# Design of Structural Elements

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15 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

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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].

A
11

A
12

A
22

D
11

D
22

D
12

D
66

Remember that these values depend on
laminate thickness.

Composite panel design

For convenience,
D
1

= D
11
, D
2

= D
22
,

D
3

= D
12

-

2 D
66

For a homogeneous orthotropic plate,
thickness h:

D
1

= E
x

h
3

/ 12
m

D
2

= E
y

h
3

/ 12
m

D
66

= G
xy

h
3

/ 12

where
m

= 1
-

n
xy

n
yx

= 1
-

n
xy
2

E
y

/ E
x

Composite panel design

For in
-
are used in the normal way.

Under uniaxial compression, a plate is
likely to buckle at some critical load N
x
’.

Buckling loads depend on geometry, edge
conditions and flexural properties.

Thin plates may fail by shear buckling

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

3
2
2
2
2
2
1
2
2
2
'
D
b
a
D
a
b
D
b
N
x

2
1
1
2
4
'
b
K
D
N
x

1
3
2
/
1
1
2
1
5
.
0
D
D
D
D
K

Transverse point load P, or uniform
pressure p, so that P = p a b:

Maximum transverse panel deflection is:

with max bending moments

and

2
2
D
Pa
w

P
M
x
1

P
M
y
2

a

b

The design parameters

,

1

and

2

depend
on plate aspect ratio, flexural stiffness, edge

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:

where D is the flexural rigidity and Q is the
shear stiffness.

Q
L
D
D
PL
w
2
3
1

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 Fibre
-
Polymer 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

Sandwich panels are a very efficient way of
providing high bending stiffness at low weight.
The stiff, strong facing skins carry the bending
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
the core resists shear

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
-

high strength and
stiffness, but brittle

-

~ 50% reduction of properties at 40
-
60
o
C

-

chemical breakdown (HCl vapour) at
200
o
C

Foam core comparison

PU

-

inferior to PVC at ambient temperatures

-

better property retention (max. 100
o
C)

Phenolic

-

poor mechanical properties

-

good fire resistance

-

strength retention to 150
o
C

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
0
50
100
150
200
250
300
50
100
150
density (kg/m
3
)
MPa
tensile modulus
shear modulus
shear strength
Material
Foam includes
– polyvinyl chloride
(PVC)

polymethacrylimide
– polyurethane
– polystyrene

phenolic

polyethersulfone (PES)
Wood-based includes
– plywood
– balsa
– particleboard
Property
Relatively low crush
strength and stiffness
Increasing stress with
increasing strain
Friable
Limited strength
Fatigue
Cannot be formed around
curvatures
Very heavy density
Subject to moisture
Flammable
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
Excellent strength-to-weight ratio
Excellent moisture resistance
Self-extinguishing, low smoke
versions available
Why honeycomb?

List compiled by company (Hexcel) which sells honeycomb!

Sandwich constructions
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
0
100
200
300
400
500
600
30
40
50
60
70
80
density (kg/m
3
)
shear modulus
L' direction
'W' direction
'L' direction plate shear modulus
0
100
200
300
400
500
600
20
40
60
80
density (kg/m
3
)
MPa
Nomex
Al
Aluminium generally has superior properties to
Nomex honeycomb, e.g:

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

h

core: tensile modulus E
c

shear modulus G
c

skin: tensile modulus E
s

d = c + t

Sandwich Construction
-

flexural rigidity

Neglecting the core stiffness:

Including the core:

If core stiffness is low:

12
3
3
c
h
b
E
D
s

12
2
6
3
2
3
bc
E
btd
E
bt
E
D
c
s
s

2
2
btd
E
D
s

Sandwich Construction
-

flexural rigidity

Shear stiffness is likely to be significant:

where shear stiffness Q = b c G
c

If D/L
2
Q < 0.01, shear effects are small.

If D/L
2
Q > 0.1, shear effects are dominant.

Q
L
D
D
PL
w
2
3
1

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 G
c
. a is the longest side of a
rectangular panel.

Q
a
D
D
Pa
w
2
2
2
2
1

Shear correction factor (pressure
1
1.5
2
2.5
3
3.5
4
0
1000
2000
3000
span (mm)
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:

D
h
ME
s
s
2

2
4
4
2
2
y
c
E
td
E
D
S
c
s
c

bd
S
c

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

Hexcel Honeycomb Sandwich Design
Technology:
http://www.hexcel.com/NR/rdonlyres/80127A98
-
7DF2
-
4D06
-
A7B3
-
7EFF685966D2/0/7586_HexWeb_Sand_Design.pdf

Eric Green Associates,
Marine Composites
-

chapter 3

(1999):
http://www.marinecomposites.com