Structural topology optimization with predetermined breaking points

This paper addresses the concept of predetermined breaking points in topology optimization. The aim is to propose and investigate a novel formulation to design optimized topologies in which one can control where failure will occur first in case of overload; in addition, the optimized topology must withstand the design load after the damaged part is removed. In order to achieve this goal, a stress-constrained formulation based on two realizations of material distributions is proposed: one realization represents the nominal design, without damage, and the other represents the damaged design. In the nominal design, the predetermined damage region is defined, which is the region where failure is programmed to occur first in case of overload. The design constraints are defined in a way that ensures that a structural member is formed within the predetermined damage region and that the maximum von Mises equivalent stress of this member is slightly larger than the maximum von Mises stress in the rest of the structure. After failure has occurred, stress constraints are employed to ensure that the resulting design without the damaged part still resists the applied load. Two design problems with several variants are addressed: the L-shaped and the MBB beam problems. Numerical investigations demonstrate that: (1) the conventional design is extremely sensitive to localized damage of structural members and, moreover, its almost fully stressed configuration does not allow to predict where failure will occur first in case of overload; (2) the proposed formulation for predetermined breaking points is able to provide optimized structures where one knows in advance the region where failure is expected to occur first; in addition, the structure remains safe after the damaged part is removed.