Abstract :
In 1993, Y.M. Xie and G.P. Steven introduced an approach called evolutionary structural optimization (ESO). ESO is based on the simple idea that the optimal structure (maximum stiffness, minimum weight) can be produced by gradually removing the ineffectively used material from the design domain. The design domain is constructed by the FE method, and furthermore, external loads and support conditions are applied to the element model. Considering the engineering aspects, ESO seems to have some attractive features: the ESO method is very simple to program via the FEA packages and requires a relatively small amount of FEA time. Additionally, the ESO topologies have been compared with analytical ones, e.g. Michell trusses, and so far the results are quite promising. On the other hand, ESO does not have a solid theoretical basis, and consequently, the ESO minimization problem is still unresolved. Since the good agreement between the results cannot be just a coincidence, in this paper, we will study whether the gradual removal of material can be explained mathematically and whether the theoretical basis of ESO can be outlined.
