2.1 Plate/Shell Hypotheses and Applications to Linear Analysis
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beam hypothesis for vibration suppression of smart structures. Applying the Timoshenko beam hypothesis, Narayanan and Balamurugan [54], and Marinaki et al. [55]
developed FE models for vibration control of smart structure, while Zu [56] investigated for energy harvesting.
2.2 Geometrically Nonlinear Modeling in Composites
2.2.1 Simplified Nonlinear Modeling
Geometrically linear models are only valid for structures undergoing small displacements and rotations. Geometrically nonlinear models were first developed for
composite laminated structures or single layer monolithic structures. For simplicity, imposed with additional assumptions like small or moderate rotations, or weak
nonlinear effect, yields various geometrically nonlinear theories, here called simplified nonlinear theories. The von Kármán type nonlinear theory is the simplest
geometrically nonlinear theory, which only considers the nonlinear effect resulting
from the transverse displacements and under the assumption of small rotations. A
large number of publications can be found that developed von Kármán type nonlinear FE models for plates and shells based on classical theory [57], FOSD [58] and
TOSD [59–61] hypotheses.
With consideration of strong nonlinear effects, more nonlinear strain-displacement
terms are included in the models. This kind of nonlinear theory is usually defined as
moderate rotation theory, which was first proposed and developed by Librescu and
Schmidt [62], Schmidt and Reddy [63], Schmidt and Weichert [64]. Later, Palmerio et al. [65, 66], Kreja et al. [67] implemented the moderate rotations theory into
finite element analysis of composite structures.
2.2.2 Large Rotation Nonlinear Modeling
The von Kármán type nonlinear theory is restricted to weak nonlinearity and small
rotations, while the moderate rotation theory is limited to moderately strong nonlinearity and rotations. Both of them are invalid for structures with strong nonlinearity
and large rotations. To consider strong nonlinear effects, full geometrically nonlinear strain-displacement relations based on FOSD hypothesis were first developed
by Habip [68], Habip and Ebcioglu [69] for static and dynamic equations of shells.
Librescu [70] developed fully geometrically nonlinear plate and shell theory for
composite laminated structures.
In order to analyze thin-walled structures with large rotations, fully geometrically nonlinear models with finite rotations based on the FOSD hypothesis were
applied into FE analysis by Gruttmann et al. [71], Basar et al. [72, 73], Sansour and
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beam hypothesis for vibration suppression of smart structures. Applying the Timoshenko beam hypothesis, Narayanan and Balamurugan [54], and Marinaki et al. [55]
developed FE models for vibration control of smart structure, while Zu [56] investigated for energy harvesting.
2.2 Geometrically Nonlinear Modeling in Composites
2.2.1 Simplified Nonlinear Modeling
Geometrically linear models are only valid for structures undergoing small displacements and rotations. Geometrically nonlinear models were first developed for
composite laminated structures or single layer monolithic structures. For simplicity, imposed with additional assumptions like small or moderate rotations, or weak
nonlinear effect, yields various geometrically nonlinear theories, here called simplified nonlinear theories. The von Kármán type nonlinear theory is the simplest
geometrically nonlinear theory, which only considers the nonlinear effect resulting
from the transverse displacements and under the assumption of small rotations. A
large number of publications can be found that developed von Kármán type nonlinear FE models for plates and shells based on classical theory [57], FOSD [58] and
TOSD [59–61] hypotheses.
With consideration of strong nonlinear effects, more nonlinear strain-displacement
terms are included in the models. This kind of nonlinear theory is usually defined as
moderate rotation theory, which was first proposed and developed by Librescu and
Schmidt [62], Schmidt and Reddy [63], Schmidt and Weichert [64]. Later, Palmerio et al. [65, 66], Kreja et al. [67] implemented the moderate rotations theory into
finite element analysis of composite structures.
2.2.2 Large Rotation Nonlinear Modeling
The von Kármán type nonlinear theory is restricted to weak nonlinearity and small
rotations, while the moderate rotation theory is limited to moderately strong nonlinearity and rotations. Both of them are invalid for structures with strong nonlinearity
and large rotations. To consider strong nonlinear effects, full geometrically nonlinear strain-displacement relations based on FOSD hypothesis were first developed
by Habip [68], Habip and Ebcioglu [69] for static and dynamic equations of shells.
Librescu [70] developed fully geometrically nonlinear plate and shell theory for
composite laminated structures.
In order to analyze thin-walled structures with large rotations, fully geometrically nonlinear models with finite rotations based on the FOSD hypothesis were
applied into FE analysis by Gruttmann et al. [71], Basar et al. [72, 73], Sansour and