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 A22D11

D22 D12D66

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 / 12D2 = Ey h3 / 12D66 = Gxy h3 / 12

where = 1 - xy yx = 1 - xy2 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):

• For long, simply-supported plates with a/b > 2, buckling is independent of length:

where

32

2

22

2

12

2

2' Db

aD

a

bD

bNx

21

124'

b

KDNx

1

3

2/1

1

21 5.0

D

D

D

DK

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

2

2

D

Paw

PMx 1 PMy 2

a

b

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:

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

QL

D

D

PLw

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 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

0

50

100

150

200

250

300

50 100 150

density (kg/m3)

MP

a

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 crushstrength and stiffnessIncreasing stress withincreasing strainFriableLimited strengthFatigueCannot be formed aroundcurvatures

Very heavy densitySubject to moisturedegradationFlammable

Honeycomb Advantages

Excellent crush strength andstiffnessConstant crush strengthStructural integrityExceptionally high strengthsavailableHigh fatigue resistanceOX-Core and Flex-Core cellconfigurationsfor curvatures

Excellent strength-to-weight ratioExcellent moisture resistanceSelf-extinguishing, low smokeversions available

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

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

0

100

200

300

400

500

600

30 40 50 60 70 80

density (kg/m3)

shea

r m

od

ulu

s

L' direction

'W' direction

'L' direction plate shear modulus

0

100

200

300

400

500

600

20 40 60 80

density (kg/m3)

MP

a 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

tc h

core: tensile modulus Ec

shear modulus Gc

skin: tensile modulus Es

d = c + t

Sandwich Construction - flexural rigidity• Neglecting the core stiffness:

• Including the core:

• If core stiffness is low:

12

33 chbED s

1226

323 bcEbtdEbtED css

2

2btdED s

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.

QL

D

D

PLw

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 Gc. a is the longest side of a rectangular panel.

Qa

D

D

Paw

22

2

2

1

Shear correction factor (pressure loaded panel)

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 forcey is distance from neutral axis

• If core stiffness can be neglected:

D

hMEss 2

2

4

422y

cEtdE

D

S csc

bd

Sc

Further reading:

L Hollaway (ed.), Handbook of Polymer Composites for Engineers, Woodhead (1994).

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

Eric Green Associates, Marine Composites - chapter 3 (1999): http://www.marinecomposites.com