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

Table 10

Maximum values of 𝑟 with corresponding coordinates of cutout centres and zones where 𝑟≤90 and 𝑟≥95 for +45/−45/+45/−45 hypar shells.

Boundary Condition	Maximum values of 𝑟	Co-ordinate of cutout centre	Area in which the value of 𝑟≤90	Area in which the value 𝑟≥95
CCCC	100.00	(0.5,0.5)	0.2≤𝑥^−≤0.3, 0.2≤𝑦^−≤0.8; 0.7≤𝑥^−≤0.8, 0.2≤𝑦^−≤0.8	0.4≤𝑥^−≤0.6; 𝑦^−=0.5
CSCC	120.39	(0.4,0.3)	0.3≤𝑥^−≤0.6, 𝑦^−=0.8	0.2≤𝑥^−≤0.8; 0.2≤𝑦^−≤0.6
CCSC	120.74	(0.7,0.4)	𝑥^−=0.2, 0.4≤𝑦^−≤0.6	0.5≤𝑥^−≤0.8; 0.2≤𝑦^−≤0.8
CCCS	120.35	(0.4,0.7), (0.6,0.7)	0.4≤𝑥^−≤0.6; 𝑦^−=0.2	0.2≤𝑥^−≤0.8; 0.4≤𝑦^−≤0.8
CSSC	103.22	(0.4,0.2)	𝑥^−=0.6; 𝑦^−=0.8	0.4≤𝑥^−≤0.8; 0.2≤𝑦^−≤0.6
CCSS	103.35	(0.6,0.7)	𝑥^−=0.6; 𝑦^−=0.2	0.2≤𝑥^−≤0.8; 0.4≤𝑦^−≤0.8
CSCS	104.23	(0.3,0.6)	Nil	0.2≤𝑥^−≤0.8; 0.3≤𝑦^−≤0.7
SCSC	105.58	(0.7,0.8)	Nil	0.3≤𝑥^−≤0.7; 0.2≤𝑦^−≤0.8
CSSS	106.17	(0.3,0.4), (0.3,0.6)	Nil	0.2≤𝑥^−≤0.8; 0.3≤𝑦^−≤0.7
SSSC	106.42	(0.4,0.7), (0.6,0.7)	Nil	0.3≤𝑥^−≤0.7; 0.2≤𝑦^−≤0.8
SSCS	106.17	(0.7,0.4), (0.7,0.6)	0.2≤𝑥^−≤0.4; 𝑦^−=0.8	0.2≤𝑥^−≤0.8; 0.3≤𝑦^−≤0.7
SSSS	100.37	(0.4,0.4), (0.6,0.4); (0.4,0.6), (0.6,0.6)	𝑥^−=0.2, 0.4≤𝑦^−≤0.6; 𝑥^−=0.8, 0.4≤𝑦^−≤0.6	0.3≤𝑥^−≤0.7; 0.3≤𝑦^−≤0.7

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.