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Analysis of optimality conditions for some topology optimization problems in elasticity

Luis Trabucho — 2002

International Journal of Applied Mathematics and Computer Science

The subject of topology optimization has undergone an enormous practical development since the appearance of the paper by Bendso e and Kikuchi (1988), where some ideas from homogenization theory were put into practice. Since then, several engineering applications as well as different approaches have been developed successfully. However, it is difficult to find in the literature some analytical examples that might be used as a test in order to assess the validity of the solutions obtained with different...

On the curvature and torsion effects in one dimensional waveguides

Guy Bouchitté;  M. Luísa Mascarenhas;  Luís Trabucho — 2007

ESAIM: Control, Optimisation and Calculus of Variations

We consider the Laplace operator in a thin tube of ℝ 3 with a Dirichlet condition on its boundary. We study asymptotically the spectrum of such an operator as the thickness of the tube's cross section goes to zero. In particular we analyse how the energy levels depend simultaneously on the curvature of the tube's central axis and on the rotation of the cross section with respect to the Frenet frame. The main argument is a -convergence theorem for a suitable sequence of quadratic energies.

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