Analytic sensitivities for shape optimization in equivalent plate structural wing models

Livne, Eli

doi:10.2514/3.46585

Cited by 24 publications

(12 citation statements)

References 10 publications

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“…By appropriate modifications in the utilised code, new applications of this numerical approach to more realistic orthotropic plate models, such as the ones proposed by Giles (26,27) and Livne (28,29) for modeling with the Ritz analysis generic multipanel planform wing box structures, can be envisaged. In such a way the optimisation of the skins thickness profile throughout the wing surface for true cases of aircraft in a high supersonic flow, and in critical flutter conditions, can be actually carried out.…”

Section: Discussionmentioning

confidence: 99%

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Polynomial series expansion for optimisation of wing plane structures in idealised critical flutter conditions

Tizzi

2005

Aeronaut. j.

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A numerical procedure, which utilises polynomial power series expansions for the optimisation of multipanel wing structures in idealised critical flutter conditions, is introduced and developed. It arises from the Rayleigh-Ritz method and employes trial polynomial describing functions both for the flexural displacement and for the thickness variation over the multipanel surface. An idealised structural plate model, according to the Kirchhoff's theory, together with a linearised supersonic aerodynamic approach, are supposed. The classical Euler-Lagrange optimality criterion, based on variational principles, has been utilised for the optimisation operations, where by imposing the stationary conditions of the Lagrangian functional expression, a nonlinear algebraic equations system is obtained, whose solution is found by an appropriate algorithm. By utilising an iterative process it is possible to reach the reference structure critical conditions, with an optimised thickness distribution throughout the multipanel surface. The final part of the work consists in searching the minimum weight of the multipanel planform wing structure with optimised thickness profile vs the flutter frequency, considered as a variable imput parameter, for fixed flutter speed and equal to the critical one of the reference uniform structure. NOMENCLATURE EYoung's modulus f (a) aerodynamic distributed force over the multipanel structure surface f i trial describing functions of the dimensionless flexural displacement behaviour over the wing plane structure g l t trial describing functions of the nondimensional thickness behaviour over the wing plane structure h wing plate thickness I o second moment of inertial area per unit length of the reference plate structure k ij , k nj stiffness matrix elements k ij (l t3 ) generic components of the stiffness matrix elements k ij * matrix elements which take into account both the structural and the aerodymic forces presence L cantilever length of the wing structure m ij , m nj mass matrix elements m ij (l t ) , m nj (l t ) generic components of the mass matrix elements N whole number of the degrees of freedom N a , N b + 1 numbers of the coefficients and describing functions in the flexural displacement series expansions along the axes x and y, respectively N t whole number of the coefficients and describing functions in the nondimensional thickness series expansion N tx , N ty number of the coefficients and describing functions in the non-dimensional thickness series expansions along axes x and y, respectively N t3 whole number of the coefficients and describing functions in the series expansion of the nondimensional thickness cubic power N t3x , N t3y number of the coefficients and describing functions in the series expansion of the nondimensional thickness cubic power behaviour along the axes x and y, respectively N w whole number of the coefficients and describing functions in the flexural displacement series expansion P(x, y) generic point on the multipanel structure surface q dynamic pre...

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Section: Discussionmentioning

confidence: 99%

“…where the components W l t of W have been introduced and defined in Equations (28) and (29). In view of Equation (17) one obtains:…”

Section: The Main Relationsmentioning

confidence: 99%

Polynomial series expansion for optimisation of wing plane structures in idealised critical flutter conditions

Tizzi

2005

Aeronaut. j.

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“…(8)(9)(10)(11)(12)(13)(14) in terms of the Lagrangian DOFs, which determine the strain and kinetic energy, and consequently the stiffness and mass matrix elements, are shown in a separate paper [14].…”

Section: Ribsmentioning

confidence: 99%

Dynamic Analysis of Three-Dimensional Semimonocoque Wing Structures

Tizzi

2013

Journal of Aircraft

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“…Interesting studies involving equivalent plate models encompass analytical sensitivities computation for shape optimization purposes (Livne, 1994a), probabilistic assessment of the design space of an innovative configuration (Mavris and Hayden, 1997), fuselage modeling (Giles, 1999), damage detection (Krishnamurthy and Mason, 2006), morphing applications (Gern et al, 2002(Gern et al, , 2005Ameri et al, 2008Ameri et al, , 2009) and analysis of a composite wing with a control surface (Na and Shin, 2013).…”

Section: Introductionmentioning

confidence: 99%

Coupling equivalent plate and beam models at conceptual design level

Riccobene

Ricci

2015

Aircraft Eng & Aerospace Tech

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Purpose -The purpose of this paper is to present a formulation that couples equivalent plate and beam models for aircraft structures analysis, suitable in conceptual design in which fast model generation and efficient analysis capability are required. Design/methodology/approach -Assembling the complete model with common techniques such as Lagrange multipliers or penalty function method would require a solver capable of handling the combined set of linear equation. The alternative approach proposed here is based on a static reduction of the beam model at specified connection points and the subsequent "embedding" into the equivalent plate model using a coordinate transformation, translating physical dfs in Ritz coordinates, i.e. polynomial coefficients. Displacements and forces on beam elements are recovered with the inverse transformation once the solution is computed. Findings -An aeroelastic trim analysis on a Transonic CRuiser (TCR) civil aircraft conceptual model validates the hybrid model: as the TCR features a slender flexible fuselage and a wide root chord wing, the capability to reduce the beam model for the fuselage at more than one connection point improved aeroelastic corrections to steady longitudinal aerodynamic derivatives. Originality/value -Although the equivalent model proposed is simpler than others found in literature, it offers automatic mesh generation capabilities, and it is fully integrated into an aeroelastic framework. The hybrid model represents an enhancement allowing both dynamical and static analyses. NeoCASS (Cavagna et al., 2011a) is a suite of modules that combines state of the art computational, analytical and semi-empirical methods to tackle all the aspects of the aero- NeoCASS environment Conceptual design level

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Analytic sensitivities for shape optimization in equivalent plate structural wing models

Cited by 24 publications

References 10 publications

Polynomial series expansion for optimisation of wing plane structures in idealised critical flutter conditions

Polynomial series expansion for optimisation of wing plane structures in idealised critical flutter conditions

Dynamic Analysis of Three-Dimensional Semimonocoque Wing Structures

Coupling equivalent plate and beam models at conceptual design level

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