Topology optimization of fail-safe structures using a simplified local damage model

Topology optimization of mechanical structures often leads to efficient designs which resemble statically determinate structures. These economical structures are especially vulnerable to local loss of stiffness due to material failure. This paper therefore addresses local failure of continuum structures in topology optimization in order to design fail-safe structures which remain operable in a damaged state. A simplified model for local failure in continuum structures is adopted in the robust approach. The complex phenomenon of local failure is modeled by removal of material stiffness in patches with a fixed shape. The damage scenarios are taken into account by means of a minimax formulation of the optimization problem which minimizes the worst case performance. The detrimental influence of local failure on the nominal design is demonstrated in two representative examples: a cantilever beam optimized for minimum compliance and a compliant mechanism. The robust approach is applied successfully in the design of fail-safe alternatives for the structures in these examples.