论文标题
多物理学和多标准形状优化的分析研究
An analytical study in multi physics and multi criteria shape optimization
论文作者
论文摘要
一个简单的多物理系统，用于流体通过裹尸布的电势流，其中将机械组件（如涡轮叶片）放置在数学上进行建模。然后，当允许组件的形状在一定的一组第二阶hölder连续可区分的转换下，基线形状具有相同连续性类别的边界时，我们考虑了多个标准形状优化问题。作为目标函数，我们考虑了一个简单的流体动力学效率损失模型以及由于反复应用源于流体的静压的负载而导致的组件故障概率。对于这个多物理系统，可以表明，在某些条件下，帕累托前部是最大的，从某种意义上说，可行套装的帕累托前部与其闭合的帕累托前部一致。我们还表明，相对于优先参数连续（在Hausdorff Metric中）连续变形了所有最佳形式的集合。
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, when the shape of the component is allowed to vary under a certain set of 2nd 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 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.
