WingOpt - An MDO Research Tool for Concurrent Aerodynamic Shape and Structural Sizing Optimization of Flexible Aircraf

1. WingOpt - An MDO Research Tool for Concurrent Aerodynamic Shape and Structural Sizing Optimization of Flexible Aircraft Wings. Prof. P. M. Mujumdar, Prof. K. Sudhakar H. C. Ajmera, S. N. Abhyankar, M. Bhatia Dept. of Aerospace Engineering, IIT Bombay

2. Develop a software for MDO of aircraft wing - Study issues of integrating MDA for formal design optimization Aeroelastic optimization as an MDO problem - Concurrent aerodynamic shape and structural sizing optimization of a/c wing Realistic MDO problem - Showcase a reasonably complex aircraft design optimization problem with high fidelity analysis Aims and Objectives

3. Study different MDO architectures – reformulations of the optimization problem Influence of fidelity level of structural analysis Study computational performance Benchmark problem for MDO framework development Aims and Objectives

4. Design Drivers/Constraints for the WingOpt Architechture • Definition of a meaningful overall design problem based on available analysis and optimization capability • Limited disciplines considered: Geometry, Aerodynamics, Structures, Trim/Maneuver • Aeroelasticity as basis for coupling disciplines • Software integration within confines of high level programming languages (FORTRAN/C) through students • At least one discipline taken to its highest fidelity (structures) • Emulate some elements of a general purpose framework

5. Identify array of all variables/functions associated with the system analysis Identify all possible candidates for design variables/constraints Partition variables database to fixed and design parameters. Tag user codes to all variables/functions Define subset optimization problem through tags Create location look-up tables for selected subset variables/constraints Variables & Function Database

6. Types of Optimization Problems Structural sizing optimization Aerodynamic shape optimization Simultaneous aerodynamic and structural optimization Features of WingOpt

7. Flexibility Easy and quick setup of the design problem Aeroelastic module can be switched ON/OFF Selection of structural analysis (FEM / EPM) Selection of Optimizer (FFSQP / NPSOL) Selection of MDO Architecture (MDF / IDF) and their variants Design variable linking Load Case specification. Variables/design constraints attached to load cases Features of WingOpt

8. Software modules integrated • Gradient based optimizers • FFSQP; NPSOL (Source codes) • Aerodynamic Analyses • VLM (source code) • Semiempirical (Raymer/Roskam) (source code) • Structural Analyses • Equivalent Plate Method (source code) • Finite Element Method (commercial licensed software (executable)) • Source code integration with minimal modifications to code through I/O files

9. Architecture of WingOpt I/P processor Problem Setup Optimizer History I/P MDO Control Analysis Block O/P O/P processor INTERFACE

10. Baseline aircraft  Boeing 737-200 Objective  min. load carrying wing-box structural weight No. of span-wise stations  6 No. of intermediate spars (FEM)  2 Aerodynamic meshing  12*30 panels Optimizer  FFSQP Test Problem

11. Design Variables Skin thicknesses - S Wing Loading Aspect ratio Sweep back angle t/croot Test Problem A

12. Test Problem

13. Constraints Stress – LC 1 fuel volume MDD – LC 3 Range – LC 2 Take-off distance Sectional Cl – LC 1 Test Problem - Structural - Geometric Aerodynamic

14. Test Cases

15. Results

16. Results

17. Results

18. Aeroelasticity analysis leads to significant weight reduction Simultaneous structural and aerodynamic optimization significant impact on design IDF-AAO failed MDF1 loop stability not related to physical divergence Stability information in IDF and IDF-AAO cannot be captured Conclusions

19. In MDF1 time taken in aerodynamic very high compared to structures MDF1 most efficient, iteration convergence is fastest, however not fully reliable MDF2 and MDF-AAO are very robust and took almost same computational time Direct method much efficient than indirect method Conclusions

20. Simultaneous optimization are very time consuming With non-linearity (more time consuming analysis) IDF and AAO might be more benificial Maintaining history saves significant computational time Conclusions

21. Software for MDO of wing was developed Simultaneous structural and aerodynamic optimization Focused around aeroelasticity Handles internal loop instability MDO Architectures formulated and implemented Methods for accelerating convergence formulated and implement Multiple load case implemented User interface improved Summary

22. IDF and IDF-AAO for FEM Additional features Buckling composites Aileron control efficiency Multilevel MDO Architectures Non linear problem Parallel computation High fidelity aerodynamics analysis Future Work

23. Aerodynamic Geometry Structural Geometry Design Variables Load Case Functions Computed Optimization Problem Setup Examples Problem Formulation

24. Aerodynamic Geometry • Planform • Geometric Pre-twist • Camber • Wing t/c • single sweep, tapered wing • divided into stations • S, AR, λ, Λ y Λ AR = b2/S λ = citp/croot croot citp Wing stations b/2 x

25. Aerodynamic Geometry • Planform • Geometric Pre-twist • Camber • Wing t/c • constant α' per station • α'i, i = 1, N y x

26. Aerodynamic Geometry • Planform • Geometric Pre-twist • Camber • Wing t/c • formed by two quadratic curves • h/c, d/c Point of max. camber Second curve First curve h d c

27. Aerodynamic Geometry • Planform • Geometric Pre-twist • Camber • Wing t/c • linear variation in wing box-height stations t

28. A A Structural Geometry Cross-section Box height Skin thickness Spar/ribs • symmetric • front, mid & rear boxes • r1, r2 y Structural load carrying wing-box Front box r1 = l1/c r2 = l2/c A A Mid box Rear box l1 l2 c x

29. y A A x Structural Geometry Cross-section Box height Skin thickness Spar/ribs • linear variation in spanwise & chordwise direction • hroot , h'1i , h'2i ; where i = 1, N A A hfront hrear h'1 = hrear /hfront

30. y A A x Structural Geometry Cross-section Box height Skin thickness Spar/ribs • Constant skin thickness per span • tsi , where s = upper/lower • i = 1, N tupper A A tlower

31. y Structural Geometry Cross-section Box height Skin thickness Spar/ribs • modeled as caps • linear area variation along length • Asjki , where s = upper/lower • j = cap no.; k = 1,2; i =1, N A rib Aupper12 A A spar cap x 1 2 intermediate spar rear spar front spar

32. Wing loading Sweep Aspect ratio Taper ratio t/croot Mach number Jig twist* Camber* Skin thickness* Rib/spar position* Rib/spar cap area* t/c variation* wing-box chord-wise size and position Design Variables Aerodynamics Structures * Station-wise variables

33. Altitude (h) Mach number (M) ‘g’ pull (n) Aircraft weight (W) Engine thrust (T) Load Case Definition

34. Aerodynamics Sectional Cl (VLM) Overall CL (VLM) CD (VLM + empirical)) Take-off distance Range (Brueget) Drag divergence Mach number (Semi-empirical) Structural Stresses (σ1 , σ2) Load carrying Structural Weight(Wt) Deformation Function (w(x,y)) Geometric Fuel Volume (Vf) Functions Computed

35. Select objective function Select design variables and set its bound Set values of remaining variables (constant) Define load cases Set Initial Guess Select constraints and corresponding load case Select optimizer, method for structural analysis, aeroelasticity on/off, MDO method. Optimization Problem Set Up

36. Design Case – Example 1 Aerodynamic Structural X S AR λ Λ α'i h/c d/c r1 r2 hroot h'1 h'2i tsi Asjki F Cl CDi CL Vstall Mdd - - Wt W(x,y) Vf - - - σ Structural Sizing Optimization: Baseline Design Objective Desg. Vars. Constraint

37. Design Case – Example 2 Aerodynamic Structural AR X S λ Λ α'i h/c d/c r1 r2 hroot h'1 h'2i Asjki tsi F Cl CDi CL Vstall Mdd - - σ Wt W(x,y) Vf - - - Simultaneous Aerod. & Struc. Optimization Objective Desg. Vars. Constraint

38. FFSQP Feasible Fortran Sequential Quadratic Programming Converts equality constraint to equivalent inequality constraints Get feasible solution first and then optimal solution remaining in feasible domain NPSOL Based on sequential quadratic programming algorithm Converts inequality constraints to equality constraints using additional Lagrange variables Solves a higher dimensional optimization problem Optimizers

39. Why ? All constraints are evaluated at first analysis Optimizer calls analysis for each constraints !! Lot of redundant calculations !! HISTORY BLOCK Keeps tracks of all the design point Maintains records of all constraints at each design point Analysis is called only if design point is not in history database History

40. Keeps track of the design variables which affect AIC matrix Aerodynamic parameter varies  calculate AIC matrix and its inverse History

41. 1 Look-up Table 2 X1 P1 3 Partitioning Logic X2 P2 4 To input processors P3 X3 5 . . . . . . . . . Selected Variables n Interface Block • Design Variables un-scaled • Design Variable Superset updated • Design Variable Superset partitioned • Analysis routines called through MDO control • Required function value returned to optimizer

42. VLM EPM/ FEM Analysis Block Diagram Aerodynamic mesh, M, Pdyn Cl Trim ( L-nW = e ) From MDO Control e {α}rigid+{Dα}str. Aerodynamic pressure To MDO Control Pressure Mapping Structural Loads Structural deflections To MDO Control Deflection Mapping {Dα}str. stresses Structural Mesh, Material spec., non.–aero Loads

43. Panel Method (VLM) Generate mesh Calculate [AIC] Calculate [AIC]-1 {p}=[AIC]-1{a} Calculate total lift, sectional lift and induced drag Aerodynamic Analysis

44. Loads Aerodynamic pressure loads Engine thrust Inertia relief Self weight (wing – weight) Engine weight Fuel weight Structures

45. Self-weight calculated using an in-built module in EPM Engine weight is given as a single point load Fuel weight is given as pressure loads Self-weight is calculated internally as loads by MSC/NASTRAN Engine weight is given as equivalent downward nodal loads and moments on the bottom nodes of a rib Fuel weight is given as pressure loads on top surface of elements of bottom skin Inertia Relief EPM FEM

46. Transfer of panel pressures of entire wing planform to the mid-box as pressure loads as a coefficients of polynomial fit of the pressure loads Transfer of panel pressures on LE and TE surfaces as equivalent point loads and moments on the LE and TE spars Transfer of panel pressures on the mid-box as nodal loads on the FEM mesh using virtual work equivalence Aerodynamic Load Transformation EPM FEM

47. EPM  w(x,y) is Ritz polynomial approx. FEM  w(x,y) is spline interpolation from nodal displacements Deflection Mapping

48. Energy based method Models wing as built up section Applies plate equation from CLPT Strain energy equation: Equivalent Plate Method (EPM)

49. Polynomial representation of geometric parameters Ritz approach to obtain displacement function Boundary condition applied by appropriate choice of displacement function Merit over FEM Reduction in volume of input data Reduction in time for model preparation Computationally light Equivalent Plate Method (EPM)

50. Analysis Block (FEM) Aerodynamic Loads on Quarter Chord points of VLM Panels FEM Nodal Co-ordinates Load Transformation NASTRAN Interface Code Loads Transferred on FEM Nodes Wing Geometry Meshing Parameters Input file for NASTRAN (Auto mesh & data-deck Generation) MSC/ NASTRAN Output file of NASTRAN (File parsing) Max Stresses, Displacements, twist and Wing Structural Mass Nodal displacements Displacement Transformation Panel Angles of Attack