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

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.

GivEn -- Shape Optimization for Gas Turbines in Volatile Energy Networks

“…We couple internal and external PDEs in order to describe the various forces that are inflected on the component. In this framework, using techniques based on pre-compactness of embedding between Hölder spaces of different index like in [43,12], we are able to show [40] the existence of Pareto optimal shapes in terms of subsection 2.5.1 which form a Pareto front, see also [20] for a related result. We also prove the completeness of the Pareto front in the sense that the Pareto front coincides with the Pareto front of the closure of the feasible set (which is equivalent to the fact that every non-Pareto admissible shape is dominated by a Pareto optimal shape).…”

“…Under suitable assumptions on the contuinuous dependency of the scalarization method on the scalarization parameter, we are able to show a continuous dependency of the optimal shapes spaces on the parameter as well. For details we refer to the forthcoming work [40].…”

Anti-Roll Bar Optimization of an Urban Electric Bus

“…The correct selection of material and shape is effective in the design of an optimum part (Gottschalk & Reese, 2021). Optimization involves the approach of determining the difference between the ideal target to be achieved in a structure or a system under consideration and the existing structure and eliminating this difference under various conditions.…”

Probabilistic Modeling of LCF Failure Times Using an Epidemiological Crack Percolation Model

“…In [29,31], some of the authors proposed an empirical local model for low cycle fatigue on the basis of a Poisson process model. This line of research has been applied to gas turbine design [30,31], shape optimization [2,10,14,13,12] and tolerance design [24]. Further developments include notch support factors into the model [25,19], see also [1,21,22,23,35] for related approaches.…”