1. Airframe Structural Modeling and Design Optimization
Ramana V. Grandhi
Distinguished Professor
Department of Mechanical and Materials Engineering
Wright State University

2. VIM/ITRI Relevance
Computational Mechanics is a field of study in which numerical tools are developed for predicting the multi-physics behavior, without actually conducting physical experiments
Study the behavior of
-- materials
-- environmental effects
-- strength/service life
-- signature, radar cross-section
-- etc.
Experiments are conducted mainly for validation and verification

3. Modeling of individual components
Vertical Tail
Fuselage
Missile
Elevator
Nose
Wing

4. Simulation Based Design
Physical Modeling
Simulations
Cost Functions Design Variables Performance Limits
Design Optimization
Forging Extrusion Rolling Sheet Drawing
Manufacturing Schemes
Simulations
Database Generation
Experiments
Rapid Access/Decision Making

5. Create a Parametric definition,
Airframe Design
Create a Parametric definition,
Structural Model
Generate a Finite Element Model of the structure
Perform a Finite Element Analysis
Optimize the design for improved performance and reliability

6. Structural model
Tip chord
Leading edge
Trailing Edge
Root chord

7. Simulation Based Design - Goals
Study the complex multi-physics behavior of the warfighter at hypersonic speeds and in combat environment
Study the behavior of shocks in transonic region due to flow non-linearities – vehicle response and control
Develop high fidelity models for accurate performance measures
Analyze wing structures with attached missiles.
Reduce the modern vehicle development costs by performing simulations rather than costly physical experiments.
--quickly and accurately analyze anything we can imagine

8. Development Challenges
High fidelity simulation of integrated system behavior
-- structures/aerodynamics/control/signature/plasma
Design of lightweight high performance affordable vehicles
Increase the structural safety, reliability and predictability
Design critical components such as wing structures by including non-linear behavior models.
Facilitate simulation of large-scale airframe structures in interdisciplinary design environment.
Develop analysis procedures which are reliable for reaching the goal of “certification by analysis” instead of expensive trial-and-error component test procedures.

9. Material Characteristics
Exceptional strength and stiffness are essential features of airframe parts.
Low airframe weight boosts aircraft performance in pivotal areas, such as, range, payload, acceleration, and turn-rate.
Advanced composite materials and high temperature materials offer reduced life-cycle costs – but manufacturability challenges

10. Generating a Finite Element Model
Finite element model is a discretized representation of a continuum into several elements.
where is the elemental stiffness matrix
is the elemental displacement matrix
is the elemental load matrix
Quadrilateral element
Triangular element θ

11. Finite Element Analysis
Equations describing the behavior of the individual elements are joined into an extremely large set of equations that describe the behavior of the whole system
where assembled stiffness matrix
assembled displacement matrix
assembled load matrix
Finite Element model is used to study deflection, stress, strain, vibration, and buckling behavior in structural analysis
Assembly of finite elements

12. Finite Element Analysis (FEA)
It is one of the techniques to study the behavior of an Airframe structure by performing:
Stress Analysis
Frequency Analysis
Buckling Analysis
Flutter Analysis
Missiles and their influence
Multidisciplinary design Optimization

13. Stress Analysis
A structure can be subjected to air loads, pressure loads, thermal loads, and dynamic loads from shock or random vibration excitation and the airframe responses can be analyzed using FEA techniques.
FEA takes into account any combination of these loads.
A detailed finite element analysis, shows the stress distribution on a F -16 aircraft wing.

14. Forces acting on the wing
Leading edge
Tip chord
Trailing Edge
Root chord

15. Stress distributions along the wing
Minimum Stress at tip chord
Maximum Stress at root chord

16. Finite Element Analysis (FEA)
It is one of the techniques to study the behavior of an Airframe structure by performing:
Stress Analysis
Frequency Analysis
Buckling Analysis
Flutter Analysis
Missiles and their influence
Multidisciplinary design Optimization

17. Frequency Analysis
The dynamic response of a structure which is subjected to time varying forces can be predicted using finite element analysis.
Frequency Analysis is performed to determine the eigenvalues (resonant frequencies) and mode shapes (eigenvectors) of the structure. An eigenvalue problem is represented as:
where is an eigenvalue (natural frequencies)
is an eigenvector (mode shapes)
The model can be subjected to transient dynamic loads and/or displacements to determine the time histories of nodal displacements, velocities, accelerations, stresses, and reaction forces.

18. Mode 1: Bending mode (9.73 Hz)
Mode shapes of the Wing
48’’
Shear Elements
Quadrilateral Elements
26.5’’
108’’
Rod Element
Structural model
Mode 1: Bending mode (9.73 Hz)
This shows the structural and aerodynamic model of the wing. The structure is made up of CQUAD4 elements which represents the top and bottom skin. The CQUAD4 element is used with bending stiffness capability. The CSHEAR elements represent the spars and the rib. The CROD represent the posts. There are in all 120 elements. The aerodynamic root chord is 90 inch. tip chord is 48 inch. the semi-span is 108 inch both for structure and aerodynamic model.
There are 400 panels have been used to represent the aerodynamic model. There 20 chordwise panels and 20 spanwise panels.

19. Mode 2: Torsion mode (34.73 Hz)
Wing Mode Shapes
48’’
Shear Elements
Quadrilateral Elements
26.5’’
108’’
Rod Element
Structural model
Mode 2: Torsion mode (34.73 Hz)
This shows the structural and aerodynamic model of the wing. The structure is made up of CQUAD4 elements which represent the top and bottom skin. The CQUAD4 element is used with bending stiffness capability. The CSHEAR elements represent the spars and the rib. The CROD represent the posts. There are in all 120 elements. The aerodynamic root chord is 90 inch. tip chord is 48 inch. the semi-span is 108 inch both for structure and aerodynamic model.
There are 400 panels have been used to represent the aerodynamic model. There 20 chordwise panels and 20 spanwise panels.

20. Fluid- Structure Interaction
Fluid structure interaction plays an important role in predicting the effect of a flow field upon a structure and vice-versa.
This interaction helps in accurately capturing the various aerodynamic effects such as angle of attack/deflections/ shocks. .. . M x + C x
+ Kx = A(t) = Aerodynamic forces
Structure
Flow Field

21. Occurrence of Shocks Wing Model Shock on the wing Tip chord
Root chord
Trailing Edge
Leading edge
Tip chord

22. Shock transmission on the wing

23. Finite Element Analysis (FEA)
It is one of the techniques to study the behavior of an Airframe structure by performing:
Stress Analysis
Frequency Analysis
Buckling Analysis
Flutter Analysis
Missiles and their influence
Multidisciplinary design Optimization

24. Buckling Analysis
Buckling means loss of stability of an equilibrium configuration, without fracture or separation of material.
Buckling mainly occurs in long and slender members that are subjected to compressive loads.
Long Slender member
F = compressive load
Before Buckling
After Buckling

25. Buckling Phenomena in a Sensorcraft
AFRL/VA Sensorcraft Concept
Finite Element Model
Buckling Phenomenon
1562 grid pts
3013 elements
Next

26. Finite Element Analysis (FEA)
It is one of the techniques to study the behavior of an Airframe structure by performing:
Stress Analysis
Frequency Analysis
Buckling Analysis
Flutter Analysis
Missiles and their influence
Multidisciplinary design Optimization

27. Flutter Analysis
Flutter is an aerodynamically induced instability of a wing, tail, or control surface that can result in total structural failure.
Flutter occurs when the frequency of bending and torsional modes coalesce.
It occurs at the natural frequency of the structure.

29. Finite Element Analysis (FEA)
It is one of the techniques to study the behavior of an Airframe structure by performing:
Stress Analysis
Frequency Analysis
Buckling Analysis
Flutter Analysis
Missiles and their influence
Multidisciplinary design Optimization

30. Missiles and their influence
Wing Tip Missile
Under wing Missile

31. Structural dynamic effect
Influence of a Missile
Missile Influence
Structural dynamic effect
Aerodynamic effect
Flutter speed of the wing increases/decreases depending on missile placement.
As the center of gravity moves towards the leading edge the flutter speed increases.
Design optimization is performed to place the missile at an optimal position.
The natural frequency of the wing reduces due to increased mass
This shows that frequency is inversely proportional to mass.

32. Wing Model with Missile at the tip
Structural Model
Mode 1: Bending Mode (3.8 Hz)
Missile
This is a structural and aerodynamic representation of the wing with tip store.
Here, the store has been of the tip chord of the wing. This is one of the cases, which I am trying to demonstrate…I have also done the flutter analysis of wing with tip and 32.5% tip chord. Due to the shortage of time, I am presenting only one case. i.e.,50% tip chord.
The second figure is a combination of structural model superimposed over the aerodynamic model.
The aerodynamic center is 1/4th of the aerodynamic root chord.
Frequency of the wing first mode without a missile : Bending mode (9.73 Hz)

33. Wing Model with Missile at the tip
Structural Model
Mode 2: Torsion mode (7.84 Hz)
Frequency of the wing second mode without a missile : Torsion mode (34.73 Hz)

34. Finite Element Analysis (FEA)
It is one of the techniques to study the behavior of an Airframe structure by performing:
Stress Analysis
Frequency Analysis
Buckling Analysis
Flutter Analysis
Missiles and their influence
Multidisciplinary design Optimization

35. Design Optimization Tools used for optimization are:
Optimization is required for:
Improved performance
High reliability
Manufacturability
Higher strength
Less weight
Tools used for optimization are:
Sensitivity Analysis
Approximation Concepts
Graphical Interactive Design
Conceptual and Preliminary Design
Design with Uncertain and Random Data

36. Sensitivity Analysis
Sensitivity analysis measures the impact of changing a key parameter in system response.
The plot shows that the elements near the root chord are the most sensitive, and change in these element parameters will effect the stress distribution
-3.07E-02
-3.04E-02
-2.37E-02
-1.71E-02
-1.04E-02
-3.35E-03
2.91E-03
9.58E-02
-3.74E-02
-4.37E-02
1.62E-02
Sensitivity analysis plot

37. Optimization of design variables (Thickness)
Optimum Thickness Distribution

38. Simulation Based Design
Physical Modeling
Simulations
Cost functions Design variables Performance limits
Design Optimization
Forging Extrusion Rolling Sheet Drawing
Manufacturing Schemes
Simulations
Database Generation
Experiments
Rapid Access/Decision Making

39. Forging Process

40. Forging Illustration

41. 3-D view of a Mechanical part : Case study

42. Forging Simulation (Peanut Shaped Billet) Top die Billet Bottom die
Conventional approach
(Peanut Shaped Billet)

43. Challenges in Process Simulation
Modeling of forging dies
Collection of material flow-data
Thermal expansion
Heat conductivity
Flow stresses
Appropriate boundary conditions.
Nonlinear material behavior
Optimal forging process parameters
Press velocity
Die and Billet temperature
Die Shape Optimization
Preforming Stages
Preform Shapes
Infinite paths to reach the final shape

44. Optimal Design Objectives
Design for manufacturability
Reduce material waste, i.e. achieve a net shape forging process by optimizing material utilization and scrap minimization.
Eliminate surface defects, i.e. laps and voids.
Eliminate internal defects, i.e. shear cracks and poor microstructure.
Minimize effective strain and strain-rate variance in workpiece.
Design optimal process parameters such as forming rate (die velocity) and initial workpiece and die temperatures.

45. Preform Design Engineering
Preform Design Methods:
Empirical guidelines based on designer’s experience
Computer aided design/geometric mapping
Backward Deformation Optimization Method (BDOM)
Current Design Methods:
Backward tracing method
Numerical optimization method

46. Preform Design of the billet
Trimming the scrap
Reducing the scrap
Section After Die fill

47. Backward Simulation – Preform Design
Optimization Approach

48. Scrap Comparison for different initial billets
Peanut Shape
5 % Scrap
Preform Shape

49. Crankshaft (Ford Motor Company)

50. Crankshaft Forging - Initial Stage
Top Die
Billet
Bottom die

51. Crankshaft undergoing deformation

52. Forging Challenges
Incomplete die fill

53. Database Development & Rapid access
Computational Engineering
Visualize complex dynamics in multi-physics behavior
Understand system response
Visualization
Modeling
Database Development & Rapid access
Visualize product quality (shape, defects)
Identify design limits
High fidelity simulations for certification
Defect detection
Imaging
Simulation
Based
Design
Manufacturing process
Features extraction
Design under competing goals