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