  In this article we develop a duality principle and concerning computational
method for a structural optimization problem in elasticity. We consider the
problem of finding the optimal topology for an elastic solid which minimizes
its structural inner energy resulting from the action of external loads to be
specified. The main results are obtained through standard tools of convex
analysis and duality theory. We emphasize our algorithm do not include a filter
to process the results, so that the result obtained is indeed a critical point
for the original optimization problem. Finally, we present some numerical
examples concerning applications of the theoretical results established.
