Chapter 8
Conclusion and Future Work
Due to the excellent properties of smart structures, a wide applications can be found in
aerospace, civil and automotive engineering. Smart structures are usually appearing
with beam-, plate- and shell-shaped structures. There is a great concern about the
appropriate computation approaches for smart structures undergo large displacement
and under strong electric filed. This report dealt with geometrically nonlinear and
electroelastic materially nonlinear modeling techniques for both composite laminated
and piezoelectric integrated thin-walled structures.
The report first reviewed literatures on modeling and simulation techniques for
smart structures. The literature survey includes through thickness hypotheses for
beam, plate and shell structures, geometrically nonlinear analysis of composite
and piezoelectric integrated structures, electroelastic materially nonlinear modeling
methods, multi-physics coupled modeling for recently developed smart structures,
and vibration control of smart structures. The literature survey reveals that most publications focused on linear modeling of piezoelectric integrated smart structure, few
researchers did nonlinear analysis of smart structures, especially the electro-elastic
materially nonlinear. Moreover, there are less references on multi-physics coupled
simulation of newly advanced smart structures.
The second part of the report presented the mathematical preliminaries, kinematics of shell structures, and various geometrically nonlinear strain-displacement
relations. Based on the first-order shear deformation hypothesis, geometrically nonlinear strain field in terms of six parameters were developed for the theories of fully
geometrically nonlinear with large rotations (LRT56). Additionally, nonlinear strain
field in term of five parameters were developed for the simplified nonlinear theories
with the assumption of moderate rotations (RVK5, MRT5 and LRT5). Among all
the mentioned geometrically nonlinear theories, LRT56 and LRT5 has fully geometrically nonlinear strain-displacement relations, MRT5 has selected nonlinear terms
due to in-plane displacements, while RVK5 only includes nonlinear terms result from
transverse displacements.
In the next part, constitutive relations for piezoelectric and composite materials
were discussed. For deep understanding of piezo effect, the fundamental equations
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Singapore Pte Ltd. 2021
S.-Q. Zhang, Nonlinear Analysis of Thin-Walled Smart Structures, Springer Tracts
in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9857-9_8
153
Conclusion and Future Work
Due to the excellent properties of smart structures, a wide applications can be found in
aerospace, civil and automotive engineering. Smart structures are usually appearing
with beam-, plate- and shell-shaped structures. There is a great concern about the
appropriate computation approaches for smart structures undergo large displacement
and under strong electric filed. This report dealt with geometrically nonlinear and
electroelastic materially nonlinear modeling techniques for both composite laminated
and piezoelectric integrated thin-walled structures.
The report first reviewed literatures on modeling and simulation techniques for
smart structures. The literature survey includes through thickness hypotheses for
beam, plate and shell structures, geometrically nonlinear analysis of composite
and piezoelectric integrated structures, electroelastic materially nonlinear modeling
methods, multi-physics coupled modeling for recently developed smart structures,
and vibration control of smart structures. The literature survey reveals that most publications focused on linear modeling of piezoelectric integrated smart structure, few
researchers did nonlinear analysis of smart structures, especially the electro-elastic
materially nonlinear. Moreover, there are less references on multi-physics coupled
simulation of newly advanced smart structures.
The second part of the report presented the mathematical preliminaries, kinematics of shell structures, and various geometrically nonlinear strain-displacement
relations. Based on the first-order shear deformation hypothesis, geometrically nonlinear strain field in terms of six parameters were developed for the theories of fully
geometrically nonlinear with large rotations (LRT56). Additionally, nonlinear strain
field in term of five parameters were developed for the simplified nonlinear theories
with the assumption of moderate rotations (RVK5, MRT5 and LRT5). Among all
the mentioned geometrically nonlinear theories, LRT56 and LRT5 has fully geometrically nonlinear strain-displacement relations, MRT5 has selected nonlinear terms
due to in-plane displacements, while RVK5 only includes nonlinear terms result from
transverse displacements.
In the next part, constitutive relations for piezoelectric and composite materials
were discussed. For deep understanding of piezo effect, the fundamental equations
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Singapore Pte Ltd. 2021
S.-Q. Zhang, Nonlinear Analysis of Thin-Walled Smart Structures, Springer Tracts
in Mechanical Engineering, https://doi.org/10.1007/978-981-15-9857-9_8
153