A study on fail-safe topological design of continuum structures with stress concentration alleviation

The design philosophy of fail-safe structures was first proposed in the aerospace industry to provide redundant load paths as back-ups when local damage happens. Most fail-safe topology optimization methods paid more attention to minimizing compliance of the worst failure case. However, the stress concentration due to local failure may lead to secondary damage and further destroy the structure. In the current work, the von Mises stress of damaged structures is considered as the optimization objective, to alleviate the stress concentration caused by possible local failures. Two sorts of topology optimization objectives are investigated: (1) the worst-case formulation; (2) the mean-performance formulation. To avoid the ‘singularity’ problem, the stress is penalized through the RAMP interpolation scheme. The Kreisselmeier-Steinhauser (KS) aggregation function is used to approximate the global stress level. Concerning the highly nonlinear stress behavior, the Method of Moving Asymptotes (MMA) solver is adopted. Finally, the benefits and drawbacks of these two objective functions are systematically compared and discussed through several numerical examples.