2.3 Geometrically Nonlinear Modeling for Smart Structures
15
nonlinear strain-displacement relations should be considered for smart structures. If
the assumption of moderate rotations is still imposed, the resulting theory is fully geometrically nonlinear theory with moderate rotations. Due to the kinematic hypothesis
of moderate rotations, the results obtained by fully geometrically nonlinear theory
with moderate rotations are close to those obtained by moderate rotation nonlinear
theory.
Based on the Kirchhoff-Love hypothesis, Moita et al. [139] developed a fully
geometrically nonlinear FE model for static analysis of smart structures. Based on
the FOSD hypothesis, fully geometrically nonlinear FE models were developed by
Kundu et al. [140] for buckling and post-buckling analysis, by Gao and Shen [114] for
dynamic analysis. Implementation of the TOSD hypothesis into fully geometrically
nonlinear FE model, Dash and Singh [141] studied for dynamic analysis.
Considering geometrical imperfections in the thickness direction, fully geometrically nonlinear FE models were developed by Amabili [142] based on the FOSD
hypothesis, and by Amabili [143] based on the TOSD hypothesis. Additionally,
based on the higher-order shear deformation hypothesis, Alijani and Amabili [144,
145] built fully geometrically nonlinear FE models with consideration of thickness stretching. Amabili [146], Amabili and Reddy [147] included both geometrical
imperfection and thickness stretching in the fully geometrically nonlinear FE models
for composite structures.
2.3.4 Large Rotation Nonlinear Theory
The nonlinear theories including von Kármán type nonlinear theory, moderate rotation nonlinear theory, and fully geometrically nonlinear theory with moderate rotations, are only applicable to structures undergoing large displacements and moderate
rotations. Due to this limitations, the theories invalid for the structures undergoing
large displacements and rotations, which are thus classified as simplified nonlinear
theories.
Considering fully geometrically nonlinear strain-displacement relations with large
rotations yields large rotation nonlinear theory. Chró´ scielewski et al. [148–150]
developed a 1D FE model of large rotation nonlinear theory for shape and vibration control of arches. Zhang and Schmidt [136–138, 151] proposed a large rotation
nonlinear FE model with the FOSD hypothesis for static and dynamic analysis of
piezolaminated plate and shell structures. The unrestricted rotations are updated
by using Euler rotation formulation. Analogously, Rao and Schmidt [152], Rao et
al. [153] studied a similar large rotation nonlinear model by using Rodrigues rotation
formulation.
15
nonlinear strain-displacement relations should be considered for smart structures. If
the assumption of moderate rotations is still imposed, the resulting theory is fully geometrically nonlinear theory with moderate rotations. Due to the kinematic hypothesis
of moderate rotations, the results obtained by fully geometrically nonlinear theory
with moderate rotations are close to those obtained by moderate rotation nonlinear
theory.
Based on the Kirchhoff-Love hypothesis, Moita et al. [139] developed a fully
geometrically nonlinear FE model for static analysis of smart structures. Based on
the FOSD hypothesis, fully geometrically nonlinear FE models were developed by
Kundu et al. [140] for buckling and post-buckling analysis, by Gao and Shen [114] for
dynamic analysis. Implementation of the TOSD hypothesis into fully geometrically
nonlinear FE model, Dash and Singh [141] studied for dynamic analysis.
Considering geometrical imperfections in the thickness direction, fully geometrically nonlinear FE models were developed by Amabili [142] based on the FOSD
hypothesis, and by Amabili [143] based on the TOSD hypothesis. Additionally,
based on the higher-order shear deformation hypothesis, Alijani and Amabili [144,
145] built fully geometrically nonlinear FE models with consideration of thickness stretching. Amabili [146], Amabili and Reddy [147] included both geometrical
imperfection and thickness stretching in the fully geometrically nonlinear FE models
for composite structures.
2.3.4 Large Rotation Nonlinear Theory
The nonlinear theories including von Kármán type nonlinear theory, moderate rotation nonlinear theory, and fully geometrically nonlinear theory with moderate rotations, are only applicable to structures undergoing large displacements and moderate
rotations. Due to this limitations, the theories invalid for the structures undergoing
large displacements and rotations, which are thus classified as simplified nonlinear
theories.
Considering fully geometrically nonlinear strain-displacement relations with large
rotations yields large rotation nonlinear theory. Chró´ scielewski et al. [148–150]
developed a 1D FE model of large rotation nonlinear theory for shape and vibration control of arches. Zhang and Schmidt [136–138, 151] proposed a large rotation
nonlinear FE model with the FOSD hypothesis for static and dynamic analysis of
piezolaminated plate and shell structures. The unrestricted rotations are updated
by using Euler rotation formulation. Analogously, Rao and Schmidt [152], Rao et
al. [153] studied a similar large rotation nonlinear model by using Rodrigues rotation
formulation.