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

Table 2

Nondimensional fundamental frequencies (𝜔⁻) for hypar shells (lamination (0/90)₄) with concentric cutouts.

𝑎^/𝑎	(Chakravorty et al. [8])		Present finite element model
	Simply supported	Clamped	Simply supported			Clamped
			8×8	10×10	12×12	8×8	10×10	12×12
0.0	50.829	111.600	50.573	50.821	50.825	111.445	111.592	111.612
0.1	50.769	110.166	50.679	50.758	50.779	109.987	110.057	110.233
0.2	50.434	105.464	50.323	50.421	50.400	105.265	105.444	105.443
0.3	49.165	101.350	49.045	49.157	49.178	101.110	101.340	101.490
0.4	47.244	97.987	47.132	47.242	47.141	97.670	97.985	97.991

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.