Behaviour and Optimization Aids of Composite Stiffened Hypar Shell Roofs with Cutout under Free Vibration

Table 9

Maximum values of 𝑟 with corresponding coordinates of cutout centres and zones where 𝑟≤90 and 𝑟≥95 for 0/90/0/90 hypar shells.

Boundary Condition	Maximum values of 𝑟	Coordinate of cutout centre	Area in which the value of 𝑟≤90	Area in which the value 𝑟≥95
CCCC	100.03	(0.3,0.5), (0.4,0.5), (0.6,0.5), (0.7,0.5)	Nil	0.2≤𝑥^−≤0.8; 0.2≤𝑦^−≤0.8
CSCC	100.35	(0.5,0.3)	Nil	0.2≤𝑥^−≤0.8; 0.2≤𝑦^−≤0.8
CCSC	100.38	(0.8,0.5)	Nil	0.2≤𝑥^−≤0.8; 0.2≤𝑦^−≤0.8
CCCS	100.35	(0.5,0.7)	Nil	0.2≤𝑥^−≤0.8; 0.2≤𝑦^−≤0.8
CSSC	100.95	(0.8, 0.3)	Nil	0.2≤𝑥^−≤0.8; 0.2≤𝑦^−≤0.8
CCSS	100.91	(0.8,0.6)	Nil	0.2≤𝑥^−≤0.8; 0.2≤𝑦^−≤0.8
CSCS	100.00	(0.5,0.5)	0.2≤𝑥^−≤0.8, 𝑦^−=0.2; 0.2≤𝑥^−≤0.8, 𝑦^−=0.8	0.2≤𝑥^−≤0.8; 0.4≤𝑦^−≤0.6
SCSC	100.00	(0.5,0.5)	𝑥^−=0.2, 0.2≤𝑦^−≤0.8; 𝑥^−=0.8, 0.2≤𝑦^−≤0.8	0.4≤𝑥^−≤0.6; 0.2≤𝑦^−≤0.8
CSSS	103.90	(0.7,0.5)	0.2≤𝑥^−≤0.8, 𝑦^−=0.2; 0.2≤𝑥^−≤0.8, 𝑦^−=0.8	0.2≤𝑥^−≤0.8; 0.4≤𝑦^−≤0.6
SSSC	103.95	(0.5,0.3)	𝑥^−=0.2, 0.2≤𝑦^−≤0.8; 𝑥^−=0.8, 0.2≤𝑦^−≤0.8	0.4≤𝑥^−≤0.6; 0.2≤𝑦^−≤0.8
SSCS	103.90	(0.3,0.5)	0.2≤𝑥^−≤0.8, 𝑦^−=0.2; 0.2≤𝑥^−≤0.8, 𝑦^−=0.8	0.2≤𝑥^−≤0.8; 0.4≤𝑦^−≤0.6
SSSS	100.00	(0.5,0.5)	𝑥^−=0.2,0.2≤𝑦^−≤0.8; 𝑥^−=0.8,0.2≤𝑦^−≤0.8	0.4≤𝑥^−≤0.6; 0.4≤𝑦^−≤0.6

𝑎/𝑏=1, 𝑎/ℎ=100, 𝑎^/𝑏^=1, 𝑐/𝑎=0.2; 𝐸₁₁/𝐸₂₂=25, 𝐺₂₃=0.2𝐸₂₂, 𝐺₁₃=𝐺₁₂=0.5𝐸₂₂, 𝜈₁₂=𝜈₂₁=0.25, 𝑏_st/ℎ=1, 𝑑_st/ℎ=2. Each stiffener has a single lamina with fibres along its length.