Improvements in the treatment of stress constraints in structural topology optimization problems

Topology optimization of continuum structures is a relatively new branch of the structural optimization field. Since the basic principles were first proposed by Bendsøe and Kikuchi in 1988, most of the work has been dedicated to the so-called maximum stiffness (or minimum compliance) formulations. However, since a few years different approaches have been proposed in terms of minimum weight with stress (and/or displacement) constraints.These formulations give rise to more complex mathematical programming problems, since a large number of highly non-linear (local) constraints must be taken into account. In an attempt to reduce the computational requirements, in this paper, we propose different alternatives to consider stress constraints and some ideas about the numerical implementation of these algorithms. Finally, we present some application examples.