Multidisciplinary Optimisation V. Selmin

1. Multidisciplinary Optimisation V. Selmin Multidisciplinary Computation and Numerical Simulation

2. Development of a new generation of numerical tools New Trends in Design Drivers: Reduce product development costs and time to market • Single discipline optimisation process • From analysis/verification to design/optimisation • From single to multi-physics • Integration of different disciplines, Interfaces between disciplines, • Concurrent Engineering • Multidisciplinary optimisation process • Integration of different disciplines within the design process, • Optimisation, Concurrent Engineering Multidisciplinary Optimisation

3. Problem Definition Problem Definition Initial Models Database Initial Models Database Multi- Models Generation Multi- Models Generation Multidisciplinary Computations Optimisation Algorithm Multidisciplinary Computations Optimisation Algorithm Objective Constraints Objective Constraints Optimised Models Database Optimised Models Database Multidisciplinary Design Optimisation Mathematical tools, such as sensitivity analysis, modelling methods, and optimisation solvers, provide a mechanism by which working together can be accomplished. Multidisciplinary Optimisation

4. Multidisciplinary Design Optimisation • THAT MEANS • Automatic overall process management and monitoring • Automatic generation of models related to different disciplines • Parametrisation: Design Variables • Capability of executing single discipline solvers on heterogeneous platforms • Efficient and robust optimisation strategy • Definition of objective function and constraints for multidisciplinary problems • Education of engineer (no more thinking single discipline but multi disciplines) • Working Groups or Multidisciplinary Engineers IN THIS PRESENTATION Aerodynamics + Structural Mechanics + Aeroelasticity Multidisciplinary Optimisation

5. Multi Models Generation CFD Grid Generator • unstructured grid generation capability (front advancing method) • multiblock structured grid capability • hybrid grid generation features • Surface grid generation integrated with the actual CAD surfaces • Node movement capability for grid deformation and grid optimisation Grid generation from CAD model Grid generation from MASTER model Multidisciplinary Optimisation

6. Multi Models Generation FEM Generator (wing box) • Structural elements: • shell elements (skin, ribs and spar webs) • rod elements (stringers and stiffners ) • connection elements (RBE3) • Properties: • skin panels thickness • rods section area • composite lay-up (composite materials) • Materials: • isotropic materials (metallic alloys) • anisotropic materials (composite) • Features: • engines (mass, thrust) • wing concentrated masses (fuel, equipments, …) Multidisciplinary Optimisation

7. Multi Models Generation FEM Generator (wing box) • Automatic discretisation of the geometry • Only few information about ribs and stringers spacings • and bays alignment are needed • Different planforms can be easily taken into account Multidisciplinary Optimisation

8. Multi Models Generation FEM Generator (wing box) Multidisciplinary Optimisation

9. Multi Models Generation Loads Transfer • reduced axis approach • only valid for wings of high aspect ratios • interpolation from CFD solution to CSM grid • not accurate for coarse structure representation • association to each structural skin elements of • a portion of the CFD surface grid • complex but accurate • outside wing box contributions Multidisciplinary Optimisation

10. Multi Models Generation Displacement • reduced axis approach • only valid for wings of high aspect ratios • interpolation from CSM grid to CFD grid • association of each CFD surface node to a CSM • skin element • outside wing box nodes treatment Multidisciplinary Optimisation

11. Aerodynamic Solver RANS Solver • Node-centred based Finite Volume spatial discretisation • Blended second- and fourth order dissipation operators • Operates on structured, unstructured and hybrid grids • Time integration based on Multistage Algorithm (5 stages) • Residual averaging and local timestepping • Preconditioning for low Mach number • Pointwise Baldwin-Barth, K-Rt (EARSM) turbulence models • Chimera strategy implementation • ALE implementation for moving grid • Time accurate simulation provided by using Dual Timestepping • Scalar, vector and parallel implementation Multidisciplinary Optimisation

12. Structural Analysis and Optimisation Structural Solver Based essentially on MSC - NASTRAN software • SOL101 for static analysis • SOL200 for structural optimisation based on • DOT optimiser (SQP) • In the case of aeroelastic simulations, use of • own software both for direct and modal • formulations with extraction of the structural • matrices from NASTRAN solutions. Multidisciplinary Optimisation

13. Grid Deformation Spring Analogy Source terms allow to control mesh quality Multidisciplinary Optimisation

14. Gradient based methods • Finite Difference • Adjoint formulation • Automatic differentiation • Evolution strategies • Genetic algorithms • NN & Fuzzy logics • Games theory Disciplines • Aerodynamics (inviscid and viscous flows) • Aeroelasticity • Structural Optimisation Features • Functional minimisation with constraints • Multi-Point Design Capability • Automatic Generation of Models • Automatic Deformation of the CFD Grid • Aeroelastic Deformation of the Geometry • Starting Point Structure Computation • Automatic overall process management and monitoring Shape Optimisation System Multidisciplinary Optimisation

15. Shape Optimisation System Optimisation system • Optimisation Algorithm: • Method of Feasible Directions • Sequential Quadratic Programming • Gradient Based methods • Gradient Computation: • Finite Differences • Adjoint methods • Automatic Differentiation • Features: • Account for constraints within the minimisation • process Multidisciplinary Optimisation

16. CFD CSM Structural Optimisation Application Wing + winglet Design: Definition of a structure for the wing and the winglet. Definition of the jig shape from the knowledge of a flying shape Multidisciplinary Optimisation

17. Structural Optimisation Application Design Operations NB: Sref=780 sqm, MTOW= 535 tons 1. Heavy cruise condition 2. Take-off condition 3. Pull-up: 2.5g pull-up manoeuvre required in the case of an aborted landing at maximum weight 4. Push-down: -1g traffic avoidance manoeuvre at maximum weight Multidisciplinary Optimisation

18. Structural Optimisation Application • Structural Layout • Three-spars central & inboard wing + two-spars outboard wing. • Metallic wing (generic Al alloy) • Wing spars, ribs & skins thickness sized by structural optimisation for pull-up & • push-down manoeuvres. • Available CAD models are related to jig or flying shapes? –> Jig shape. Multidisciplinary Optimisation

19. Structural Optimisation Application • Structural optimisation • Objective function: Minimisation of Mass • Parameterisation: upper skin thickness, lower skin thickness, wing spars thickness, • ribs thickness. (272 design variables) • Sizing conditions: Pull-up (2.5 g) & push-down (-1 g) manoeuvres. • Constraints: metallic wing (Al), maximum stresses, buckling, maximum tip rotation less • than 5°, maximum tip deflection less than 4 m. • Results: M=31430 kg, max. tip rotation= 4.5°, max. tip deflection= 3.64 m. Multidisciplinary Optimisation

20. Structural Optimisation Application Skin thickness Multidisciplinary Optimisation

21. Structural Optimisation Application • Jig shape identification process • Assumption: flying shape model accounts only for twist effects • Aerodynamic conditions: M=0.85, Cl=0.494. • Models: Structural model and grid related to flying shape. • 1- Starting point: Jig shape approximation from a reverse aeroelastic computation (-F) • 2- Direct aeroelastic computation from the jig shape approximation (--> test shape) • 3- Comparison between jig shape and test shape. • To be in perfect equilibrium the deviations from the flying shape must be equal but • with opposite signs. • 4- Correction of the jig shape. • Add to the previous jig shape an average of the deviations computed from the • previous step • 5- Continue the process (go to step 2) until the correction is zero (< ε) Multidisciplinary Optimisation

22. Structural Optimisation Application Multidisciplinary Optimisation

23. Structural Optimisation Application Aero-elastic effects: M=0.85, z=10065 m Multidisciplinary Optimisation

24. Multi-spars layout Details at the wing-winglet junction Metallic: 860 kg Composite: 460 Kg Structural Optimisation Application • Structural Layout • Multi-spars layout. • Metallic/composite winglet. • Winglet spars, ribs & skins thickness sized by structural optimisation for pull-up & • push-down manoeuvres. Wing structure assume to be frozen (< 0.95 semi-span). • Constraints on maximum stresses, buckling, maximum tip rotation (< 2.5°) & • maximum tip deflection (< 0.2 m). Mass minimisation Multidisciplinary Optimisation

25. Multidisciplinary Design Optimisation Application Multidisciplinary Optimisation

26. Multidisciplinary Design Optimisation Application Design Operations 1. Cruise conditions 2. Pull-up: 2.5g pull-up manoeuvre required in the case of an aborted landing at maximum weight 3. Push-down: -1g traffic avoidance manoeuvre at maximum weight Multidisciplinary Optimisation

27. Multidisciplinary Design Optimisation Application Optimisation Problem Definition Objective function OBJ= (Cd-Cd*) [in drag counts] + 16.0 (Mass-Mass*) [in tons] Constraints 1. Optimisation of Drag in Cruise Conditions 2. Modification of the Jig Shape --> Computation of Static Aeroelastic Deformation 3. Constraint on the lift coefficient (> 0.996 Cl*) 4. Constraint on the Pitch Moment (variation of less than 1% allowed) 5. Constraint on the fuel volume (> 11250 l t) 6. Maximum Tip Deflection in Manoeuvre less than 1 Meter. 7. Maximum Tip Rotation in Manoeuvre less than 3°. 8. Maximum Stresses below Material Allowables. 9. Buckling not allowed. Models • Wing Alone Geometry • Wing Box StructuralModel Multidisciplinary Optimisation

28. Design Variables & Hierarchical Approach Design Variables related to the Wing Structure: Skin, ribs and spar webs thicknesses. Spar caps and stiffners cross-section areas Design Variables related to the Wing Shape: 1. First level: Thickness distribution (spanwise): Th Planform parameters: Sw,AR,Srf,TR,… 2. Second level: Thickness location (spanwise): Xth Twist distribution (spanwise): Tw 3. Third level: Camberline perturbation (chordwise) defining parameters Other thickness distribution (chordwise) defining parameters Optimisation approach: Shape optimiser linked to aerodynamic and aeroelastic analysis and structural optimisation Multidisciplinary Optimisation

29. Starting Point Structural Layout Layout of the structure in equilibrium with the aerodynamic loads evaluated at wing box sizing conditions (in general critical manoeuvres). Needed in order to start the optimisation process if wing structure not available. Multidisciplinary Optimisation

30. Cruise condition Push-down manoeuvre Pull-up manoeuvre Starting Point Structural Layout Aerodynamic Conditions Multidisciplinary Optimisation

31. Starting Point Structural Layout Normal -Y Stresses without buckling constraint: s* = -2.37 E+06 with buckling constraint: s* = -13.9E+06 Multidisciplinary Optimisation

32. Starting Point Structural Layout Thickness Distribution without buckling constraint with buckling constraint Multidisciplinary Optimisation

33. Cruise condition Starting Point Structural Layout Structural mass history Multidisciplinary Optimisation

34. Pull-up manoeuvre Push-down manoeuvre Starting Point Structural Layout Multidisciplinary Optimisation

35. Angle of attack • Sweep Angle • Root thickness • Inboard thickness • Crank thickness • Tip thickness Multidisciplinary Design Optimisation Design Variables • Skin thickness • Ribs thickness • Spars thickness Multidisciplinary Optimisation

36. Multidisciplinary Design Optimisation Objective function and constraints Multidisciplinary Optimisation

37. Multidisciplinary Design Optimisation Design Variables History Multidisciplinary Optimisation

38. Multidisciplinary Design Optimisation Cp distribution: MDO Multidisciplinary Optimisation

39. Multidisciplinary Design Optimisation Cp distribution: Aero Multidisciplinary Optimisation

40. Upper side Upper side Lower side Lower side Initial shape Optimised shape Multidisciplinary Design Optimisation Skins Thickness Multidisciplinary Optimisation

41. Multidisciplinary Design Optimisation Ribs Thickness Initial shape Final shape Multidisciplinary Optimisation

42. Multidisciplinary Design Optimisation Spars Thickness Initial shape Final shape Multidisciplinary Optimisation

43. Involvement of large intellectual, human and financial resources Education Think on a multidisciplinary basis Multidisciplinary Design Optimisation • Methods • Automatic overall process management and monitoring • Automatic generation of models related to different disciplines • Ensure adequate accuracy of interfaces between disciplines • Efficient and robust analysis & optimisation strategies • Genuine treatment of constraints • Needs • Greater collaboration & integration between pure mathematics, applied mathematics and • engineering sciences (New good ideas) • Data/methods for the verification & validation of tools/strategies • Spread/enforce MDO philosophy within Companies & Industry Multidisciplinary Optimisation