This paper presents a novel probabilistic approach for fail-safe robust topology optimization with the following novelties: (1) the probability for failure to occur at a specified location is considered; (2) the possibility 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 performance 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.

本文提出了一种用于故障安全鲁棒拓扑优化的新概率方法，具有以下新颖性：（1）考虑了在指定位置发生故障的概率；(2) 包含随机失效大小的可能性；(3) 追求多目标问题，包括结构性能的预期值及其方差作为稳健性标准。与替代的基于最坏情况的公式相比，所采用的概率框架允许设计人员承担一定程度的风险，避免由于低概率损坏配置而导致结构性能的不期望增加；(4) 替代故障安全拓扑优化中的大多数现有工作，考虑基于密度的方法，本文首次探索了一种优化技术，其中结构边界由最优准则域的等值级隐式表示，该技术使用二分法逐渐演变。这种技术的一个关键优势是它在优化过程中为不同的体积分数提供了优化的解决方案，允许有效地找到结构性能、成本和稳健性之间的权衡。最后，数值结果证明了所提出的公式能够提供平滑和明确定义的结构边界，并增强相对于传统确定性设计的结构稳健性。这种技术的一个关键优势是它在优化过程中为不同的体积分数提供优化的解决方案，允许有效地找到结构性能、成本和稳健性之间的权衡。最后，数值结果证明了所提出的公式能够提供平滑和明确定义的结构边界，并增强相对于传统确定性设计的结构稳健性。这种技术的一个关键优势是它在优化过程中为不同的体积分数提供了优化的解决方案，允许有效地找到结构性能、成本和稳健性之间的权衡。最后，数值结果证明了所提出的公式能够提供平滑和明确定义的结构边界，并增强相对于传统确定性设计的结构稳健性。