Optimization Problems for Curved Mechanical Structures

We study optimal design problems for three-dimensional curved rods and for shells under minimal regularity assumptions for the geometry. The results that we establish concern the existence of optimal shapes and the sensitivity analysis. We also compute some numerical examples for the optimization of curved rods. The models used have been investigated in our previous works [A. Ignat, J. Sprekels, and D. Tiba, Math. Methods Appl. Sci., 25 (2002), pp. 835--854], [J. Sprekels and D. Tiba, Adv. Math. Sci. Appl., 12 (2002), pp. 175--190]. A complete study of Kirchhoff--Love arches and of related minimization questions has been performed in [A. Ignat, J. Sprekels, and D. Tiba, SIAM J. Control Optim., 40 (2001), pp. 1107--1133]