Prof. P. M. Mujumdar, Prof. K. Sudhakar H. C. Ajmera, S. N. Abhyankar, M. Bhatia

1. WingOpt - An MDO 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 Aeroelastic optimization Concurrent aerodynamic shape and structural sizing optimization of a/c wing Realistic MDO problem Aims and Objectives

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

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

5. 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) Design variable linking Features of WingOpt

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

7. 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

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

9. Load Case 1 (max. speed) Altitude = 25000 ft Mach no.= 0.8097 (*1.4) ‘g’ pull = 2.5 Aircraft weight = Wto Load Case 2 (max. range) Altitude = 35000 ft Mach no.= 0.7286 ‘g’ pull = 1 Aircraft weight = Wto Test Problem

10. Constraints Stress – LC 1 fuel volume – LC 1 MDD – LC 1 Range – LC 2 Take-off distance Sectional Cl – LC 1 Test Problem - S A

11. Structural Optimization (with and w/o aeroelasticity) Aerodynamic Optimization Simultaneous structural and aerodynamic optimization without aeroelasticity Simultaneous structural and aerodynamic optimization with aeroelasticity (6 MDO architectures) Test Problem

12. Test Cases

13. Results

14. Results

15. Software for MDO of wing was developed Simultaneous structural and aerodynamic optimization Focused around aeroelasticity Handles internal loop instability MDO Architectures implemented Summary

16. Further Testing of IDF Additional constraints Buckling Aileron control efficiency Extension to full AAO Future Work

17. Thank You

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

20. 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

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

22. 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

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

24. 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

25. 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

26. 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

27. 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

28. 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

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

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

31. 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

32. 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

33. 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

34. 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

35. 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

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

37. 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

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

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

40. 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

41. 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

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

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

44. 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)

45. 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

46. FEM within the optimization cycle Batch mode Automatic generation Mesh Input deck for MSC/NASTRAN Extracting stresses & displacements Need for MSC/NASTRAN Interface Code

47. Flowchart of the MSC/NASTRAN Interface Code

48. Meshing - 1

49. Meshing - 2 Skins – CQuad4 shell element

50. Meshing - 3 Rib/Spar web – CQuad4 shell element