An ES-MITC3 Finite Element Method Based on Higher-Order Shear Deformation Theory for Static and Free Vibration Analyses of FG Porous Plates Reinforced by GPLs

Table 3

Nondimensional natural frequencies of fully clamped FG porous square plates reinforced by GPLs with and .

GPLs pattern		Method	1	2	3	4	5	6
U-P
GPL-S	0.2	Yang	0.6887	1.3696	1.3696	1.9758	2.3744	2.3902
		Present	0.6892	1.3778	1.3891	2.0138	2.4337	2.4502
		MITC3	0.6968	1.4008	1.4178	2.0650	2.5048	2.5230
		MITC4	0.6904	1.3926	1.3936	2.0109	2.4785	2.4952
	0.4	Yang	0.6612	1.3149	1.3149	1.8969	2.2795	2.2947
		Present	0.6602	1.3203	1.3311	1.9303	2.3332	2.3490
		MITC3	0.6674	1.3423	1.3558	1.9794	2.4014	2.4188
		MITC4	0.6613	1.3344	1.3354	1.9273	2.3759	2.3919
	0.6	Yang	0.6285	1.2500	1.2500	1.8032	2.1670	2.1814
		Present	0.6269	1.2541	1.2644	1.8341	2.2173	2.2323
		MITC3	0.6338	1.2751	1.2906	1.8808	2.2822	2.2986
		MITC4	0.6279	1.2676	1.2685	1.8313	2.2579	2.2730
GPL-U	0.2	Yang	0.6202	1.2383	1.2383	1.7918	2.1574	2.1711
		Present	0.6242	1.2579	1.2684	1.8505	2.2455	2.2596
		MITC3	0.6309	1.2782	1.2936	1.8948	2.3084	2.3238
		MITC4	0.6193	1.2521	1.2526	1.8113	2.2362	2.2507
	0.4	Yang	0.5954	1.1888	1.1888	1.7202	2.0712	2.0844
		Present	0.5975	1.2044	1.2145	1.7722	2.1508	2.1643
		MITC3	0.6039	1.2238	1.2386	1.8148	2.2111	2.2259
		MITC4	0.5928	1.1991	1.1996	1.7352	2.1426	2.1564
	0.6	Yang	0.5660	1.1301	1.1301	1.6353	1.9690	1.9815
		Present	0.5669	1.1429	1.1525	1.6822	2.0419	2.0546
		MITC3	0.5729	1.1614	1.1755	1.7227	2.0992	2.1131
		MITC4	0.5625	1.1382	1.1387	1.6475	2.0346	2.0478