Biomedical Engineering Reference
In-Depth Information
bottom plate was substituted with only two supports. Since the bottom surface of the
bottom part was mechanically constrained, this simplification did not affect the results.
This model consisted of two end supports, a top plate with three hanging beams and PVDF
films, which were sandwiched between the supports and top plate and also attached to
the beams, as shown in Figure 4.17. The material properties of 180
m thick silicon were
considered to be
E
= 130 GPa and
v = 0.28
for the supports and top plate. The material
properties of the 28
μ
m thick PVDF films used in this model were taken from Goodfellow
[17] and are summarized in Table 3.2. The SOLID92 and SOLID98 elements were used
for the structural (silicon) parts and the piezoelectric films, respectively. SOLID92 is
a 3D 10 node tetrahedral element which has three DOFs at each node: translations in
the nodal
x
,
y
,and
z
directions. On the other hand, SOLID98 is a tetrahedral element
with a quadratic displacement behavior and is defined by 10 nodes with up to six DOFs
at each node. When KEYOPT(1)
1
= 3, the degrees of freedom are
U
x
,
U
y
,
U
z
,and
VOLT. The governing constitutive equations for piezoelectric materials are described in
Chapter 3.
μ
4.2.2.1 Simulation Results
To assess the accuracy of the finite element model, the response of the FEM was compared
to that of existing closed form relationship for clamped - clamped beams. As illustrated
in Figure 4.20, a distributed load was applied to the first beam and its two supports. The
deflection curve, due to the distributed load of 111 kPa, is shown in Figure 4.21.
Figure 4.20
The deflected structure when a distributed load of 111 kPa was applied to the first
beam and its two supports (See Plate 4)
1
Some ANSYS elements have additional options, known as KEYOPTs and are referred to as KEYOPT(1), KEY-
OPT(2), and so on. For instance, here KEYOPT(1) = 3 sets the type and number of degrees of freedom of the
element. KEYOPTs can be specified using the ET command or the KEYOPT command.
