Design of Structural Elements

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Design of Structural Elements
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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.

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A11
D66
D22
D12
A12
D11
A22
Remember that these values depend on laminate
thickness.
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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 / 12where m 1 - nxy nyx 1 - nxy2 Ey / Ex

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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.

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Buckling of Composite Panels

• For small aspect ratios (0.5 lt a/b lt 2)
• For long, simply-supported plates with a/b gt 2,
  buckling is independent of length
  where

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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
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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
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Thin walled beam design

• Standard isotropic design formulae for
  deflections may be used, but check whether a
  shear correction is requiredwhere D is the
  flexural rigidity and Q is the shear stiffness.

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

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

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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

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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?

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Both images from www.marinecomposites.com
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Why honeycomb? List compiled by company
(Hexcel) which sells honeycomb!
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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).
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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
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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
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Aluminium generally has superior properties to
Nomex honeycomb, e.g
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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
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Sandwich Construction

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

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Design Formulae for Sandwich Construction
t
c
h
core tensile modulus Ec shear
modulus Gc skin tensile modulus Es d c t
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Sandwich Construction - flexural rigidity

• Neglecting the core stiffness
• Including the core
• If core stiffness is low

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Sandwich Construction - flexural rigidity

• Shear stiffness is likely to be
  significantwhere shear stiffness Q b c Gc
• If D/L2Q lt 0.01, shear effects are small.
• If D/L2Q gt 0.1, shear effects are dominant.

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Sandwich Construction - flexural rigidity

• Plate stiffnesses can be calculated by CLA, but
  shear effects must be considered.
• Formula for plate deflection is of the
  formwhere the transverse shear stiffness is
  now Q c Gc. a is the longest side of a
  rectangular panel.

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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 stresswhere S is the shear forcey
  is distance from neutral axis
• If core stiffness can be neglected

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Further reading L Hollaway (ed.), Handbook of
Polymer Composites for Engineers, Woodhead
(1994). Hexcel Honeycomb Sandwich Design
Technology http//www.hexcel.com/NR/rdonlyres/80
127A98-7DF2-4D06-A7B3-7EFF685966D2/0/7586_HexWeb_S
and_Design.pdf Eric Green Associates, Marine
Composites - chapter 3 (1999)
http//www.marinecomposites.com