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

Transcription

1 Development of a computational method for the topology optimization of an aircraft wing Fabio Crescenti Ph.D. student 21 st November

2 Overview Introduction and objectives Theoretical background and method Problem formulation and results Conclusions and outlook 2

3 Introduction and objectives The wing box design The wing box general layout of a civil aircraft has not changed significantly over many decades. Shear load à spars (beam-like structure) cover Aerodynamic shape à skins Local buckling à stingers rib Skin support, attachment points à ribs stringer spar Fuel storage à closed volume Fig. 1: Wing box elements. 3

4 Introduction and objectives Alternative designs A recent study published by Nasa [1] considered some parametric a-priori changes in the wing internal structure. -5.6% weight, +13.9% flutter speed, (layout q in fig. 2). No optimization (constant thickness). [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 Fig. 2: Variants of the CRM wing box evaluated in [1]. 4

5 Introduction and objectives Objectives 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. 5

6 Introduction and objectives Objectives 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 [3] Aerostructural Optimization of the Common Research Model Configuration. Kenway, G.K.W., Martins, J.R.R.A., Kennedy, G.J.. 15 th AIAA/ISSMO Conference, [4] Multidisciplinary Design Optimization for Aircraft Mass Estimation. Dababneh, O., Ph.D. thesis 2016, Cranfield University. 6

7 Theoretical background and method Topology optimization 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): Small number of constraints. * Solid Isotropic Material (Microstructure) with Penalization E = ρ % E & [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 , [6] A critical review of established methods for structural topology optimization. Rozvany, G.I.N.. Struct. Multidisc. Optim

8 Theoretical background and method Software for topology optimization 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 Deaton, J.D., Grandhi, R.V.. Struct. Multidisc. Optim. Vol 49, pp 1-38,

9 Theoretical background and method Parametric framework In order to introduce changes in the geometry an in-house parametric CAD is used. Parametric geometry: change aspect ratio and sweep. Aerodynamic loads: panel method. Parametric CAD External shape wing box volume Aero load Low-fidelity aero loads Topology Optimization: OptiStruct Topology Optimization: geometry + BCs. Optimized layout Fig. 3: Flow chart of the parametric framework. 9

10 Theoretical background and method Aero-structural optimization Topology optimization provides the input for the high-fidelity MDO. Size Optimization Optimized layout Elements idealization Parametric CAD MDO Aerodynamic Optimization Fig. 4: Flow chart from Topology Optimization to MDO. Topology Optimization is performed for a fixed aerodynamics. Then the layout is idealized and converted into a parametric model which becomes the input for the next MDO framework. 10

11 Problem formulation Common Research Model wing The CRM wing is a research model developed by Nasa [8], representative of a modern single-aisle aircraft (Boeing 777). wingspan [m] AR 9 Taper ratio Sweep angle (LE) 35 deg Kink 37% (semispan) Fig. 5: CRM wing box volume. [8] Development of Common Research Model for Applied CFD Validation Studies. Vassberg, J.C, DeHaan, M.A., Rivers, S.M., Wahls, R.A.. 26 th AIAA,

12 Problem formulation Discretization and properties 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 = 73 GPa, ρ = 2.78 ) ton/mm ; Fig. 6: Discretization of the CRM wing box. 12

13 Problem formulation The problem is formulated to minimize compliance (elastic strain energy) for a given volume fraction V =. compliance load vector self-weight load vector min C = 1 2 f + G T u f + G = Ku V V & ) V = fraction of volume available total volume The Linear Static Solution is computed. 13

14 Problem formulation Aerodynamic loading The chord wise pressure distribution has been computed in correspondence of 20 stations along the semi-span. Cruise condition: M = 0.85, C K = Linear interpolation along the span-wise direction. Fig. 7: Pressure distribution computed using the panel method code. 14

15 Problem formulation Concentrated loads 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] : W KM = 0.025W NOP W NK 4000 kg [9] Advanced Aircraft Design. Conceptual design, analysis and optimization of civil airplanes. Torenbeek, E.. 15

16 Problem formulation Engine and landing gear position Engine position and data*: Main landing gear Mass :7800 kg Thrust (take off): 360 kn * GE90. Source Wikipedia 16

17 Results Case of aerodynamic loading The load case is here represented by the pressure distribution. Case of V = = 0.5. Fig. 8: Material distribution for the aerodynamic load. Density values above 0.5 Fig. 9: Sections along the wing span. No ribs. [10] Aerostructural Level Set Topology Optimization for a Common Research Model Wing. Dunning, P.D., Stanford, B.K., Kim, H.A. NASA paper,

18 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. 10: V = = iterations until convergence. Displacement at the tip ) 10 X Fig. 11: V = = iterations until convergence. Displacement at the tip ) 10 V 18

19 Results Extrusion constraint and self-weight Two new effects have been introduced. The self-weight and the extrusion constraint [10] [11]. Fig. 12: V = = 0.3. Introduction of the extrusion constraint. [11] Topology Optimization of Aircraft with Non-Conventional Configuration. Toropov, E. J., Thompson, V. V., Gaskell, H. L., Doherty, P. H., J. J. Harris, 8 th World Congress of Structural and Multidisciplinary Optimization, June [12] Altair OptiStruct version 14.0, User s Manual. 19 Fig. 13: V = = 0.5. Effect of the gravity superimposed to the aerodynamic load.

20 Results Engine and landing gear The introduction of multiple masses force the material to be redistributed to connect all the attachment points. 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. 20

21 Results Multiple attached masses High-lift mass estimated around 10% of the wing mass [9]. This load is superimposed 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. 21

22 Conclusions and outlook Conclusions 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 ( ) have been selected. Each contribution has been evaluated separately in order to select the most effective. 22

23 Conclusions and outlook Future works 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. 23

24 Thank you for your attention Any question? 24

25 Aero-structural optimization Parameters and metrics Parameters: Planform (Aspect ratio, sweep) Number of structural elements and shape Metrics Structural weight Stress threshold Aeroelastic modes (natural frequencies and frequencies separation). 25

26 Optimization in OptiStruct Gradient-based topology optimization 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) 26