Uncertain dynamic topology optimization based on the interval reliability evaluation and equivalent static loads (ESLs) algorithm

This study investigates an interval reliability-based topology optimization (IRBTO) scheme for the lightweight design of continuum structures under unknown-but-bounded (UBB) dynamic performances. The dynamic response equation is first discretized, and the optimal design can be further converted into a multi-case time-invariant format using the equivalent static loads (ESLs) approach. In view of the inevitability of multi-source uncertainties during the whole design optimization procedure, the set quantitative model and interval dimension-by-dimension method (IDDM) are proposed for the acquisition of the reasonable characterization of uncertain dynamic responses in each iterative layout configuration. For reasons of structural safety and robustness, a new non-probabilistic reliability index oriented to structural average dynamic compliance is defined via the set-interference principle, and its design sensitivity for each elemental intermediate density is correspondingly analyzed. The method of moving asymptotes (MMA) is employed as the optimization problem solver. The usage and validity of the proposed techniques are demonstrated with several numerical examples, eventually.