150
7 Numerical Analysis of Macro-fiber Composite Structures
R
=
9 0 . 4 m m
S H
S H
S H
S M
S M
S H
S H
S M
S M
Θ
3
Θ
2
Fig. 7.15 Cantilevered semicircular cylindrical shell bonded with multi-MFC actuators, reprinted
from Ref. [5], copyright 2016, with permission from ELSEVIER
plane are respectively 284 mm and 44 mm. The host semicircular shell is comprised
of graphite/epoxy angle-ply laminates stacked as [−45
◦
/45
◦ ] from the inner to outer
direction. The total thickness of the host shell is 0.2 mm and thickness of each
substrate layer is 0.1 mm. The dimensions of MFC-d33 patch are 56 × 28 × 0.3 mm
3 .
The MFCs are distributed with equal arc length S H = 12 mm. The distance of two
electrodes in MFC-d33 patches is h E = 0.5 mm.
The fiber orientation angle is assumed to be 0
◦ , meaning that the fiber orientation
is along the Θ
1 line. All the MFC patches are under a uniform driving voltage up
to 300 V. Implementing linear and nonlinear theories into the analysis, tip displacements are computed and presented in Fig. 7.16. It can be seen from the figure that
large deviations occur among linear and various nonlinear models when the driving
electric voltage is over about 50 V. This also confirms that the linear and simplified nonlinear theories are not accurate enough for the multi-MFC semicircular shell
structure. As discussed in the above chapters, the performance of LRT5 and MRT5
nonlinear models are very similar. However, in this example the static curves of
LRT5 and MRT5 are no longer close to each other. The load-displacement curve of
LRT5 approach to that of LRT56. This can be explained that the nonlinear straindisplacement relations perform the main influence on the structural response, rather
than large rotations. In the next simulation, a constant driving voltage of 300 V is
applied to all MFC patches. The radial displacements of the central line in the hoop
direction are calculated and presented in Fig. 7.17. Similar conclusions can be drawn
from the central line displacements.
7 Numerical Analysis of Macro-fiber Composite Structures
R
=
9 0 . 4 m m
S H
S H
S H
S M
S M
S H
S H
S M
S M
Θ
3
Θ
2
Fig. 7.15 Cantilevered semicircular cylindrical shell bonded with multi-MFC actuators, reprinted
from Ref. [5], copyright 2016, with permission from ELSEVIER
plane are respectively 284 mm and 44 mm. The host semicircular shell is comprised
of graphite/epoxy angle-ply laminates stacked as [−45
◦
/45
◦ ] from the inner to outer
direction. The total thickness of the host shell is 0.2 mm and thickness of each
substrate layer is 0.1 mm. The dimensions of MFC-d33 patch are 56 × 28 × 0.3 mm
3 .
The MFCs are distributed with equal arc length S H = 12 mm. The distance of two
electrodes in MFC-d33 patches is h E = 0.5 mm.
The fiber orientation angle is assumed to be 0
◦ , meaning that the fiber orientation
is along the Θ
1 line. All the MFC patches are under a uniform driving voltage up
to 300 V. Implementing linear and nonlinear theories into the analysis, tip displacements are computed and presented in Fig. 7.16. It can be seen from the figure that
large deviations occur among linear and various nonlinear models when the driving
electric voltage is over about 50 V. This also confirms that the linear and simplified nonlinear theories are not accurate enough for the multi-MFC semicircular shell
structure. As discussed in the above chapters, the performance of LRT5 and MRT5
nonlinear models are very similar. However, in this example the static curves of
LRT5 and MRT5 are no longer close to each other. The load-displacement curve of
LRT5 approach to that of LRT56. This can be explained that the nonlinear straindisplacement relations perform the main influence on the structural response, rather
than large rotations. In the next simulation, a constant driving voltage of 300 V is
applied to all MFC patches. The radial displacements of the central line in the hoop
direction are calculated and presented in Fig. 7.17. Similar conclusions can be drawn
from the central line displacements.