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

Table 7

Values of “𝑟” for 0/90/0/90 hypar shells.

Edge condition	𝑦	𝑥
		0.2	0.3	0.4	0.5	0.6	0.7	0.8
CCCC	0.2	97.52	98.19	99.14	99.69	99.12	98.17	97.49
	0.3	98.23	98.83	99.51	99.87	99.51	98.81	98.22
	0.4	99.25	99.61	99.86	99.96	99.86	99.6	99.23
	0.5	99.86	100.03	100.03	100	100.03	100.03	99.86
	0.6	99.23	99.6	99.86	99.97	99.86	99.61	99.25
	0.7	98.22	98.81	99.51	99.86	99.51	98.83	98.23
	0.8	97.49	98.16	99.09	99.68	99.1	98.16	97.51
CSCC	0.2	99.53	99.69	100.03	100.24	100.03	99.68	99.47
	0.3	100.24	100.15	100.25	100.35	100.26	100.16	100.21
	0.4	100.09	99.84	100	100.19	100.02	99.86	100.1
	0.5	97.94	98.62	99.33	100	99.34	98.63	98.79
	0.6	97.34	97.15	98.3	99.78	98.29	97.16	97.35
	0.7	96.37	95.99	96.98	99.42	96.98	96	96.38
	0.8	95.87	95.29	95.69	96.68	95.7	95.3	95.89
CCSC	0.2	96.21	96.77	97.75	99.07	100.12	100.13	99.48
	0.3	95.57	96.35	97.51	98.83	99.83	100.09	99.72
	0.4	95.66	97.17	98.52	99.42	99.96	100.24	100.13
	0.5	95.95	99.59	99.9	100	100.13	100.35	100.38
	0.6	95.58	97.08	98.46	99.39	99.96	100.24	100.13
	0.7	95.52	96.3	97.46	98.8	99.83	100.1	99.72
	0.8	96.21	96.75	97.68	98.99	100.1	100.12	99.49
CCCS	0.2	95.89	95.31	95.71	96.64	95.67	95.29	95.87
	0.3	96.38	96	96.97	99.41	96.96	95.99	96.37
	0.4	97.35	97.16	98.29	99.78	98.29	97.15	97.34
	0.5	98.79	98.63	99.34	100	99.33	98.62	98.78
	0.6	100.1	99.86	100.02	100.19	100	99.84	100.08
	0.7	100.21	100.16	100.26	100.35	100.25	100.15	100.21
	0.8	99.32	99.49	99.83	100.05	99.83	99.47	99.31
CSSC	0.2	98.79	98.82	99.2	99.86	100.55	100.89	100.79
	0.3	98.95	99.27	99.66	100.08	100.48	100.8	100.95
	0.4	98.27	100.33	100.3	100.38	100.43	100.46	100.57
	0.5	96.25	97.59	98.9	100	100.32	99.93	99.75
	0.6	96.09	96.3	97.29	99.15	100.22	99.4	99.01
	0.7	96.62	96.19	96.67	98.31	100.17	98.95	98.66
	0.8	97.57	96.83	96.72	97.23	98.56	98.61	98.7
CCSS	0.2	97.54	96.8	96.73	97.24	98.51	98.56	98.64
	0.3	96.61	96.18	96.66	98.3	100.13	98.91	98.62
	0.4	96.14	96.34	97.32	99.15	100.2	99.37	98.99
	0.5	96.32	97.69	98.95	100	100.29	99.9	99.73
	0.6	98.28	100.3	100.27	100.34	100.38	100.41	100.53
	0.7	98.84	99.19	99.6	100.03	100.44	100.76	100.91
	0.8	98.65	98.67	98.92	99.56	100.32	100.69	100.63
CSCS	0.2	86.53	86.51	86.95	86.16	86.97	86.49	86.48
	0.3	92.9	92.77	92.84	92.87	92.84	92.75	92.84
	0.4	96.52	96.4	97.17	97.7	97.17	96.38	96.47
	0.5	97.17	97.41	98.85	100	98.84	97.41	97.17
	0.6	96.47	96.39	97.17	97.7	97.17	96.4	96.5
	0.7	92.84	92.75	92.84	92.88	92.84	92.77	92.9
	0.8	86.17	86.18	86.66	87.02	86.73	86.33	86.33
SCSC	0.2	86.38	92.89	97.14	98.25	97.12	92.87	86.36
	0.3	86.43	92.92	96.97	98.23	96.93	92.87	85.96
	0.4	86.9	92.92	97.45	99.25	97.39	92.87	86.84
	0.5	87.13	92.85	97.71	100	97.71	92.85	87.13
	0.6	86.84	92.87	97.39	99.25	97.45	92.92	86.9
	0.7	86.39	92.87	96.93	98.22	96.95	92.92	86.43
	0.8	86.27	92.76	97.09	98.14	97.05	92.8	86.31
CSSS	0.2	87.55	87.4	87.57	88.03	88.73	89.14	88.85
	0.3	94.37	94.44	94.06	94.01	95.18	96.65	96.62
	0.4	98.85	98.84	98.33	98.33	99.99	101.94	101.87
	0.5	100.37	100.28	99.82	100	101.89	103.9	103.68
	0.6	98.76	98.77	98.29	98.31	99.99	101.94	101.87
	0.7	94.28	94.37	94.02	93.98	95.16	96.63	96.59
	0.8	87.17	87.1	87.29	87.74	88.4	88.85	88.6
SSSC	0.2	89.01	96.86	102.03	103.78	102.03	96.86	88.99
	0.3	89.2	96.84	102.06	103.95	102.06	96.82	89.16
	0.4	88.7	95.26	100.02	101.88	100.03	95.26	88.7
	0.5	87.94	94.02	98.32	100	98.39	94.1	88
	0.6	87.47	94.07	98.36	99.88	98.44	94.18	87.55
	0.7	87.29	94.47	98.9	100.4	98.98	94.56	87.38
	0.8	87.34	94.26	98.78	100.33	98.84	94.35	87.42
SSCS	0.2	88.83	89.09	88.68	88	87.53	87.34	87.45
	0.3	96.58	96.62	95.15	93.97	94.01	94.37	94.27
	0.4	101.85	101.94	99.98	98.3	98.27	98.77	98.78
	0.5	103.67	103.9	101.89	100	99.82	100.28	100.36
	0.6	101.87	101.94	99.98	98.33	98.32	98.83	98.83
	0.7	96.61	96.65	95.17	94	94.05	94.44	94.37
	0.8	88.43	88.7	88.33	87.77	87.26	87.21	87.22
SSSS	0.2	83.79	86.96	87.85	88.06	87.93	87.06	83.88
	0.3	87.24	93.04	94.61	94.75	94.7	93.12	87.28
	0.4	88.2	94.89	98.09	98.78	98.2	94.94	88.2
	0.5	88.38	95.08	99.09	100	99.09	95.08	88.38
	0.6	88.21	94.95	98.2	98.78	98.09	94.89	88.2
	0.7	87.28	93.12	94.68	94.75	94.61	93.04	87.24
	0.8	83.72	86.9	87.65	87.76	87.44	86.79	83.43

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.