Biomedical Engineering Reference
In-Depth Information
charge
Q
, as defined in Equation 3.27, is different to that of
Q
3
, as defined in Equation
3.19. Some authors have defined a new symbol,
d
33
[21], which relates the applied normal
load to the output charge and is not necessarily equal to
d
33
, except in a frictionless state.
The contribution of the friction component to the total output depends on several factors,
including the magnitude of the applied normal load, the friction coefficient between contact
surfaces and the contact area of the PVDF film.
In order to obtain the output of the sandwiched PVDF film in the presence of friction, a
contact FE model was developed in ANSYS and similar experiments were also conducted
in order to validate the theoretical results of this analysis. In the following sections, details
of the modeling, as well as the experimental work, are explained.
3.8 Finite Element Analysis of Sandwiched PVDF
Since FE contact problems in which friction involves, produces non-symmetrical stiffness,
it is preferable to use a symmetrization algorithm designed to perform speedy and efficient
calculations such as those developed by Laursen and Simo [23] and ANSYS Inc. [24]. One
approach to solving contact problems is the Pure Penalty method, which requires matrices
showing contacts containing normal and tangential stiffness values. Higher stiffness values
decrease the amount of penetration, but can lead to ill-conditioning of the global stiffness
matrix and convergence difficulties. The stiffness should be high enough so that contact
penetration is acceptably small, but low enough so that the problem will be well-behaved
in terms of convergence. The contact traction vector is defined as:
⎨
⎩
⎬
⎭
P
τ
x
τ
y
where:
P
= normal contact pressure
τ
x
= tangential contact stress in the
x
-direction
τ
y
= tangential contact stress in the
y
-direction.
The contact pressure is:
0
|
u
n
>
0
K
n
u
n
,
|
u
n
≤
0
where
K
n
and
u
n
are contact normal stiffness and contact gap size, respectively. The
frictional stress is obtained by Coulomb's law:
P
=
K
s
u
x
,
|
τ<
0
τ
x
=
μK
n
u
n
,
|
τ
=
0
τ
x
+
τ
y
−
μP
where
τ
=
K
s
= tangential contact stiffness
u
x
= contact slip distance in x direction
μ
= frictional coefficient.
