A Coupling Electromechanical Inhomogeneous Cell-Based Smoothed Finite Element Method for Dynamic Analysis of Functionally Graded Piezoelectric Beams

Table 3

Displacement u₃ and electrical potential φ at the loading point with the gradient parameter n = −5, −1, 0, 1, and 5 of the FGPM beam based on PZT-5H.

Time (s)	Field variables	n = −5		n = −1		n = 0		n = 1		n = 5
		ISFEM	FEM	ISFEM	FEM	ISFEM	FEM	ISFEM	FEM	ISFEM	FEM
0.0001	u3 × 10^−10 m	13.691	13.424	2.951	2.942	1.826	1.821	1.076	1.074	0.0802	0.0800
	φ × 10^−2 V	12.098	12.493	0.413	0.403	0.190	0.194	0.0825	0.0843	0.000624	0.000649
0.0004	u3 × 10^−9 m	31.394	31.196	5.583	5.561	3.381	3.367	2.050	2.042	0.207	0.206
	φ × 10^−1 V	5.901	6.057	0.599	0.607	0.349	0.350	0.192	0.190	0.0736	0.0735
0.0025	u3 × 10^−8 m	16.122	16.006	2.017	2.003	1.118	1.117	0.741	0.736	0.107	0.106
	φ (V)	2.522	2.584	0.219	0.219	0.122	0.123	0.0691	0.0689	0.00392	0.00393
0.004	u3 × 10^−9 m	76.019	75.052	10.339	10.264	6.264	6.261	3.795	3.768	0.501	0.496
	φ (V)	1.402	1.437	0.113	0.113	0.0649	0.0653	0.0351	0.0350	0.00179	0.00178