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Dealing with discreteness. Laminate thickness must be integer multiple of basic ply thickness. Ply orientations often need to be selected from a small set of angles, e.g. In terms of optimization algorithms we transition from algorithms that use derivatives to algorithms that do not.

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dealing with discreteness
Dealing with discreteness
  • Laminate thickness must be integer multiple of basic ply thickness.
  • Ply orientations often need to be selected from a small set of angles, e.g.
  • In terms of optimization algorithms we transition from algorithms that use derivatives to algorithms that do not.
  • Integer programming is usually NP hard.
miki s diagram for
Miki’s diagram for
  • Finite number of points and excluded regions
  • Which points do we lose with balance condition?
  • Diagram is for 8-ply laminate. What will change and what will remain the same for 12 plies?
continuous example 4 2 1
Continuous Example 4.2.1
  • Graphite epoxy w
  • Design Laminate with

Where on diagram?

different visualization
Different visualization
  • Fig. 4.1 (feasible domain)
example 4 3 1
Example 4.3.1
  • Solve 4.2.1 for 16-ply balanced symmetric laminate of plies.
  • What is common for the first five designs besides the shear modulus?
2 3 bending deformation of isotropic layer classical lamination theory
2.3 Bending deformation of isotropic layer –classical lamination theory
  • Bending response of a single layer
  • Bending stresses proportional to curvatures
hooke s law
Hooke’s law
  • Moment resultants
  • D-matrix (EI per unit width)
bending of symmetrically laminated layers
Bending of symmetrically laminated layers
  • As in in-plane case, we add contributions of all the layers.
  • We still get M=D, but
the power of distance from mid plane
The power of distance from mid-plane
  • In Example 2.21 we had a laminate made of brass and aluminum
  • For in-plane loads laminate was twice as close to aluminum than brass.
  • For bending, brass contribution proportional to . Aluminum contribution
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