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Geometrically-exact multilayer structural theory.
Multilayered structures have widespread applications in engineering.
Laminated composite structures, initially developed for use in
the aerospace industry, have played an increasingly important
role in robotics and machine systems that require high operating
speed. The low weight and high stiffness offered by laminated
composite structures help reduce the power consumption, increase
the ratio of payload/self-weight, and would contribute to improve
the accuracy in the motion characteristics and the reduction in
the level of acoustic emission of these systems. It is shown from
computer simulations with experimental corroboration that the
low weight/stiffness ratio of laminated composites is essential
for obtaining high performance in slider-crank and four-bar linkage
systems. More recently, considerable attention has been given
to a class of smart structures with embedded piezoelectric layers
as sensors and actuators for monitoring the strain level and for
vibration control. Large overall motion of multilayered structures
can be found in robot arms or space structures with embedded sensors/actuators.
Yet another example of multilayered structures can be found in
the damping of structural vibration by the use of constrained
The cardinal features of our geometrically-exact multilayer
formulation are as follows: (i) The dynamics of a (possibly
unrestrained) flexible structure is referred to a fixed
inertial frame, (ii) The models can describe large deformation
and large overall motion, (iii) Shear deformation
in beams and shells are accommodated for, (iv) The continuity
in the displacement across the layer interface is
preserved, (v) The number of layer is unrestricted, while the
reference layer can be selected to be any of the layers.
displacements of all layers are expressed in terms of those of
the reference layer, which is not necessarily the middle layer.
Figure 4.3.2 shows a sequence of snapshots of the free flying
of a flexible beam, where both large deformation and large overall
motion can be seen. No magnification of the deformation was used
in the figure. Figure 4.3.3 shows the profile of a multilayer
shell structure with arbitrary reference layer (gray shaded) and
with ply drop-offs. Figure 4.3.4 displays the deformed shape of
an initially flat two-layer plate with a ply drop-off, subjected
to a tip moment.
For single-layer structures, Dr. Vu-Quoc contributed, together
with the late Prof. J.C. Simo of Stanford University, to pionneer
the development of geometrically-exact structural theory since
the beginning. For multilayer structures, the topic that Dr. Vu-Quoc
initiated at UF, he has co-authored a number of papers with Prof.
I.K. Ebcioglu, and his graduate students H. Deng, S. Li, X.G.
formulation has found applications in many areas of engineering:
Flexible/rigid multibody dynamics, satellite dynamics, multilayer
(composite) structures. In a review paper titled "Computational
Strategies for Flexible Multibody Systems", to appear in the Applied
Mechanics Review, T.M. Wasfy and A.K. Noor (Center for Advanced
Computational Technology, University of Virginia) classify the
Simo/Vu-Quoc geometrically-exact methodology---which they call
the "fixed inertial frame approach"---as the most recent of the
three principal methods of formulation.
Surprisingly, geometrically-exact beams have also been used
to study the deformation and the supercoiling of DNA molecules
in biology. Our first three papers in this field, all appeared
in 1986, have a combined number of citations close to
300 times (as
of Mar 2000). Several mechanics software companies have also implemented
our formulations in their simulation software. At present, Dr.
Vu-Quoc and his students K.S. Mok and X.G. Tan are studying the
incorporation of complex, nonlinear materials (e.g., shape-memory
alloy) into geometrically-exact multilayer shells.