Abstract
We focus on a particular class of optimal design problems in elasticity where the objective function depends on the stresses along the boundary to be optimized. This is an issue of interest with many engineering applications. This work describes a gradient-type method to solve the finite element numerical approximation of such problems. The descent direction of the discrete cost functional is computed as a discrete projection of the continuous gradient formula, which is derived systematically from shape derivatives and a careful local coordinates calculus. The computational procedure is presented together with an illustrative example, namely the optimization of a cross-sectional tunnel vault immersed in a linearly elastic terrain to obtain uniform compression along the vault.
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