Dealing with discreteness

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# Dealing with discreteness - PowerPoint PPT Presentation

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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Presentation Transcript
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
• 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
• Graphite epoxy w
• Design Laminate with

Where on diagram?

Different visualization
• Fig. 4.1 (feasible domain)
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
• Bending response of a single layer
• Bending stresses proportional to curvatures
Hooke’s law
• Moment resultants
• D-matrix (EI per unit width)
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
• 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