Approximate solution of minimum induced drag of wings with given structural weight

Klein, Armin; Viswanathan, S

doi:10.2514/3.44425

Cited by 43 publications

(25 citation statements)

References 2 publications

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“…However, with a given lift and bending moment constraint, then the elliptic distribution may not be obtainable, hence the solution of Jones [48] (which is a specific solution of a result later proved by Klein and Viswanathan [49]) becomes the optimal result:…”

Section: Resultsmentioning

confidence: 99%

Global Optimization of Multimodal Aerodynamic Optimization Benchmark Case

Poole

Allen

Rendall

2017

35th AIAA Applied Aerodynamics Conference

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. An investigation into a multimodal aerodynamic optimization benchmark case using an approximate global optimization approach is presented. A new benchmark case of the AIAA Aerodynamic Design Optimization Discussion Group that involves the drag minimization of a rectangular NACA0012 wing subject to lift and root bending moment, as well as other geometric constraints, that is currently believed to be multimodal has been suggested. In this paper, optimization of that case using a constrained populationbased global optimization framework is presented, with three independent runs of the optimizer (each with different starting locations) having been performed. The runs are all coarsely-converged to give approximately converged solutions such that rapid run-times can be achieved and used to demonstrate any pitfalls that may be encountered when using a gradient-based optimizer. All three of the runs converged onto drag values close to the theoretical optimum, however with substantially different final shapes. This likely indicates the presence of a flat optimum region within the design space, where a substantial number of wing shapes are able to obtain the theoretical optimum span loading.

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Section: Resultsmentioning

confidence: 99%

Global Optimization of Multimodal Aerodynamic Optimization Benchmark Case

Poole

Allen

Rendall

2017

35th AIAA Applied Aerodynamics Conference

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“…(38) in Eqs. (35) and (37) gives a wingspan that is 4.98 percent larger than the wingspan allowed by the elliptic lift distribution and a drag reduction of 4.25 percent over the elliptic lift distribution for wings of equal weight. Like Prandtl, Hunsaker et al 37 limited their analysis to a rectangular wing.…”

Section: B Hunsaker's Formulationmentioning

confidence: 93%

“…Gopalarathnam and Norris 33 varied camber to find an optimal lift distribution with constraints on root bending moment. Klein and Viswanathan 34,35 found the optimal lift distribution at a given lift coefficient with constraints on both root and integrated bending moment. McGeer 36 considered aeroelastic effects.…”

Section: Introductionmentioning

confidence: 99%

Numerical Algorithm for Wing-Structure Design

Taylor

Hunsaker

Joo

2018

2018 AIAA Aerospace Sciences Meeting

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“…As previously covered in Poole et al [37], the root bending moment constraint of this problem inhibits the conventional optimal elliptic loading result. Instead, the optimal loading of this result is given by the solution of Jones [54] (which is a specific solution of a result later proved by Klein and Viswanathan [55]):…”

Section: Va Problem Definitionmentioning

confidence: 99%

Identifying Multiple Optima in Aerodynamic Design Spaces

Poole

Allen

Rendall

2018

2018 Multidisciplinary Analysis and Optimization Conference

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Parallel niching optimization algorithms are developed and applied to a multimodal aerodynamic optimization case to identify multiple optima in the design space. Previous work by the authors has presented niching optimization algorithms that use differential evolution with feasible selection as a basis that can identify multiple optima in constrained search spaces, which is necessary for aerodynamic optimization. In this paper, these algorithms are further developed for application to aerodynamic optimization by reformulating each to provide a parallel decomposition of the objective function evaluation at each iteration of the optimization process. These algorithms are tested on an analytical optimization problem. The parallel, constrained form of both local nearest-neighbourhood and local crowding are shown to be the best performing algorithms with a 99% confidence level. A variation on the AIAA ADODG case 6 multimodal wing optimization case is also studied. A multi-start gradient-based approach is used to show multimodality of the design space. The local nearest-neighbourhood-based algorithm is then applied to the aerodynamic optimization case and is able to successfully identify two minima in the design space, with one being close to the global minimum and one in a different part of the design space, which is a local minimum. * Senior Teaching Associate.

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Approximate solution of minimum induced drag of wings with given structural weight

Cited by 43 publications

References 2 publications

Global Optimization of Multimodal Aerodynamic Optimization Benchmark Case

Global Optimization of Multimodal Aerodynamic Optimization Benchmark Case

Numerical Algorithm for Wing-Structure Design

Identifying Multiple Optima in Aerodynamic Design Spaces

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