In conventional fail-safe optimization of frame structures the damage is usually modelled as complete removal of one or more members. We propose and incorporate two additional types of damage models into the fail-safe design problem. The first describes thickness degradation caused e.g. by corrosion. The second describes severe local damage by removal of a part of a member that causes a gap and free ends in the member. The latter damage model can cause undesirable local vibration modes. By combining the two damage models, local thickness degradation in a part of a member can be modelled. The considered design problem minimizes structural mass and includes local stress constraints and limits on eigenfrequencies. Besides the new damage models, a working-set algorithm is applied on the fail-safe optimization problem to reduce the computational cost. Numerical experiments on two-dimensional frame structures illustrate that the working-set algorithm can effectively handle the relatively large number of constraints and damage scenarios in fail-safe optimization.

在框架结构的传统故障安全优化中，损坏通常被建模为一个或多个构件的完全移除。我们提出了两种额外类型的损坏模型并将其合并到故障安全设计问题中。第一个描述了例如由腐蚀引起的厚度退化。第二个描述了通过移除部件的一部分而导致部件中产生间隙和自由端的严重局部损坏。后一种损坏模型会导致不希望的局部振动模式。通过结合两种损伤模型，可以对构件的局部厚度退化进行建模。所考虑的设计问题最小化结构质量并包括局部应力约束和对特征频率的限制。除了新的损伤模型外，还对故障安全优化问题应用了工作集算法以降低计算成本。