This paper presents a risk-averse approach in the context of fail-safe topology optimization. The main novelty is the minimization of two risk functions quantifying the costs inherent to partial or full collapses, whose occurrence is considered as a source of uncertainty. This provides the designer with the flexibility to explicitly incorporate probabilistic information of occurrence of different structural failures, in contrast to the worst case approach, that penalizes all the damage configurations regardless their probability of occurrence. For the first time in the context of fail-safe topology optimization, a level-set method is employed. The level-set function is updated by means of a reaction–diffusion equation incorporating the topological derivative of the two risk-averse functions considered. Finally, the numerical experiments reveal the capability of the proposed formulations to yield redundant structures less sensitive to inherent losses of stiffness resulting from possible failures, whilst allowing designers to assume an acceptable level of risk. The benefits and drawbacks of the formulations proposed are compared against deterministic and fail-safe worst-case formulations.

本文在故障安全拓扑优化的背景下提出了一种规避风险的方法。主要的新颖之处在于最小化两个风险函数，量化部分或完全崩溃的固有成本，其发生被认为是不确定性的来源。与最坏情况方法相反，这为设计人员提供了明确合并不同结构故障发生概率信息的灵活性，最坏情况方法会惩罚所有损坏配置，而不管其发生概率。在故障安全拓扑优化的背景下，首次采用了水平集方法。水平集函数通过反应扩散方程更新，该方程包含所考虑的两个风险规避函数的拓扑导数。最后，数值实验揭示了所提出的公式能够产生冗余结构，这些结构对可能的故障造成的固有刚度损失不太敏感，同时允许设计人员承担可接受的风险水平。所提出的公式的优缺点与确定性和故障安全最坏情况公式进行了比较。