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Airframe Structural Modeling andDesign Optimization
Ramana V. Grandhi
Distinguished Professor
Department of Mechanical and Materials Engineering
Wright State University
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
Nose
Missile
Fuselage
Vertical Tail
Wing
Elevator
Modeling of individual components
Physical Modeling
Design OptimizationCost Functions Design Variables Performance Limits
Manufacturing Schemes
Simulations
Forging Extrusion Rolling Sheet Drawing
Simulation Based Design
Database GenerationSimulations
Experiments
Rapid Access/Decision Making
Optimize the design for improved performance and reliability
Perform a Finite Element Analysis
Generate a Finite Element Model of the structure
Airframe Design
Create a Parametric definition,
Structural Model
Structural model
Root chord
Trailing Edge
Leading edge
Tip chord
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
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.
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
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
}{}]{[ pqk =
][k
}{q}{p
Quadrilateral element
Triangular element
θ
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
}{}]{[ PQK =
][K}{Q
}{P
Finite Element Analysis
Assembly of finite elements
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
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.
Root chord
Leading edge
Trailing Edge
Tip chord
Forces acting on the wing
Stress distributions along the wing
Maximum Stress at root chord
Minimum Stress at tip chord
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
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.
}]{[}]{[ xMxK λ=
λ}{x
48’’
Shear Elements
Quadrilateral Elements
26.5’’
108’
’
Rod Element
Structural model
Mode shapes of the Wing
Mode 1: Bending mode (9.73 Hz)
48’’
Shear Elements
Quadrilateral Elements
26.5’’
108’
’
Rod Element
Structural model
Wing Mode Shapes
Mode 2: Torsion mode (34.73 Hz)
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.
+ Kx = A(t) = Aerodynamic forcesxCxM +...
Flow FieldStructure
Occurrence of Shocks
Root chord
Trailing Edge
Leading edge
Tip chord
Wing ModelShock on the wing
00.2
0.40.6
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Shock transmission on the wing
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
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.
Buckling Analysis
F = compressive load
Before Buckling After Buckling
Long Slender member
Buckling Phenomena in a Sensorcraft
1562 grid pts3013 elements
AFRL/VA Sensorcraft Concept
Finite Element Model Buckling Phenomenon
Next
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
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.
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
Wing Tip Missile
Under wing Missile
Missiles and their influence
Missile Influence
Structural dynamic effect Aerodynamic effect
The natural frequency of the wing reduces due to increased mass
This shows that frequency is inversely proportional to mass.
mk /=ν
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.
Influence of a Missile
Wing Model with Missile at the tip
Structural Model Mode 1: Bending Mode (3.8 Hz)
Missile
Frequency of the wing first mode without a missile : Bending mode (9.73 Hz)
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)
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
Design Optimization
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
Sensitivity Analysis
-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 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
Sensitivity analysis plot
4.23E-01
3.74 E-017.05E-01
7.05 E-01
2.71 E-01
2.37 E-01
2.03 E-01
1.68 E-01
1.34 E-01
1.00 E-01
4.08 E-01
0
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1
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Rib1 Rib2 Rib3 Rib4 Rib5 Rib6 Rib7 Rib8 Rib9
Initial valueOptimum value
Thic
knes
s
Optimum Thickness DistributionDesign Variables
Optimization of design variables(Thickness)
Physical Modeling
Design OptimizationCost functions Design variables Performance limits
Manufacturing Schemes
Simulations
Forging Extrusion Rolling Sheet Drawing
Simulation Based Design
Database GenerationSimulations
Experiments
Rapid Access/Decision Making
Forging Process
Forging Illustration
3-D view of a Mechanical part :Case study
Conventional approach
(Peanut Shaped Billet)
Forging Simulation
Top die
Bottom die
Billet
Modeling of forging diesCollection of material flow-data
Thermal expansionHeat conductivityFlow stresses
Appropriate boundary conditions.Nonlinear material behaviorOptimal forging process parameters
Press velocityDie and Billet temperature
Die Shape OptimizationPreforming StagesPreform Shapes
Infinite paths to reach the final shape
Challenges in Process Simulation
Optimal Design ObjectivesOptimal 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.
Preform Design EngineeringPreform 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
Trimming the scrap
Preform Design of the billet
Section After Die fill
Reducing the scrap
Optimization Approach
Backward Simulation – Preform Design
Scrap Comparison for differentinitial billets
Peanut Shape
Preform Shape
12 % Scrap
5 % Scrap
Crankshaft (Ford Motor Company)
Crankshaft Forging - Initial Stage
Top Die
Billet
Bottom die
Crankshaft undergoing deformation
Forging Challenges
Incomplete die fill
Modeling
Imaging
Visualization
SimulationBased Design
Manufacturing process Design under
competing goals
Computational Engineering
Visualize product quality (shape, defects)
Visualize complex dynamics in multi-physics behavior
Identify design limits
Understand system response
High fidelity simulations for certificationDefect detection
Features extraction
Database Development
& Rapid access
