### Combinatorial mechanics

*Combinatorial mechanics* is the name given by
my collaborators and me to describe a special body of problems
that may be seen as dual to the standard question of mechanical
engineering: Instead of asking for a design to bear a given load,
we ask how a given design should be loaded. For example, one
canonical question is how to place loads on a structure so that
the resultant center of gravity lies as close as possible to a
given target point. This is the problem of stowing cargo in
planes, trucks, or ships.

- Heuristics for balancing turbine fans, with S. V. Amiouny and J. H. Vande Vate;
Operations Research
**48**(4):591-602 (2000). A turbine is easier to balance if it has a number of
blades that is evenly divisible by 4.
- Minimizing deflection and bending moment in a beam, with S. V. Amiouny and J. H.
Vande Vate; Mechanics of Structures and Machines
**21**(2):167-184 (1993). An approximation
algorithm whose worst-case performance is bounded.
- Balanced loading, with S. V. Amiouny, J. H. Vande Vate, and J. Zhang; Operations
Research
**40**(2):238-246 (1992). How to load an aircraft so that its center of gravity lies within a
specified region.

This work was supported by the Air force Office of Scientific Research and by the National S
cience Foundation.