Abstract :
The method of cylindrical algebraic decomposition (CAD) of the kdiiensional space
constitutes a classical technique for the efficient solution of quantifier eli&ation.(QE) problems in
algorithmic, computer-aided algebra. Here we apply this method to some applied mechanics prob-
!ems under appropriate constraints. At first, we study the problem of a straight elastic beam under
a restriction on the maximum permissible deflection~along this beam (which can easily be reduced
to the construction of a onedimensional CAD) as well as the probJem of a cimular isotropic elastic
medium where a stress component should not exceed a critical value (which requires the construction
of a thre&iiensional CAD). In both these problems, we derive also the required quaatifier-free
formulae @FFs) not inchtding the fundamental variables, but only the parameters involved. Much
more di@ult CAD/QFFderivation applicatiohs, concerning.anelliptical elastic medium again @h
an upper, bound for a stress component, a special case of failure by yielding in fracture mechanics,
related to Sih’s strain-energydetisit) factor, and a f?ictiokWs contact problem for ah elastic halfplane
are also. considered and ekjrlkftly solved with the help of already available CAD-produced
results although, evidently, CAD ia not expected to produce QFFs in extremuly diBicult problems.
Finally, additional possible applications of CAD/CQE to applied mechanics problems are also
suggested. 6 1997 Elsevier Science Ltd
