1. Flexural stiffness design using Miki’s diagram
Flexural lamination parameters
Boundaries of the domain
What laminates have the same position on the Miki in-plane diagram as on the Miki flexural diagram?

2. Examples (0/90)s : 𝑧 0 =−2𝑡, 𝑧 1 =−𝑡, 𝑧 2 =0,h=4t 0 2 ± 45 :
𝑠 0 = 𝑡 3 − 𝑡 3 +8 𝑡 3 =0.875,
𝑠 90 = 𝑡 𝑡 3 =0.125
𝑊 1 ∗ =0.875cos 0 𝑜 cos 180 𝑜 =0.75 𝑊 3 ∗ =0.875cos 0 𝑜 cos 360 𝑜 =1
0 2 ± 45 :
   𝑊 1 ∗ =0.875cos 0 𝑜 cos 90 𝑜 =0.875,    𝑊 3 ∗ =0.875cos 0 𝑜 cos 180 𝑜 =0.75

3. Stiffest laminate under lateral loads
Recall displacement under sine load
To find stiffest laminate we need to maximize S= 𝐷 𝐷 𝐷 𝑎 𝑏 𝐷 𝑎 𝑏 4
From Table 2.1
This implies that S is a linear function of the lamination parameters, and the stiffest laminate is an angle ply. Why?

4. Example 8.2.1a
Design a 16-layer 20x15” laminated graphite epoxy plate to maximize its fundamental frequency. Material properties are: 𝐸 1 =18.5,  𝐸 2 =1.89,  𝐺 12 =0.93𝑀𝑠𝑖,  𝜈 12 =0.3, 𝑡=0.005", 𝜌=0.057𝑙 𝑏 𝑖 𝑛 3
Tsai-Pagano material properties (in Msi) are 𝑈 1 =8.3252,  𝑈 2 =8.3821,  𝑈 3 =1.9643,  𝑈 4 =2.5366,  𝑈 5 =2.8943

5. Normalized fundamental frequency
Normalized frequency
For our data
For maximum frequency we want negative 𝑊 1 ∗ and negative 𝑊 3 ∗ , so angles near 60-deg.
Why?

6. Maximization of frequency
Iso-frequency contours on Diagram.
Maximum where iso-frequency line is tangent to diagram
Get
Text suggests ± 𝑠
Can we do better?
Should be omega21 in figure