Reliability-based topology optimization for freely vibrating continuum structures with unknown-but-bounded uncertainties

This study investigates a novel reliability-based topology optimization framework to determine optimal material configurations for freely vibrating continuum structures with unknown-but-bounded uncertainties. Firstly, the optimization formulation for freely vibrating continuum structures with fundamental eigenfrequency and eigenfrequency gap constraints is described. Uncertainty quantification analysis is conducted to determine the feasible bounds of the natural eigenfrequencies under unknown-but-bounded uncertainties. For safety reasons, the non-probabilistic reliability concept is introduced in the optimization model and the performance measure approach is proposed to overcome the convergence difficulties. Meanwhile, the sensitivity analysis is further discussed based on the chain rule, in which the sensitivities of the target performance measure to the bounds of eigenfrequencies are calculated and the sensitivities of the eigenfrequencies with respect to the design variables are deduced. Numerical examples are eventually given to demonstrate the validity of the developed reliability-based topology optimization methodology.