128
6 Nonlinear Analysis of Piezoceramic Laminated Structures
Fig. 6.31 Static response of
the PZT laminated
semicircular cylindrical shell
under a concentrated force in
the hoop direction: a hoop
deflection, b radial
deflection, c sensor output
voltage of the inner PZT
layer, reprinted from
Ref. [6], copyright 2014,
with permission from
ELSEVIER
(a)
0
0.1
0.2
0.3
0.4
0.5
0.6
0
50
100
150
200
Hoop deflection (m)
Load F1 (N)
LRT56 (SH851URI)
LRT5 (SH851URI)
MRT5 (SH851URI)
RVK5 (SH851URI)
LIN5 (SH851URI)
(b)
0
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
0
50
100
150
200
Radial deflection (m)
Load F1 (N)
LRT56 (SH851URI)
LRT5 (SH851URI)
MRT5 (SH851URI)
RVK5 (SH851URI)
LIN5 (SH851URI)
(c)
0
100
200
300
400
500
600
0
50
100
150
200
Sensor voltage of inner layer (V)
Load F1 (N)
LRT56 (SH851URI)
LRT5 (SH851URI)
MRT5 (SH851URI)
RVK5 (SH851URI)
LIN5 (SH851URI)
The piezoelectric layers in the bimorph beam have opposite polarizations, pointing outwards and perpendicular to the mid-surface. The two substrate layers assume
perfectly bonded at both the negative electrodes that are connect to ground. The material parameters for 3203HD are given in Table 6.7. The bimorph beam is meshed
by 2 × 10 eight-node quadrilateral elements with 5 mechanical DOFs at each node
and 1 electric DOF at each element. An equal electric potential is applied on both
top and bottom surfaces of 3203HD patches. The displacement of tip point is com-