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

Table 2

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-4.

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	12.852	12.658	2.760	2.751	1.707	1.702	1.006	1.004	0.0756	0.0754
	φ × 10^−2 V	11.848	11.912	0.442	0.427	0.212	0.207	0.0961	0.0944	0.00112	0.00110
0.0004	u3 × 10^−9 m	28.517	28.367	4.735	4.715	2.855	2.842	1.738	1.731	0.187	0.187
	φ × 10^−1 V	5.851	5.747	0.597	0.582	0.349	0.339	0.193	0.188	0.0805	0.782
0.0025	u3 × 10^−8 m	13.345	13.191	1.538	1.528	0.917	0.913	0.564	0.561	0.0882	0.0873
	φ (V)	2.447	2.391	0.198	0.191	0.112	0.109	0.0621	0.0605	0.00386	0.00372
0.004	U3 × 10^−9 m	77.799	77.682	10.154	10.146	6.165	6.123	3.727	3.725	0.514	0.516
	φ (V)	1.434	1.406	0.129	0.125	0.0756	0.0740	0.0414	0.0401	0.00224	0.00221