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6 Nonlinear Analysis of Piezoceramic Laminated Structures
Fig. 6.39 Tip displacements
of the semicircular shell with
geometric and material
nonlinearities: a hoop
displacement, b radial
displacement, reprinted
from Ref. [23], copyright
2017, with permission from
ELSEVIER
(a)
0
500
1000
1500
0
100
200
300
400
500
600
Driven electric field (V/mm)
Hoop displacement (mm)
LRT56SE
LRT5SE
MRT5SE
RVK5SE
LIN5SE
LIN5WE
(b)
0
500
1000
1500
0
50
100
150
200
250
Driven electric field (V/mm)
Radial displacement (mm)
LRT56SE
LRT5SE
MRT5SE
RVK5SE
LIN5SE
LIN5WE
low driving electric field is applied (lower than about 500 V/mm), the semicircular
shell undergoes only small displacements and rotations. This will lead to weak geometrically nonlinear effect in the shell structure. Therefore, load-deflection curves
of all models are close to each other, but are different to linear curve. This can be
explained by the fact that electroelastic material nonlinearity dominates the nonlinear
structural behavior rather than weak geometrically nonlinear effect.
Increasing the driving electric field, the structure undergoes large displacements
and rotations. The influence of geometrically nonlinear effect increases, as the figure
shows large deviations occurring between linear and various nonlinear predictions.
The RVK5SE model, which includes the simplest nonlinear terms of the straindisplacement relations, has a similar performance of LIN5SE model. The electroelastic nonlinearity is the main nonlinear effect in the structure. Considering more nonlinear strain-displacement terms in the limitation of moderate rotations, MRT5SE and
LRT5SE models perform excellently at a relative small electric field (<800 V/mm