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In this article we develop a duality principle and concerning computationalmethod for a structural optimization problem in elasticity. We consider theproblem of finding the optimal topology for an elastic solid which minimizesits structural inner energy resulting from the action of external loads to bespecified. The main results are obtained through standard tools of convexanalysis and duality theory. We emphasize our algorithm do not include a filterto process the results, so that the result obtained is indeed a critical pointfor the original optimization problem. Finally, we present some numericalexamples concerning applications of the theoretical results established.

A duality principle and related computational method for a class of structural optimization problems in elasticity