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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 viscoelastic layers.

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. The 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. Tan.

Geometrically-exact 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.