Design of Structural Elements
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].
A11
A12
A22
D11
D22
D12 D66
Remember that these values depend on
laminate thickness.
Composite panel design
• For convenience, D1 = D11, D2 = D22,
D3 = D12 - 2 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
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.
Buckling of Composite Panels
• For small aspect ratios (0.5 < a/b < 2):
2 

b2
a2
N x '  2  D1 2  D2 2  2D3 
b  a
b

• For long, simply-supported plates with a/b
> 2, buckling is independent of length:
N x '  4 2D1
K1
b2
where
 D 1/ 2 D 
K1  0.5  2   3 
D1 
 D1 

Transverse Loading of Composite Panels
• Transverse point load P, or uniform
pressure p, so that P = p a b:
a
b
• Maximum transverse panel deflection is:
w
Pa2
D2
with max bending moments
M x  1P and My   2P
Transverse Loading of Composite Panels
The design parameters , 1 and 2 depend
on plate aspect ratio, flexural stiffness, edge
conditions and load:
Hollaway (ed), Handbook of
Polymer Composites for Engineers
Thin walled beam design
• Standard isotropic design formulae for
deflections may be used, but check
whether a shear correction is required:
w
PL3 
D 
1  2 
D  LQ
where D is the flexural rigidity and Q is the
shear stiffness.
Hollaway (ed), Handbook of
Polymer Composites for Engineers
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 FibrePolymer Laminates
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.
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:
Bending stiffness is increased by making
beams or panel thicker - with sandwich
construction this can be achieved with very little
increase in weight:
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
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
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
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?
Both images from
www.marinecomposites.com
Airex R63 linear PVC
300
MPa
250
200
tensile modulus
150
shear modulus
100
shear strength
50
0
50
100
150
3
density (kg/m )
Why honeycomb?
List compiled by company (Hexcel) which sells honeycomb!
Material
Property
Honeycomb Advantages
Foam includes
– polyvinyl chloride
(PVC)
– polymethacrylimide
– polyurethane
– polystyrene
– phenolic
– polyethersulfone (PES)
Relatively low crush
strength and stiffness
Increasing stress with
increasing strain
Friable
Limited strength
Fatigue
Cannot be formed around
curvatures
Excellent crush strength and
stiffness
Constant crush strength
Structural integrity
Exceptionally high strengths
available
High fatigue resistance
OX-Core and Flex-Core cell
configurations
for curvatures
Wood-based includes
– plywood
– balsa
– particleboard
Very heavy density
Subject to moisture
degradation
Flammable
Excellent strength-to-weight ratio
Excellent moisture resistance
Self-extinguishing, low smoke
versions available
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).
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:
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:
5056 aluminium honeycomb
600
shear modulus
500
400
L' direction
300
'W' direction
200
100
0
30
40
50
60
density (kg/m 3)
70
80
Aluminium generally has superior properties to
Nomex honeycomb, e.g:
'L' direction plate shear modulus
600
500
MPa
400
Nomex
300
Al
200
100
0
20
40
60
density (kg/m 3)
80
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
Sandwich Construction
• Many different possible failure modes exist,
each of which has an approximate design
formula.
Design Formulae for Sandwich
Construction
t
c
core: tensile modulus Ec
shear modulus Gc
skin: tensile modulus Es
d=c+t
h
Sandwich Construction - flexural rigidity
• Neglecting the core stiffness:
Es bh 3  c 3 
D
12
• Including the core:
3
2
Es bt
Es btd
Ec bc
D


6
2
12
• If core stiffness is low:
Es btd 2
D
2
3
Sandwich Construction - flexural rigidity
• Shear stiffness is likely to be significant:
w
PL3 
D 
1  2 
D  LQ
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.
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:
w
Pa2 
D2 
1  2 
D
a
Q


2
where the transverse
shear stiffness is now
Q = c Gc. a is the longest side of a
rectangular panel.
Shear correction factor (pressure
loaded panel)
4
3.5
3
2.5
2
1.5
1
0
1000
2000
span (mm)
3000
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:
MEs h
• Skin stress
s 
• Core shear stress:
2D
4



S Estd Ec c
2
  y 
c  

D 2
2 4

where S is the shear force
y is distance from neutral axis
S
• If core stiffness can be neglected:
c 
bd
Further reading:
L Hollaway (ed.), Handbook of Polymer
Composites for Engineers, Woodhead (1994).
Hexcel Honeycomb Sandwich Design
Technology:
http://www.hexcel.com/NR/rdonlyres/80127A98-7DF2-4D06A7B3-7EFF685966D2/0/7586_HexWeb_Sand_Design.pdf
Eric Green Associates, Marine Composites chapter 3 (1999): http://www.marinecomposites.com