6.3 Geometrically Nonlinear Analysis of Smart Structures
123
Fig. 6.26 Static response of
the fully clamped smart
cylindrical shell: a mid-point
displacement, b sensor
output voltage, reprinted
from Ref. [5], copyright
2014, with permission from
ELSEVIER
(a)
0
0.005
0.01
0.015
0.02
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
x 10
7
Tip displacement (m)
Load (Pa)
LRT56 (SH851URI)
LRT5 (SH851URI)
MRT5 (SH851URI)
RVK5 (SH851URI)
ANSYS (SHELL91)
Linear (SH851URI)
(b)
0
200
400
600
800
1000
0
0.5
1
1.5
2
2.5
3
3.5
x 10
5
Sensor voltage (V)
load (Pa)
LRT56 (SH851URI)
LRT5 (SH851URI)
MRT5 (SH851URI)
RVK5 (SH851URI)
Linear (SH851URI)
6.3.4.2 Nonlinear Static Analysis
In this simulation, the nonlinear static analysis are studied for both tip point displacements and sensor output voltages of inner layer. Applying a concentrated force
along the positive hoop direction, the load-displacement and load-voltage curves
are obtained and presented in Fig. 6.31. It can be seen that the RVK5 nonlinear
model performs softer behavior than the linear model. The figures show that the
load-displacement and load-voltage curves in the hoop direction obtained by MRT5
and LRT5 models are quit similar to each other. This confirms the conclusion in
Sect. 3.5 that the LRT5 theory is restricted to the range of moderate rotations even
though fully geometrically nonlinear relations are used. By comparison of the results
obtained by RVK5, MRT5, LRT5 and LRT56 in Fig. 6.31a, large deviations can be