A non-probabilistic reliability-based topology optimization (NRBTO) method of continuum structures with convex uncertainties

This paper develops a non-probabilistic reliability-based topology optimization (NRBTO) framework for continuum structures under multi-dimensional convex uncertainties. Combined with the solid isotropic material with penalization (SIMP) model and the set-theoretical convex method, the uncertainty quantification (UQ) analysis is firstly conducted to obtain mathematical approximations and boundary laws of considered displacement responses. By normalization treatment of the limit-state function, a new quantified measure of the non-probabilistic reliability is then defined and further deduced by the principle of the hyper-volume ratio. For circumventing optimization difficulties arising from large-scale design variables, the adjoint vector scheme for sensitivity analysis of the reliability index with respect to design variables are discussed as well. Numerical applications eventually illustrate the applicability and the validity of the present problem statement as well as the proposed numerical techniques.