A Refined Higher-Order Hybrid Stress Quadrilateral Element for Free Vibration and Buckling Analyses of Reissner-Mindlin Plates

Table 8

Convergence of six lowest nondimensional frequency parameters (, 0.1 and SSSS, CCCC).

	Boundary	Mesh	Mode sequence number
			1	2	3	4	5	6
(a) QH8 with modified consistent mass matrix (QH8-RCV, )
0.001	SSSS		2.0208	5.1600	5.1600	8.5457	10.7782	10.7782
			2.0044	5.0290	5.0290	8.0832	10.1251	10.1251
			2.0010	5.0066	5.0066	8.0174	10.0268	10.0268
		Ref. sol	2.000	5.000	5.000	8.000	10.000	10.000
	CCCC		3.6986	7.7478	7.7478	11.8207	14.7803	14.9043
			3.6563	7.4895	7.4895	11.1031	13.5317	13.5943
			3.6484	7.4478	7.4478	10.9922	13.3726	13.4356
		Ref. sol	3.646	7.436	7.436	10.964	13.332	13.395
0.1	SSSS		1.9440	4.6822	4.6822	7.3572	8.9607	8.9607
			1.9335	4.6062	4.6062	7.0516	8.5663	8.5663
			1.9321	4.6062	4.6062	7.0581	8.5881	8.5881
		Ref. sol	1.931	4.605	4.605	7.064	8.605	8.605
	CCCC		3.3008	6.3401	6.3401	9.0667	10.7861	10.8677
			3.2925	6.2555	6.2555	8.7327	10.2492	10.3400
			3.2943	6.2743	6.2743	8.7752	10.3198	10.4162
		Ref. sol	3.292	6.276	6.276	8.792	10.356	10.455
(b) QH8 with lumped mass matrix (QH8-LV)
0.001	SSSS		1.9997	4.9970	4.9970	7.9691	9.9694	9.9694
			2.0000	4.9999	4.9999	7.9986	10.0001	10.0001
			2.0000	5.0000	5.0000	7.9998	9.9999	9.9999
		Ref. sol	2.000	5.000	5.000	8.000	10.000	10.000
	CCCC		3.6452	7.4121	7.4121	10.8713	12.9885	13.0468
			3.6461	7.4365	7.4365	10.9637	13.3312	13.3935
			3.6460	7.4363	7.4363	10.9644	13.3318	13.3949
		Ref. sol	3.646	7.436	7.436	10.964	13.332	13.395
0.1	SSSS		1.9427	4.6385	4.6385	7.0569	8.5511	8.5511
			1.9452	4.6710	4.6710	7.1895	8.7670	8.7670
			1.9457	4.6784	4.6784	7.2173	8.8157	8.8157
		Ref. sol	1.931	4.605	4.605	7.064	8.605	8.605
	CCCC		3.3019	6.2524	6.2524	8.6322	10.0169	10.0917
			3.3155	6.3496	6.3496	8.9075	10.4886	10.5773
			3.3181	6.3688	6.3688	8.9622	10.5759	10.6670
		Ref. sol	3.292	6.276	6.276	8.792	10.356	10.455