development of a computational method for the …...computational method for the topology...

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www.cranfield.ac.uk

Development of a computational method for the topology optimization of an aircraft wing

Fabio CrescentiPh.D. student

21st November 2017

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§ Introduction and objectives

§ Theoretical background and method

§ Problem formulation and results

§ Conclusions and outlook

Overview

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The wing box general layout of a civil aircraft has not changed significantly over many decades.

§ Shear load à spars (beam-like structure)

§ Aerodynamic shape à skins

§ Local buckling à stingers

§ Skin support, attachment points à ribs

§ Fuel storage à closed volume

Introduction and objectives

The wing box design

Fig. 1: Wing box elements.

sparstringer

rib

cover

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A recent study published by Nasa[1]

considered some parametric a-priori changesin the wing internal structure.

§ -5.6% weight, +13.9% flutter speed,

(layout “q” in fig. 2).

§ No optimization (constantthickness).

[1] Internal Structural Design of the Common Research Model Wing Box for Aeroelastic Tailoring. Jutte, C.V., Stanford, B.K.,Wieseman, C.D. . NASA/TM-2015-218697.

Fig. 2: Variants of the CRM wing box evaluated in [1].

Introduction and objectives

Alternative designs

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1) Use topology optimization to investigate alternative layouts.

§ Identification of trends between the geometry/BCs and the layout.

§ Avoid a-priori modifications (design space).

§ Changes can be local or global.

Introduction and objectives

Objectives

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2) Evaluate the layout performing an aero-structural optimization.

§ Weight reduction for the optimization[2].

§ High-fidelity aero-structural framework[3, 4].

[2] Integrated Global Wing and Local Panel Optimization of Aircraft Wing. Liu, Q., Jrad, M., Mulani, S.B., Kapania, R.K. . AIAA SciTech 2015.

[3] Aerostructural Optimization of the Common Research Model Configuration. Kenway, G.K.W., Martins, J.R.R.A., Kennedy, G.J. . 15th

AIAA/ISSMO Conference, 2014.[4] Multidisciplinary Design Optimization for Aircraft Mass Estimation. Dababneh, O., Ph.D. thesis 2016, Cranfield University.

Introduction and objectives

Objectives

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Topology optimization is a technique used in conjunction with FE analysis to identify the optimal material distribution within a given volume according to the associated boundary conditions.The SIMP* method [5] is an established approach [6] for topology optimization.

§ Large number of design variables (one or more per element):

𝐸 = 𝜌%𝐸&§ Small number of constraints.* Solid Isotropic Material (Microstructure) with Penalization

[5] Generating Optimal Topologies in Structural Design Using a Homogenization Method. Bendsøe, M.P., Kikuchi, N. .Computer Methods in Applied Mechanics and Engineering, Vol 71, pp 197-224, 1988.

[6] A critical review of established methods for structural topology optimization. Rozvany, G.I.N. . Struct. Multidisc. Optim. 2008.

Theoretical background and method

Topology optimization

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Topology optimization has been implemented in several commercial software [7].

§ For this study Altair OptiStruct v 14.0 is used.

§ Single-objective optimization.

§ Handle a variety of objective functions (compliance, volume/mass fraction, frequencies).

§ Take into account manufacturing constraints (Draw direction, Extrusion,…).[7] A survey of structural and multidisciplinary continuum topology optimization: post 2000. Deaton, J.D., Grandhi, R.V. . Struct.

Multidisc. Optim. Vol 49, pp 1-38, 2014.

Theoretical background and method

Software for topology optimization

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In order to introduce changes in the geometry an in-house parametric CAD is used.

§ Parametric geometry: changeaspect ratio and sweep.

§ Aerodynamic loads: panelmethod.

§ Topology Optimization: geometry + BCs.

Theoretical background and method

Parametric framework

ParametricCAD

Aero loadLow-fidelity

Topology Optimization:

OptiStructwing box volume

aero loads

Optimized layout

Fig. 3: Flow chart of the parametric framework.

External shape

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Topology optimization provides the input for the high-fidelity MDO.

Topology Optimization is performed for a fixed aerodynamics. Then the layout isidealized and converted into a parametric model which becomes the input for thenext MDO framework.

Theoretical background and method

Aero-structural optimization

Optimized layout

Elementsidealization

Size Optimization

Aerodynamic Optimization

Fig. 4: Flow chart from Topology Optimization to MDO.

ParametricCAD MDO

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The CRM wing is a research model developed by Nasa [8], representative of a modern single-aisle aircraft (Boeing 777).

[8] Development of Common Research Model for Applied CFD Validation Studies. Vassberg, J.C, DeHaan, M.A., Rivers, S.M., Wahls, R.A. . 26th AIAA, 2008.

Problem formulation

Common Research Model wing

wingspan 58.77 [m]AR 9Taper ratio 0.725Sweep angle (LE) 35 deg

Kink 37% (semispan) Fig. 5: CRM wing box volume.

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The control space, is represented by the CRM wing box volume.

§ Lower and upper surfaces (in red): non-design regions. Discretized with 2D QUAD elements with a thickness property of 2.5 mm.

§ Internal volume (grey): 3D TRIA

elements. (~3 ) 10, elements)

§ Isotropic material properties:

𝐸 = 73𝐺𝑃𝑎, 𝜌 = 2.78 ) 1045𝑡𝑜𝑛/𝑚𝑚;

Problem formulation

Discretization and properties

Fig. 6: Discretization of the CRM wing box.

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The problem is formulated to minimize compliance (elastic strain energy) for a given volume fraction 𝑉=.

min𝐶 = 12 𝒇 + 𝑮 𝑻𝒖

𝒇 + 𝑮 = 𝑲𝒖

𝑉 ≤ 𝑉& ) 𝑉=

The Linear Static Solution is computed.

Problem formulation

complianceload vector self-weight

load vector

total volume

fraction of volume available

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The chord wise pressure distribution has been computed in correspondence of 20 stations along the semi-span.

§ Cruise condition: 𝑀 = 0.85, 𝐶K = 0.52.

§ Linear interpolation along the span-wise

direction.

Problem formulation

Aerodynamic loading

Fig. 7: Pressure distribution computed using the panel method code.

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The engine, landing gear and the secondary structure are all modelled as lumped masses [4].They are attached to the main design volume through rigid elements(RBE2).

The mass of the landing gear has been computed according to the empirical formula in [9]:

𝑊KM = 0.025𝑊NOP + 0.016𝑊NK ≅ 4000𝑘𝑔

[9] Advanced Aircraft Design. Conceptual design, analysis and optimization of civil airplanes. Torenbeek, E. .

Problem formulation

Concentrated loads

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Engine position and data*:

Mass :7800 kgThrust (take off): 360 kN* GE90. Source Wikipedia

Main landing gear

Problem formulation

Engine and landing gear position

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Results

Case of aerodynamic loading

The load case is here represented by the pressure distribution. Case of 𝑉= = 0.5.

[10] Aerostructural Level Set Topology Optimization for a Common Research Model Wing. Dunning, P.D., Stanford, B.K., Kim, H.A.NASA paper, 2017.

Fig. 8: Material distribution for the aerodynamic load.Density values above 0.5

Fig. 9: Sections along the wing span. No ribs.

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Results

Effect of the volume fraction

For the same load case results obtained for two values of volume fraction are compared. 𝑉= = 0.3 and 0.5.

The value of 𝑉=is not known a priori à convergence and global stiffness.

Fig. 11: 𝑉= = 0.3. 38 iterations until convergence. Displacement at the tip 1.204 ) 10V

Fig. 10: 𝑉= = 0.5. 28 iterations until convergence. Displacement at the tip 8.092 ) 10X

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Two new effects have been introduced. The self-weight and the extrusion constraint [10] [11].

[11] Topology Optimization of Aircraft with Non-Conventional Configuration. Toropov, E. J., Thompson, V. V., Gaskell, H. L., Doherty, P. H., J. J. Harris, 8th World Congress of Structural and Multidisciplinary Optimization, June 1-5 2009.[12] Altair OptiStruct version 14.0, User’s Manual.

Results

Extrusion constraint and self-weight

Fig. 12: 𝑉= = 0.3. Introduction of the extrusion constraint.Fig. 13: 𝑉= = 0.5. Effect of the gravity superimposed to the

aerodynamic load.

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The introduction of multiple masses force the material to be redistributed to connect all the attachment points.

Results

Engine and landing gear

Fig. 14: 𝑉= = 0.3. Effect of the landing gear attached mass. Fig. 15: 𝑉= = 0.3. Combined effect of the engine and landing gear masses.

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Results

Multiple attached masses

High-lift mass estimated around 10% ofthe wing mass [9]. This load issuperimposed to the aerodynamic load.

§ Connections appear in presence of multiple attached masses.

§ Averaging method: difference.

Fig. 16: 𝑉= = 0.5. Lumped masses attached to the volume. Averaging method: difference.

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§ I have illustrated the use of a modular framework to perform topology optimization.

§ Results are dominated by a global behaviour, (no local effect).

§ A range for the volume fraction (0.3 ÷ 0.5) have been selected.

§ Each contribution has been evaluated separately in order to select the most effective.

Conclusions and outlook

Conclusions

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§ Implement the pull-up and pull-over manoeuvers for the aerodynamic loads.

§ Change the geometry and introduce composite materials.

§ Multi-objective topology optimization.

§ Evaluate the layout within a high-fidelity aero-structural framework.

Conclusions and outlook

Future works

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Thank you for your attention

Any question?

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§ Parameters:Planform (Aspect ratio, sweep)Number of structural elements and shape

§ MetricsStructural weightStress thresholdAeroelastic modes (natural frequencies and frequencies separation).

Aero-structural optimization

Parameters and metrics

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SIMP is a gradient-based optimization method. Due to the large number of design variables the adjoint variable method is used.

Which optimizer is implemented?OptiStruct choses within a set of four optimizers [11]:1. Method of feasible directions (MFD). Is the default choice.2. Sequential Quadratic Programming (SQP)3. Dual Optimizer (DUAL, DUAL2)4. Large scale optimization algorithm (BIGOPT)

Optimization in OptiStruct

Gradient-based topology optimization