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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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## PowerPoint Slideshow about ' Dealing with discreteness' - inoke

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Presentation Transcript

• 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.

• 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?

• Graphite epoxy w

• Design Laminate with

Where on diagram?

• Fig. 4.1 (feasible domain)

• 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 lamination theory

• Moment resultants

• D-matrix (EI per unit width)

Bending of symmetrically laminated layers lamination theory

• 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 lamination theory

• 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