Application of efficient surrogate modeling to aeroelastic analyses of an aircraft wing

Sommerwerk, Kay; Michels, B.; Lindhorst, K.; Haupt, M.; Horst, Peter

doi:10.1016/j.ast.2016.06.011

Cited by 14 publications

(5 citation statements)

References 9 publications

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“…It can be a laborious task to derive these approximations by hand. We used an algorithm suitable for computer automation in the derivations of the expressions in Equations ( 8)- (10). Such algorithms are frequently taught in university courses but we did not find them in the published literature.…”

Section: Development Of a Numerical Approach For Solving The Inhomogeneous Euler-bernoulli Equationmentioning

confidence: 99%

“…Such tools are also applicable to the aeroelastic analysis of helicopter rotor blades and wind turbines. Recent research works related to aeroelastic analysis were conducted by Amoozgar et al [5], Vazhayil Thomas et al [6], Rajpal et al [7], Tsushima et al [8], Rong et al [9], Sommerwerk et al [10] and Qin et al [11]. It is with these developments in mind that the present work was undertaken.…”

Section: Introductionmentioning

confidence: 95%

On a Novel Approximate Solution to the Inhomogeneous Euler–Bernoulli Equation with an Application to Aeroelastics

Fleischmann

Könözsy

2021

Aerospace

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This paper focuses on the development of an explicit finite difference numerical method for approximating the solution of the inhomogeneous fourth-order Euler–Bernoulli beam bending equation with velocity-dependent damping and second moment of area, mass and elastic modulus distribution varying with distance along the beam. We verify the method by comparing its predictions with an exact analytical solution of the homogeneous equation, we use the generalised Richardson extrapolation to show that the method is grid convergent and we extend the application of the Lax–Richtmyer stability criteria to higher-order schemes to ensure that it is numerically stable. Finally, we present three sets of computational experiments. The first set simulates the behaviour of the un-loaded beam and is validated against the analytic solution. The second set simulates the time-dependent dynamic behaviour of a damped beam of varying stiffness and mass distributions under arbitrary externally applied loading in an aeroelastic analysis setting by approximating the inhomogeneous equation using the finite difference method derived here. We compare the third set of simulations of the steady-state deflection with the results of static beam bending experiments conducted at Cranfield University. Overall, we developed an accurate, stable and convergent numerical framework for solving the inhomogeneous Euler–Bernoulli equation over a wide range of boundary conditions. Aircraft manufacturers are starting to consider configurations with increased wing aspect ratios and reduced structural weight which lead to more slender and flexible designs. Aeroelastic analysis now plays a central role in the design process. Efficient computational tools for the prediction of the deformation of wings under external loads are in demand and this has motivated the work carried out in this paper.

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“…This is but especially for computationally expensive simulations, the direct use of Finite Element (FE) models can be extremely timeconsuming. Hence, usually, a smaller set of simulations is used to generate first a meta-model, which is used to complete the UQ analysis [8,9]. However, when the dynamic response of a structure is affected by strong nonlinearities, for example when the system has free-plays or includes rubber-like materials, the number of simulations required to generate a reliable meta-model can be still considerably high.…”

Section: Introductionmentioning

confidence: 99%

A sample-based approach to estimate the dynamic loads of components with nonlinear uncertain interfaces

Menga

Sánchez

Romero

et al. 2019

Aerospace Science and Technology

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Predicting aircraft dynamics and vibration loads at components' interfaces is a key task for ensuring a robust design and development of the product. Usually, whereas in the case of isolate components the dynamic behavior can be predicted quite accurately, when several components are assembled through discontinuous junctions the predictiveness of a model decreases. The junctions, whose mechanical properties are seldom well characterized experimentally, often introduce nonlinearities in the loads' path. Additionally, their behavior is intrinsically uncertain and as a consequence, the dynamic response of the connected structures becomes stochastic. We propose a sample-based approach which aims to cope with both aspects, nonlinearities and uncertainties, and can be split in two main tasks. First, the computational cost of each deterministic simulation is minimized considering that the global nonlinear behavior depends on localized sources of nonlinearities at the interfaces. Second, the uncertainties are propagated through the model by a non-intrusive method based on Sobol's low discrepancy design. Attention is paid to the global sensitivity indices, which are estimated by creating a meta-model based on Polynomial Chaos Expansion. An industrial application considering an aircraft component whose dynamic behavior is affected by uncertain free-plays at its interfaces is presented.

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“…Much progress has been made on the development of aerodynamic ROMs for loads calculation. The range of theory applied to the problem is wide and includes approaches based on eigen realisation algorithms (ERAs) [1,2], Proper Orthogonal Decomposition (POD) [3], Volterra theory [4], and surrogates [5,6]. In potential flow, recent efforts have been focussed on the doublet lattice method [7,8].…”

Section: Introductionmentioning

confidence: 99%

A Kriging Based Corrected Potential Flow ROM for Gust Load Calculations

Horwitz

Man

Malan

et al. 2018

2018 Applied Aerodynamics Conference

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A novel aerodynamics reduced order model (ROM) is proposed for gust load calculations on two-and three-dimensional wing geometries at transonic flow conditions. Force estimates from sectional potential flow solutions are taken as inputs to kriging models that predict the aerodynamic loads. The kriging models are trained with coupled aeroelastic CFD calculations of two gust lengths (viz. short and long) which define a range in which the ROM is applicable. An interface is developed to handle the coupling of fluid and structure in the training simulations. The interface ensures conservative transfer of forces from the fluid to the structure and reconstruction of the fluid mesh subject to structural motion. Two test cases are put forward as a means to evaluate ROM: the FFAST Crank aerofoil and the NASA Common Research Model (CRM). In the former case, individual run cost decreased by an order of magnitude and error in the aeroelastic response never exceeded 8%. At the time of writing, the CFD calculations for the CRM case are underway.

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“…In any case, but especially for computationally expensive simulations, the direct use of Finite Element (FE) models can be extremely time-consuming. Hence, usually, a smaller set of simulations is used to generate first a meta-model, which is used to complete the UQ analyis [86,87].…”

Section: Introductionmentioning

confidence: 99%

Uncertainty Quantification and Global Sensitivity Analysis in Computational Mechanics

Menga¹

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Quando penso a come é cominciata questa avventura del dottorato, non posso evitare di sentire ancora l'emozione dell'ammissione e, allo stesso tempo, la solitudine che ho provato quando, camminando per i corridoi di un'universitá a me sconosciuta, mi chiedevo chi avrebbe accettato, con i miei 38 anni, di essere il mio direttore di tesi.Cosí, quasi casualmente, finí nello studio di Ignacio e, vedendo sulla sua scrivania vari fogli con gradienti ed equazioni differenziali, dubitai di quanto veramente mi sarei potuto compromettere in un progetto del genere. Ricordo, oggi quasi sorridendo, che furono giorni di grande incertezza! Credo che Ignacio decise di darmi una possibilitá e mi propose, quasi come se sapesse quello che stessi provando, di addentrarmi insieme a lui nel mondo della quantificazione dell'incertezza. Un campo di studio completamnete nuovo anche per lui. Certamente non sarebbero mancati elementi e principi di statistica, cosicché reclutammo la mia condirettrice: Mariaje. Cosí cominciarono "i nostri Venerdí"! Ringrazio entrambi per il tempo e l'attenzione che mi hanno dedicato. É stato un percorso pieno, ricco di momenti di incessanti lavoro e soddisfazione, che mi hanno permesso di crescere professionalmente e personalmente. La tranquillitá, l'ottimismo e l'integritá professionale di Ignacio, cosí come la passione e la forza di vita di Mariaje, giunto quasi alla fine di questo percorso, li sento anche un pó miei. Con rigore accademico, entrambi, hanno saputo trasmettermi fiducia e motivazione per poter completare, al meglio delle mie possibilitá, i miei studi di dottorato. Grazie di cuore! Ringrazio, inoltre, Consuelo Huerta della disponibilitá. Il suo aiuto é stato fondamentale per completare la campagna sperimentale nel laboratorio di prove meccaniche del dipartimento di ingegneria meccanica.Allo stesso modo non posso dimenticare i ringraziamenti a Santiago per la relazione professionale e personale che, in svariati anni di collaborazione, attraverso AIRBUS, abbiamo saputo costruire. Momenti di pressione e duro lavoro sempre ricompensati dal conseguimento di ottimi risultati. Qualche anno fa, insieme, siamo riusciti a sviluppare un metodo per la dinamica strutturale non lineare che ha ispirato un capitolo di questa tesi.Non posso nascondere che il cammino é stato lungo.Quando cominciai, mia figlia, Nora, era una bimba che potevo ancora portare in braccio, oggi é giá un' adolescente. Mio figlio, Elía, arrivato nel corso di questi ultimi anni , ci ha regalato una nuova energia e, tra meno di due mesi, compirá tre anni.Ringrazio la mia compagna di vita, Vicky, che allevia sempre i momenti di difficoltá con i suoi deliziosi piatti di cucina messicana. Spesso é stata in grado di regalarmi la tranquillitá di cui avevo bisogno per concentrarmi negli studi.Sono loro a dare un senso alla mia "ricerca della felicitá" e che, ogni giorno, mi motivano a costruire, insieme, una vita piena. I miei genitori, Elio e Lia, sono la vera ragione per cui oggi posso completare questo lavoro di tesi. Mi hanno sempre dato f...

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Application of efficient surrogate modeling to aeroelastic analyses of an aircraft wing

Cited by 14 publications

References 9 publications

On a Novel Approximate Solution to the Inhomogeneous Euler–Bernoulli Equation with an Application to Aeroelastics

A sample-based approach to estimate the dynamic loads of components with nonlinear uncertain interfaces

A Kriging Based Corrected Potential Flow ROM for Gust Load Calculations

Uncertainty Quantification and Global Sensitivity Analysis in Computational Mechanics

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