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Geometrically-exact multilayer beams
with ply drop-offs:
We derive the equations of motion of geometrically-exact multilayer
beams having ply drop-offs. The beam can undergo large overall
motion and large deformation. Applications can be found in many
areas of engineering. We have been working on the computational
formulation and computer implementation for the multilayer geometrically-exact
beam theory. We successfully implemented the beam model in the
research finite element code FEAP. Several papers resulted from
this work. Two papers appeared in the ASME Journal of Applied
Mechanics; a third invited paper accepted to appear in the special
issue "Suhubi and Continuum Mechanics" of the Bulletin of the
Technical University of Istanbul; a fourth paper appeared in the
Journal of Nonlinear Science; a fifth paper will appear in the
Computer Methods in Applied Mechanics and Engineering. We have
three conference papers.
Geometrically-exact multilayer plates
We formulated the equations of motion for multilayered beams, plates
and shells using the geometrically-exact approach. Similar to the
beam model, the present shell formulation also accomodates ply drop-offs.
The 3-D shell formulation is, however, more complex than the plane
beam. The present theory canbe used to analyze structures made of
composite materials. Also one can apply the present formulation
to structures with layers of "smart material" for use as distributed
sensors and actuators. Applications of this type of structure is
widespread, from marine engineering, robotics, to space structures.
A paper will appear in the International Journal of Solids and Structures.
Three more papers are under preparation.
Force-displacement models in contact
This research effort is one component in the mechanics of granular
flow program. We have been concentrating our efforts on the contact
mechanics of particles in collision, with special attention to the
tangential force-displacement (TFD) model. The highly complex Mindlin-Deresiewicz
(MD) model has been considered in detail; we developed a MATLAB
code to compare the MD model with the simplified Walton-Braun (WB)
model. A deeper understanding of the TFD model (elastic bodies with
friction) will help to incorporate the effects of plastic deformation
at contact in the TFD model. In parallel, we have been constructing
finite element (FE) models using ABAQUS to verify the behavior predicted
by the MD model and by the WB model. The FE models will help our
effort in incorporating plastic deformation effects in the TFD model.
We have been making progress toward a completely coherent and consistent
force-displacement model (both in the normal direction and in the
tangential direction) that incorporate plastic deformation.
Development of a dry granular flow code:
- Graduate students:
- Undergraduate students:
This research effort is another in the mechanics of granular flow
program. We have successfully developed a simplified incremental
tangential-force-displacement (TFD) model for elastic-frictional
contact that is accurate compared to the Mindlin-Deresiewicz (MD)
model and to finite element analysis. We have incorporated this
new TFD model in our granular flow code. Results indicate that the
new TFD model is superior to the Walton-Braun model. We have been
coordinating our modeling effort with the Transport and Handling
group; biweekly meetings between people working on granular flow
in the two groups have been held regularly. We are working to correlate
the simulation results with experimental results.