Composite Materials Research Progress

262 Yasuhide Shindo and Fumio Narita
3. Rectangular Piezoelectric Composite Actuators
3.1. Computational Model
We performed 3D finite element calculations to present the electromechanical fields distributions
around the electrode tip. The geometry used was a four layered piezoelectric
composite actuator, as shown in Fig. 1. A rectangular Cartesian coordinate system ( x,y,z)
is used with the z-axis coinciding with the poling direction. Electrodes with length a and
width W are embedded in the piezoelectric actuator of length L and width W . An external
electrode is attached on both sides of the actuator to address each electrode. The
thickness of the layer h is chosen, and a L − a tab region exists on both sides of the layer.
The total thickness is 4h. Because of the geometric and loading symmetry, only a half
of the specimen needs to be analyzed. The electric potential on two electrode surfaces
(−L/2 ≤ x ≤−L/2 +a, |y| ≤W/2, z =0, 2h) equals the applied voltage, φ = V0.
The electrode surface (L/2 − a ≤ x ≤ L/2, |y| ≤W/2, z = h) is connected to the
ground, so that φ =0. The normal displacement and shear stress on the surface (|x| ≤L/2,
y = −W/2, |z| ≤2h) are zero. The surface (|x| ≤L/2, y = W/2, |z| ≤2h) is stress free.
W
h
h
Electrode
Poling
O
y
z
O
a
a
L
a
Figure 1. A rectangular piezoelectric composite actuator.
Each element consists of many grains, and each grain is modeled as a uniformly polarized
cell that contains a single domain. The model neglects the domain wall effects and
interaction among different domains. In reality, this is not true, but the assumption does
not affect the general conclusions drawn. The polarization of each grain initially aligns as
closely as possible with the z- direction. The polarization switching is defined for each
x
x