6.4 Electroelastic Nonlinear Analysis of Smart Structures
133
Fig. 6.38 Tip displacements
of the semicircular shell with
only geometric nonlinearity:
a hoop displacement, b
radial displacement,
reprinted from Ref. [23],
copyright 2017, with
permission from ELSEVIER
(a)
0
500
1000
1500
0
50
100
150
200
Driven electric field (V/mm)
Hoop displacement (mm)
LRT56WE
LRT5WE
MRT5WE
RVK5WE
LIN5WE
(b)
0
500
1000
1500
0
20
40
60
80
100
120
Driven electric field (V/mm)
Radial displacement (mm)
LRT56WE
LRT5WE
MRT5WE
RVK5WE
LIN5WE
by the refined von Kármán type nonlinear model (RVK5WE) are close to that of
LIN5WE model. The results of LRT56WE model have the largest deviations from
those of LIN5WE model. Due to the assumption of moderate rotations, the loaddisplacement curves of LRT5WE and MRT5WE are very similar, which deviate from
those of LRT56WE. From the results, it can clearly show that the semicircular shell
with the current boundary and loading conditions are a typical demonstration of large
rotation problem. Therefore, the simplified nonlinear models, including RVK5WE,
MRT5WE and LRT5WE, fail to predict the structural behavior. For more details of
geometrically nonlinear analysis and discussions, it refers to the publications [6, 19,
26].
With consideration of both geometric and material nonlinearities, the hoop and
radial displacements of the semicircular shell under the same loading and boundary
conditions are presented in Fig. 6.39. Compared to the results of only geometrically nonlinear models the load-displacement curves change dramatically. When