Block aggregation of stress constraints in topology optimization of structures

Topology optimization of continuum structures is a relatively new branch of the structural optimization field. Since the basic principles were first proposed by Bendsoe and Kikuchi in 1988, most of the work has been devoted to the so-called maximum stiffness (or minimum compliance) formulations. However, for the past few years a growing effort is being invested in the possibility of stating, and solving these kinds of problems in terms of minimum weight with stress (and/or or displacement) constraints formulations because some major drawbacks of the maximum stiffness statements can be avoided. Unfortunately, this also gives rise to more complex mathematical programming problems, since a large number of highly non-linear (local) constraint at the element level must be taken into account. In an attempt to reduce the computational requirements of these problems, the use of a single so-called global conistraint has been proposed. In this paper, we create a suitable class of global type conistraints by grouping the elements into blocks. Then, the local constraints corresponding to all the elements within each block are combined to produce a single aggregated constraint that limits the maximum stress within all the elements in the blcock. Thus, the number of constraints can be drastically reduced. Finally, we compare the results obtained by our block aggregation technique with the usual global constraint formulation in several application examples.