Minimum Weight with Stress Constraints Topology Optimization

Sizing and shape structural optimization problems are normally stated in terms of a minimum weight approach with constraints that limit the maximum allowable stresses and displacements. However, topology structural optimization problems have been traditionally stated in terms of a maximum stiffness (minimum compliance) approach. In this kind of formulations, the aim is to distribute a given amount of material in a certain do-main, so that the stiffness of the resulting structure is maximized (the compliance, or energy of deformation, is minimized) for a given load case. Thus, the material mass is restricted to a predefined percentage of the maximum possible mass, while no stress or displacement constraints are taken into account. In this paper we analyze and compare both approaches, and we present a FEM minimum weight with stress constraints (MWSC) formulation for topology struc-tural optimization problems. This approach does not require any stabilization tech-nique to produce acceptable optimized results, while no truss-like final solutions are necessarily obtained. Several 2D examples are presented. The optimized solu-tions seem to be correct from the engineering point of view, and their appearence could be considered closer to the engineering intuition than the traditional truss-like results obtained by means of the widespread maximum stiffness (minimum compliance) approaches.