images from www.marinecomposites.com

21. Why honeycomb? List compiled by company (Hexcel) which sells honeycomb!

22. Sandwich constructions made with other core materials (balsa, foam, etc) have a large surface are available for bonding the skins.
In honeycomb core, we rely on a small fillet of adhesive at the edge of the cell walls:
The fillet is crucial to the performance of the sandwich, yet it is very dependent on manufacturing factors (resin viscosity, temperature, vacuum, etc).

23. Honeycomb is available in polymer, carbon, aramid and GRP
Honeycomb is available in polymer, carbon, aramid and GRP. The two commonest types in aerospace applications are based on aluminium and Nomex (aramid fibre-paper impregnated with phenolic resin).
Cells are usually hexagonal:
but ‘overexpanded’ core is also used to give extra formability:

24. Core properties depend on density and cell size
Core properties depend on density and cell size. They also depend on direction - the core is much stronger and stiffer in the ‘ribbon’ or ‘L’ direction:

25. Aluminium generally has superior properties to Nomex honeycomb, e.g:

26. Aluminum Honeycomb • relatively low cost • best for energy absorption • greatest strength/weight • thinnest cell walls • smooth cell walls • conductive heat transfer • electrical shielding • machinability
Aramid Fiber (Nomex) Honeycomb • flammability/fire retardance • large selection of cell sizes, densities, and strengths • formability and parts-making experience • insulative • low dielectric properties

27. Sandwich Construction
Many different possible failure modes exist, each of which has an approximate design formula.

31. Design Formulae for Sandwich Construction
core: tensile modulus Ec shear modulus Gc
skin: tensile modulus Es
d = c + t

32. Sandwich Construction - flexural rigidity
Neglecting the core stiffness:
Including the core:
If core stiffness is low:

33. Sandwich Construction - flexural rigidity
Shear stiffness is likely to be significant: where shear stiffness Q = b c Gc
If D/L2Q < 0.01, shear effects are small.
If D/L2Q > 0.1, shear effects are dominant.

34. Sandwich Construction - flexural rigidity
Plate stiffnesses can be calculated by CLA, but shear effects must be considered.
Formula for plate deflection is of the form: where the transverse shear stiffness is now Q = c Gc. a is the longest side of a rectangular panel.

36. Bending stresses in sandwich beams
It is often assumed that the core carries no bending stress, but are under a constant shear stress. For an applied bending moment M:
Skin stress
Core shear stress: where S is the shear force y is distance from neutral axis
If core stiffness can be neglected:

38. Further reading:
L Hollaway (ed.), Handbook of Polymer Composites for Engineers, Woodhead (1994).
Hexcel Honeycomb Sandwich Design Technology:
Eric Green Associates, Marine Composites - chapter 3 (1999):