Convexity-oriented reliability-based topology optimization (CRBTO) in the time domain using the equivalent static loads method

Abstract

Owing to the wide existence of multi-source uncertainties in practical engineering, the reliability-based design optimization for structural dynamics is particularly important and meaningful. However, compared to the size and shape optimization, it has rarely been considered in topology optimization with the lack of reasonable uncertainty cognition and the difficulty in the sensitivity solution for reliability constraints calculated from dynamic characteristics. In this research, a new design strategy, which combines the equivalent static loads (ESLs) algorithm and the set-theoretical convex method, is proposed for dynamic response topology optimization under convex reliability constraints. Time-varying boundary rules of the layout response are determined using the state-space transformation and the set perturbation theory. As the safety measurement, a new non-probabilistic reliability index (related to the function of dynamic compliance near the peaks) is defined under the hypervolume-ratio principle and its design sensitivity is further analyzed by solving central finite difference (CFD) equations. Three typical optimization cases, including a rectangular plate, an equivalent control surface and a win rib, are presented to demonstrate the validity and effectiveness of the developed methodology.