2.4 Electroelastic Materially Nonlinear Modeling
17
For beam structures, Tan and Tong [173] studied a one-dimensional analytical
model with consideration of electroelastic nonlinear effect of piezoelectric fiber
reinforced composite materials through the curve-fitting method based on experimental data. Wang et al. [174] developed electroelastic nonlinear analytical models
for clamped piezoelectric bimorph and unimorph beams, with experimentally validated. Analogously, Yao et al. [175] developed a very similar nonlinear beam model
with electroelastic nonlinearity and tested by experimental investigations on bimorph
and unimorph beams.
Regarding to plates and shells integrated with piezoelectric materials, many papers
can be found in the literature that developed electroelastic materially nonlinear
numerical models. Sun et al. [176], Kusculuoglu and Royston [177] developed finite
element models with electroelastic material nonlinearity based on Reissner-Mindlin
plate hypothesis for static shape control and dynamic analysis of smart structures.
Kapuria and Yasin [178, 179] proposed nonlinear FE models based on layerwise theory for the static analysis and active vibration control of piezoelectric structure under
strong electric field. Using the model of quadratic distribution of electric potential,
Rao et al. [180] proposed an FE model with consideration of electroelastic materially
nonlinear effects for piezoelectric laminated composite plates and shells.
The above mentioned studies in this subsection are mainly focusing on geometrically linear models with electroelastic materially nonlinear effect, which allows
structures only undergoing small displacements. When structures undergo large displacements and under strong electric fields, both geometrically and electroelastic
materially nonlinear effects should be included in the numerical models. Yao et
al. [181] developed a nonlinear model with von Kármán type nonlinearity based on
the classical plate theory for structures under strong driving electric field. Zhang et
al. [182] proposed a fully nonlinear model with both geometrically nonlinear (large
rotation nonlinear) and electroelastic materially nonlinear effects for piezolaminated
smart structures.
2.5 Multi-physics Coupled Modeling
2.5.1 Functionally Graded Structures
Smart structures consist of conventional piezoelectric and metal materials. With the
development of material science, many advanced materials were invented, like carbon nanotube (CNT) reinforced functionally graded composites, functionally graded
piezoelectric materials. Piezoelectric smart structures are inherently coupled with
electro-mechanical fields. On one hand, multi-physics coupled modeling techniques
are necessary for precise structural computation, on the other hand, modeling of new
material structures should be developed.
Carbon nanotube reinforced functionally graded composites bonded with piezoelectric layers have excellent mechanical and electrical performance, attracting many
17
For beam structures, Tan and Tong [173] studied a one-dimensional analytical
model with consideration of electroelastic nonlinear effect of piezoelectric fiber
reinforced composite materials through the curve-fitting method based on experimental data. Wang et al. [174] developed electroelastic nonlinear analytical models
for clamped piezoelectric bimorph and unimorph beams, with experimentally validated. Analogously, Yao et al. [175] developed a very similar nonlinear beam model
with electroelastic nonlinearity and tested by experimental investigations on bimorph
and unimorph beams.
Regarding to plates and shells integrated with piezoelectric materials, many papers
can be found in the literature that developed electroelastic materially nonlinear
numerical models. Sun et al. [176], Kusculuoglu and Royston [177] developed finite
element models with electroelastic material nonlinearity based on Reissner-Mindlin
plate hypothesis for static shape control and dynamic analysis of smart structures.
Kapuria and Yasin [178, 179] proposed nonlinear FE models based on layerwise theory for the static analysis and active vibration control of piezoelectric structure under
strong electric field. Using the model of quadratic distribution of electric potential,
Rao et al. [180] proposed an FE model with consideration of electroelastic materially
nonlinear effects for piezoelectric laminated composite plates and shells.
The above mentioned studies in this subsection are mainly focusing on geometrically linear models with electroelastic materially nonlinear effect, which allows
structures only undergoing small displacements. When structures undergo large displacements and under strong electric fields, both geometrically and electroelastic
materially nonlinear effects should be included in the numerical models. Yao et
al. [181] developed a nonlinear model with von Kármán type nonlinearity based on
the classical plate theory for structures under strong driving electric field. Zhang et
al. [182] proposed a fully nonlinear model with both geometrically nonlinear (large
rotation nonlinear) and electroelastic materially nonlinear effects for piezolaminated
smart structures.
2.5 Multi-physics Coupled Modeling
2.5.1 Functionally Graded Structures
Smart structures consist of conventional piezoelectric and metal materials. With the
development of material science, many advanced materials were invented, like carbon nanotube (CNT) reinforced functionally graded composites, functionally graded
piezoelectric materials. Piezoelectric smart structures are inherently coupled with
electro-mechanical fields. On one hand, multi-physics coupled modeling techniques
are necessary for precise structural computation, on the other hand, modeling of new
material structures should be developed.
Carbon nanotube reinforced functionally graded composites bonded with piezoelectric layers have excellent mechanical and electrical performance, attracting many