Robust topology optimization of continuum structures under uncertain partial collapses

摘要

This paper presents a novel probabilistic approach for fail-safe robust topology optimization with the fol-lowing novelties: (1) the probability for failure to occur at a specified location is considered; (2) the pos-sibility for random failure size is incorporated; (3) a multi-objective problem is pursued encompassing both the expected value of the structural performance and its variance as a robustness criterion. Compared against alternative worst-case-based formulations, the probabilistic framework employed allows designers to assume certain level of risk, avoiding undesirable increments in structural perfor-mance due to low probability damage configurations; (4) alternatively to most existing works within fail-safe topology optimization, considering density-based methods, this paper pursues for the first time an optimization technique where the structural boundary is represented implicitly by an iso-level of an optimality criterion field, which is gradually evolved using a bisection method. A key advantage of this technique is that it provides optimized solutions for different volume fractions during the optimization process, allowing to efficiently find a trade-off between structural performance, cost and robustness. Finally, numerical results are included demonstrating the ability of the proposed formulation to provide smooth and clearly defined structural boundaries and to enhance structural robustness with respect to conventional deterministic designs. (c) 2021 Elsevier Ltd. All rights reserved.