Global versus local statement of stress constraints in topology optimization of continuum structures

Structural topology optimization problems have been traditionally set out in terms of maximum stiffness formulations. In this approach, the goal is to distribute a given amount of material in a certain region, so that the stiffness of the le resulting structure is maximized for a given load case. Even though this approach is quite convenient, it also entails some serious conceptual and practical drawbacks. The authors, in common with other research groups, have been working for a few years on the possibility of stating these kinds of problems by mean, of a FEM-based minimum weight with stress (and/or displacement) constraints formulation. The physical meaning of this approach is closer to the engineering point of view. Furthermore, most of the above mentioned drawbacks could be removed this way. However, this also leads to more complicated optimization problem, with much higher computational requirements, since a large number of highly non-linear (local) constraints must be taken into account to limit the maximum stress (and/or displacement) at the element level. In this paper, we explore the feasibility of defining a so-called global constraint, whose basic aim is to limit the maxi mum stress (and/or displacement) simultaneously within all the structure by means; of one single inequality. Should this global constraint perform adequately, the c omplexity of the underlying mathematical programming problem should be drastically reduced. Finally, we compare the results provided by both types of constraints In some application examples.