A Gradient Stable Node-Based Smoothed Finite Element Method for Solid Mechanics Problems

Table 2

First 12 natural frequencies (104 Hz) of a cantilever beam.

No. of elements	No. of nodes	FEM-T3	FEM-Q4	NS-FEM	GS-FEM	Reference FEM-Q4 (100 × 10)
(10 × 1) 10 4-node elements for FEM-Q4 and 20 triangular elements for other methods	22	0.1692	0.0992	0.0576	0.1302	0.0824
		0.9163	0.5791	0.3243	0.7161	0.4944
		1.2869	1.2834	0.7441	1.2846	1.2824
		2.1843	1.4830	0.9875	1.7230	1.3022
		3.5942	2.6183	1.0112	2.8548	2.3663
		3.8338	3.8140	1.1346	3.7728	3.6085
		5.0335	3.8824	1.2783	3.9961	3.8442
		6.2421	5.1924	1.5712	5.0417	4.9674
		6.4154	6.2345	2.3697	5.9011	6.3960
		7.5940	6.4846	3.2685	6.0277	6.4023
		8.4790	7.7039	3.7064	6.4965	7.8853
		8.7033	8.4632	3.8642	6.8162	8.9290
(20 × 2) 40 4-node elements for FEM-Q4 and 80 triangular elements for other methods	63	0.1117	0.0870	0.0675	0.0847	0.0824
		0.6539	0.5199	0.4032	0.5026	0.4944
		1.2843	1.2830	1.0518	1.2822	1.2824
		1.6748	1.3640	1.2810	1.3055	1.3022
		2.9554	2.4685	1.6467	2.3274	2.3663
		3.8424	3.7477	1.8786	3.4747	3.6085
		4.3866	3.8378	2.7823	3.8241	3.8442
		5.8836	5.1322	3.0926	4.6703	4.9674
		6.3751	6.3585	3.6783	5.8601	6.3960
		7.4046	6.5731	3.8089	6.2917	6.4023
		8.8210	8.0342	4.0543	7.0120	7.8853
		8.9411	8.8187	4.1605	8.0983	8.9290
(40 × 4) 160 4-node elements for FEM-Q4 and 320 triangular elements for other methods	205	0.0906	0.0835	0.0778	0.0814	0.0824
		0.5409	0.5004	0.4654	0.4876	0.4944
		1.2831	1.2827	1.2199	1.2801	1.2824
		1.4161	1.3174	1.2818	1.2831	1.3022
		2.5570	2.3926	1.6689	2.3175	2.3663
		3.8433	3.6462	2.2012	3.5159	3.6085
		3.8786	3.8431	3.2517	3.8391	3.8442
		5.3087	5.0150	3.3270	4.8097	4.9674
		6.3935	6.3883	3.8344	6.1531	6.3960
		6.8093	6.4561	4.5248	6.3692	6.4023
		8.3473	7.9398	4.6406	7.5141	7.8853
		8.9183	8.9057	5.3275	8.8515	8.9290