Optimisation de forme fluide-structure par un jeu de Nash

International audience This paper aims at the development of innovating methods for optimum design for multidisciplinary optimization problems in the aeronautical context. The subject is the treatment of a problem of concurrent optimization in which the aerodynamicist interacts with the structural designer, in a parallel way in a symmetric Nash game. Algorithms for the calculation of the equilibrium point have been proposed and successfully tested for this coupled aero-structural shape optimization in a situation where the aerodynamical criterion is preponderant. Cet article a pour objectif le développement de méthodes numériques innovantes pour la conception optimale de forme pour les problèmes d’optimisation multidisciplinaire dans un contexte aéronautique. On cherche à traiter un problème d’optimisation concourante où le concepteur aérodynamique interagit avec le concepteur structural, parallèlement dans un jeu symétrique de Nash. On a proposé et expérimenté avec succès des algorithmes de calcul d’équilibre pour cette optimisation couplée aéro-structurale dans une situation où le critère aérodynamique est prépondérant.

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An Algorithm for Automated Design Variable Selection in Structural Shape Optimization With Intrinsically Defined Geometry

Volume 1: 21st Design Automation Conference ◽

10.1115/detc1995-0053 ◽

1995 ◽

Author(s):

James M. Widmann ◽

Sheri D. Sheppard

Keyword(s):

Shape Optimization ◽

Optimization Problems ◽

Analysis Model ◽

Structural Shape ◽

Structural Shape Optimization ◽

Design Variables ◽

Sufficient Set ◽

Compatibility Constraint ◽

Selection Of

Abstract A major difficulty encountered in the shape optimization of structural components is the selection of an adequate set of shape design variables. The quality of the solution and the value of the optimal objective function depend on the chosen set of design variables. This paper presents an algorithm for the automated selection of intrinsically defined design variables to solve two-dimensional structural shape optimization problems. The algorithm arrives at a sufficient set of design variables by solving a series of optimization problems. Using the results of intermediate solutions, the algorithm adaptively refines the set of design variables until the solution converges. The algorithm specifies the addition and deletion of design variables and makes use of a model compatibility constraint to determine whether the analysis model must be updated. Two examples are presented which illustrate the effectiveness of the algorithm.

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Intrinsic Geometry for Shape Optimal Design With Analysis Model Compatibility

20th Design Automation Conference: Volume 2 — Robust Design Applications; Decomposition and Design Optimization; Optimization Tools and Applications ◽

10.1115/detc1994-0137 ◽

1994 ◽

Author(s):

James M. Widmann ◽

Sheri D. Sheppard

Keyword(s):

Shape Optimization ◽

Geometric Modeling ◽

Explicit Knowledge ◽

Optimization Problems ◽

Structural Response ◽

Analysis Model ◽

Intrinsic Geometry ◽

Structural Shape ◽

Structural Shape Optimization ◽

Design Variables

Abstract This paper presents a comparison of geometric modeling techniques and their applicability to structural shape optimization. A method of shape definition based on intrinsic geometric quantities is then outlined. Explicit knowledge of curvature and arc length allow for a quantitative assessment of the compatibility of analysis model with the design model when using finite elements to determine structural response quantities. The compatibility condition is formalized by controlling finite element idealization error and is incorporated into the shape optimization model as simple bounds on the curvature design variables. Several examples of shape optimization problems are solved using sequential quadratic programming which proves to be an effective tool for maintaining the geometric equality constraints that arise from intrinsically defined curves.

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