A simple multi-physical system for the potential flow of a fluid through a shroud, in which a mechanical component, like a turbine vane, is placed, is modeled mathematically. We then consider a multi-criteria shape optimization problem, where the shape of the component is allowed to vary under a certain set of second-order Hölder continuous differentiable transformations of a baseline shape with boundary of the same continuity class. As objective functions, we consider a simple loss model for the fluid dynamical efficiency and the probability of failure of the component due to repeated application of loads that stem from the fluid’s static pressure. For this multi-physical system, it is shown that, under certain conditions, the Pareto front is maximal in the sense that the Pareto front of the feasible set coincides with the Pareto front of its closure. We also show that the set of all optimal forms with respect to scalarization techniques deforms continuously (in the Hausdorff metric) with respect to preference parameters.

一种简单的多物理系统，用于通过护罩的流体的潜在流动，在该系统中对机械组件（如涡轮叶片）进行了数学建模。然后，我们考虑一个多准则形状优化问题，其中，在具有相同连续性类别边界的基线形状的一组特定二阶Hölder连续微分变换下，允许组件的形状发生变化。作为目标函数，我们考虑一个简单的损失模型，用于流体动力效率以及由于重复施加源自流体静压力的载荷而导致的组件失效概率。对于这种多物理系统，表明在某些条件下，从可行集的Pareto前沿与其闭包的Pareto前沿重合的意义上说，Pareto前沿是最大的。我们还表明，关于标量化技术的所有最佳形式的集合相对于首选项参数连续变形（在Hausdorff度量标准下）。