Laminate Descriptions

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Laminate Descriptions
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Objectives

• Define special laminates
• Determine stresses

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Laminate Stiffness and Compliance

• Plugging plate stiffness relationships into
  laminate stress and moment resultant equations in
  terms of strains and curvatures

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Coupling
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Coupling Characteristics

• Fully coupled laminate all 18 coefficeints in
  the A B D matrix are nonzero.
• Application of one load direction makes all 6
  strains non-zero.
• Avoiding this coupling is often desirable.
• Special laminates eliminate this coupling

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Laminate Types

• Symmetric
• Antisymmetric
• Balanced
• Quasi-Isotropic
• Cross-Ply
• Angle-Ply
• Specially Orthotropic

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Symmetric Laminates

• Layers of the same material, thickness, and
  orientation are symmetrical wrt to middle surface
  of laminate.
• Example q/-q/-q/q
• both balanced and symmetric
• Important characteristics
• Bij0
• Mechanical characteristics
• no bending-extension coupling

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Antisymmetric Laminates

• Pairs of layers of opposite orientation but the
  same material and thickness symmetrical wrt
  middle surface of laminate.
• Example q/-q/q/-q
• Important characteristics
• A16A260
• D16D260
• Not easy to analyze since B16 and B26 coupling
  terms are non-zero

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Balanced Laminates

• Description For every layer at q, there is
  another at -q, and for each 0? layer there is a
  90? layer
• Example 0/45/90/-45
• Characteristics
• Q16(q )-Q16(-q)
• Q26(q )-Q26(-q)
• Important characteristics
• A16A260
• D16D260
• B11B22B120
• Mechanical characteristic
• NxB16kxy

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Quasi-isotropic Laminates

• A laminate that behaves like an isotropic plate
• in-plane is similar to isotropic plates
• bending stiffness is different from isotropic
  plates
• Given by
• where k is the layer number Ntotal layers
  (gt3), q0 is arbitrary initial angle
• Equal number of plies at
• 0, 45, -45, 90 or
• 0, 60, -60
• A matrix independent of orientation
• B D matrices are not
• Mechanical uses..

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Cross-Ply and Angle-Ply Laminates

• cross-ply 0? and 90? layers only
• 16 and 26 entries for A and D 0
• Easy for analysis if symmetric also, i.e., B0
• angle-ply q? layers only
• symmetric or antisymmetric balanced laminate
• symmetric A16A260 Bij0 D16?0 D26?0
• antisymmetric A16A260 D16D260 B16?0 B26?0

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Specially Orthotropic Laminate

• Cross-ply laminates or cross-ply rotated by q
• woven or stitched bi-directional fabric also
• A16A260
• D16D260
• B16 B26 0

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Laminate Moduli

• Equivalent moduli Ex, Ey, Gxy, nxy
• Defined for balanced symmetric laminates.
• Properties of a fictitious equivalent,
  orthotropic plate that behaves like actual
  laminate under in-plane loads
• Do not use for bending loading
• since D16?0 D26?0
• Equivalent moduli are

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Stresses within Plies

• IMPORTANT We cannot simply transform from exy to
  sxy using Qbar because
• may be several plies with different fiber
  orientations
• strain can vary with thickness if k is nonzero
• Several steps involved
• 1) Calculate strains through the thickness from
  stress and moment resultants
• 2) Convert strains to material coordinate system
• 3) Calculate stresses within each ply in
  material coordinate system

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Stresses within Plies (2)

• Calculate Strains Through Thickness

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Stresses within Plies (3)

• Convert Strains to Material Coordinates
• Calculate Stresses within Each Ply

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Future Directions

• Examples of stress calculations