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An Analytical Study in Multi-physics and Multi-criteria Shape Optimization

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  • Hanno Gottschalk

    (University of Wuppertal)

  • Marco Reese

    (University of Wuppertal)

Abstract

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.

Suggested Citation

  • Hanno Gottschalk & Marco Reese, 2021. "An Analytical Study in Multi-physics and Multi-criteria Shape Optimization," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 486-512, May.
    • Handle: RePEc:spr:joptap:v:189:y:2021:i:2:d:10.1007_s10957-021-01841-y
    DOI: 10.1007/s10957-021-01841-y
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    References listed on IDEAS

    as
    1. Matthias Bolten & Hanno Gottschalk & Sebastian Schmitz, 2015. "Minimal Failure Probability for Ceramic Design Via Shape Control," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 983-1001, September.
    2. Пигнастый, Олег & Koжевников, Георгий, 2019. "Распределенная Динамическая Pde-Модель Программного Управления Загрузкой Технологического Оборудования Производственной Линии [Distributed dynamic PDE-model of a program control by utilization of t," MPRA Paper 93278, University Library of Munich, Germany, revised 02 Feb 2019.
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