Research Article
Behaviour and Optimization Aids of Composite Stiffened Hypar Shell Roofs with Cutout under Free Vibration
Table 8
Values of “” for +45/−45/+45/−45 hypar shells.
| Edge condition | | | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 |
| | 0.2 | 75.5 | 77.52 | 79.62 | 81.91 | 79.62 | 77.53 | 75.48 | | 0.3 | 77.73 | 83.09 | 88.13 | 90.22 | 87.48 | 83.1 | 77.73 | | 0.4 | 79.88 | 88.13 | 94.67 | 97.1 | 94.66 | 87.7 | 79.88 | CCCC | 0.5 | 81.64 | 90.22 | 96.18 | 100 | 96.18 | 89.43 | 81.65 | | 0.6 | 79.88 | 87.48 | 94.67 | 97.1 | 94.67 | 87.56 | 79.88 | | 0.7 | 77.73 | 83.1 | 87.78 | 90.23 | 87.45 | 83.09 | 77.73 | | 0.8 | 75.23 | 77.24 | 79.46 | 81.91 | 79.59 | 77.26 | 75.22 |
| | 0.2 | 107.37 | 111.09 | 113.43 | 114.35 | 113.44 | 111.12 | 107.33 | | 0.3 | 109.36 | 116.53 | 120.39 | 120.22 | 120.33 | 116.71 | 109.43 | | 0.4 | 110.05 | 113.46 | 112.76 | 111.31 | 112.73 | 113.62 | 110.23 | CSCC | 0.5 | 106.26 | 107.25 | 102.28 | 100 | 102.23 | 107.25 | 106.1 | | 0.6 | 103.13 | 100.64 | 95.53 | 93.26 | 95.47 | 100.66 | 102.59 | | 0.7 | 98.44 | 94.11 | 90.94 | 89 | 90.86 | 94.96 | 97.47 | | 0.8 | 92.85 | 89.98 | 87.17 | 85.77 | 87.11 | 90.07 | 92.03 |
| | 0.2 | 92.25 | 97.51 | 102.65 | 106.18 | 110.36 | 109.26 | 107.52 | | 0.3 | 90.31 | 95.06 | 100.71 | 107.15 | 113.38 | 116.61 | 111.43 | | 0.4 | 87.39 | 90.93 | 95.43 | 102.23 | 112.88 | 120.74 | 113.94 | CCSC | 0.5 | 86.01 | 88.94 | 93.11 | 100 | 111.51 | 120.59 | 114.85 | | 0.6 | 87.39 | 90.93 | 95.43 | 102.23 | 112.88 | 120.71 | 113.96 | | 0.7 | 90.31 | 95.07 | 100.71 | 107.15 | 113.39 | 116.77 | 111.39 | | 0.8 | 92.22 | 97.4 | 102.31 | 106.04 | 110.01 | 109.17 | 107.57 |
| | 0.2 | 91.86 | 90.02 | 87.14 | 85.78 | 87.14 | 90.02 | 91.86 | | 0.3 | 97.09 | 94.85 | 90.89 | 89 | 90.89 | 94.85 | 97.09 | | 0.4 | 102.26 | 100.62 | 95.5 | 93.27 | 95.5 | 100.62 | 102.25 | CCCS | 0.5 | 105.99 | 107.28 | 102.26 | 100 | 102.26 | 107.28 | 105.93 | | 0.6 | 110.5 | 113.49 | 112.73 | 111.27 | 112.72 | 113.49 | 110.06 | | 0.7 | 109.37 | 116.56 | 120.35 | 120.21 | 120.35 | 116.58 | 109.37 | | 0.8 | 106.23 | 109.95 | 112.53 | 113.65 | 112.87 | 110.26 | 106.66 |
| | 0.2 | 95.93 | 100.5 | 103.22 | 102.74 | 101.52 | 100.22 | 97.64 | | 0.3 | 93.28 | 97.34 | 101.01 | 102.67 | 103.21 | 102.67 | 100.37 | | 0.4 | 90.61 | 94.01 | 97.93 | 100.97 | 102.56 | 103.17 | 101.65 | CSSC | 0.5 | 91.13 | 94.4 | 98.11 | 100 | 100.55 | 102.33 | 102.63 | | 0.6 | 95.01 | 98.53 | 100.05 | 97.71 | 97.28 | 100.34 | 102.78 | | 0.7 | 99.07 | 101.19 | 98.19 | 93.94 | 93.32 | 96.59 | 99.91 | | 0.8 | 96.67 | 98.42 | 94.33 | 90.33 | 89.66 | 92.33 | 95.22 |
| | 0.2 | 97.17 | 98.62 | 94.38 | 90.41 | 89.83 | 92.61 | 95.51 | | 0.3 | 99.04 | 101.42 | 98.17 | 93.99 | 93.49 | 96.79 | 100.11 | | 0.4 | 95 | 98.7 | 100.12 | 97.75 | 97.43 | 100.53 | 102.97 | CCSS | 0.5 | 91.08 | 94.55 | 98.15 | 100 | 100.66 | 102.49 | 102.78 | | 0.6 | 90.55 | 94.13 | 97.97 | 101 | 102.65 | 103.29 | 101.75 | | 0.7 | 93.3 | 97.5 | 101.13 | 102.8 | 103.35 | 102.81 | 100.5 | | 0.8 | 95.63 | 100.33 | 103.41 | 102.77 | 101.64 | 100 | 97.48 |
| | 0.2 | 95.87 | 96.13 | 94.92 | 94.15 | 94.92 | 96.13 | 95.83 | | 0.3 | 103.42 | 104.06 | 100.92 | 98.89 | 100.92 | 104.06 | 103.42 | | 0.4 | 103.08 | 104.22 | 101.8 | 99.99 | 101.8 | 104.22 | 103.08 | CSCS | 0.5 | 102.11 | 103.48 | 101.55 | 100 | 101.55 | 103.48 | 102.11 | | 0.6 | 103.08 | 104.23 | 101.8 | 100 | 101.8 | 104.22 | 103.08 | | 0.7 | 103.42 | 104.06 | 100.92 | 98.89 | 100.92 | 104.06 | 103.42 | | 0.8 | 94.95 | 95.31 | 94.23 | 93.78 | 94.29 | 95.6 | 95.17 |
| | 0.2 | 96.22 | 103.6 | 103.18 | 102.26 | 103.18 | 103.6 | 96.22 | | 0.3 | 96.53 | 104.15 | 104.36 | 103.67 | 104.36 | 104.15 | 96.53 | | 0.4 | 95.31 | 100.98 | 101.85 | 101.68 | 101.85 | 100.98 | 95.31 | SCSC | 0.5 | 94.52 | 98.92 | 99.94 | 100 | 99.94 | 98.93 | 94.52 | | 0.6 | 95.31 | 100.98 | 101.85 | 101.68 | 101.85 | 100.98 | 95.31 | | 0.7 | 96.53 | 104.15 | 104.36 | 103.67 | 104.36 | 104.15 | 96.53 | | 0.8 | 96.23 | 103.59 | 103.13 | 102.19 | 103.13 | 105.58 | 96.22 |
| | 0.2 | 94.97 | 96.22 | 94.35 | 91.61 | 90.5 | 91.12 | 90.97 | | 0.3 | 103.71 | 105.89 | 102.58 | 97.88 | 96.51 | 98.02 | 98.03 | | 0.4 | 104.04 | 106.17 | 103.76 | 99.83 | 98.56 | 94.14 | 99.79 | CSSS | 0.5 | 103.07 | 105.12 | 103.26 | 100 | 98.84 | 99.89 | 99.89 | | 0.6 | 104.04 | 106.17 | 103.76 | 99.83 | 98.56 | 99.78 | 99.79 | | 0.7 | 103.71 | 105.89 | 102.58 | 97.89 | 96.51 | 98.03 | 98.03 | | 0.8 | 94.35 | 95.69 | 93.98 | 91.17 | 90.05 | 90.5 | 90.42 |
| | 0.2 | 90.77 | 97.71 | 99.57 | 99.72 | 99.58 | 97.7 | 90.77 | | 0.3 | 91.11 | 97.83 | 99.65 | 99.8 | 99.65 | 97.83 | 91.11 | | 0.4 | 90.67 | 96.5 | 98.5 | 98.79 | 98.5 | 96.51 | 90.67 | SSSC | 0.5 | 91.95 | 98 | 99.83 | 100 | 99.83 | 98 | 91.95 | | 0.6 | 94.82 | 102.81 | 103.94 | 103.44 | 103.94 | 102.81 | 94.81 | | 0.7 | 96.72 | 106.2 | 106.42 | 105.32 | 106.42 | 106.2 | 96.72 | | 0.8 | 95.38 | 104.11 | 104.24 | 103.18 | 104.22 | 104.09 | 95.38 |
| | 0.2 | 90.97 | 91.14 | 90.5 | 91.61 | 94.35 | 96.23 | 94.99 | | 0.3 | 98.03 | 98.03 | 96.51 | 97.88 | 102.58 | 105.89 | 103.71 | | 0.4 | 95.29 | 99.78 | 98.56 | 99.83 | 103.76 | 106.17 | 104.04 | SSCS | 0.5 | 99.89 | 99.89 | 98.84 | 100 | 103.26 | 105.12 | 103.07 | | 0.6 | 99.81 | 99.79 | 98.56 | 99.83 | 103.76 | 106.17 | 104.04 | | 0.7 | 98.03 | 98.03 | 96.51 | 97.89 | 102.59 | 105.89 | 103.71 | | 0.8 | 89.91 | 90.07 | 89.62 | 91.29 | 93.56 | 95.74 | 94.07 |
| | 0.2 | 90.91 | 91.7 | 89.71 | 88.65 | 89.71 | 91.7 | 90.91 | | 0.3 | 91.48 | 99.37 | 97.5 | 95.99 | 97.5 | 99.37 | 91.48 | | 0.4 | 89.64 | 97.39 | 100.37 | 99.5 | 100.37 | 97.39 | 89.64 | SSSS | 0.5 | 88.62 | 95.93 | 99.42 | 100 | 99.42 | 95.93 | 88.62 | | 0.6 | 89.64 | 97.39 | 100.37 | 99.49 | 100.37 | 97.39 | 89.64 | | 0.7 | 91.48 | 99.37 | 97.51 | 95.99 | 97.51 | 99.37 | 91.48 | | 0.8 | 90.69 | 91.02 | 89.15 | 88.3 | 89.06 | 91.21 | 90.3 |
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, , , ; = 25, , = , , , . Each stiffener has a single lamina with fibres along its length.
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