Transcript Document

Airframe Structural Modeling and
Design Optimization
Ramana V. Grandhi
Distinguished Professor
Department of Mechanical and Materials Engineering
Wright State University
VIM/ITRI Relevance
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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
Modeling of individual components
Vertical Tail
Fuselage
Missile
Elevator
Nose
Wing
Simulation Based Design
Physical Modeling
Simulations
Design Optimization
Manufacturing Schemes
Database Generation
Rapid Access/Decision Making
Cost Functions
Design Variables
Performance Limits
Forging
Extrusion
Rolling
Sheet Drawing
Simulations
Experiments
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
Structural model
Tip chord
Leading edge
Trailing Edge
Root chord
Simulation Based Design - Goals
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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
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Develop high fidelity models for accurate performance measures
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Analyze wing structures with attached missiles.
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Reduce the modern vehicle development costs by performing
simulations rather than costly physical experiments.
--quickly and accurately analyze anything we can imagine
Development Challenges
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High fidelity simulation of integrated system behavior
-- structures/aerodynamics/control/signature/plasma
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Design of lightweight high performance affordable vehicles
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Increase the structural safety, reliability and predictability
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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-anderror component test procedures.
Material Characteristics
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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
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Finite element model is a discretized representation of a
continuum into several elements.
[k ]{q}  { p}
where
[k ]
is the elemental stiffness matrix
{q} is the elemental displacement matrix
{ p} is the elemental load matrix
Quadrilateral
element
θ
Triangular
element
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
[ K ]{Q}  {P}
where
[K ]
assembled stiffness matrix
{Q}
assembled displacement matrix
{P}
assembled load matrix
Assembly of finite elements
Finite Element model is used to study deflection, stress, strain,
vibration, and buckling behavior in structural analysis
Finite Element Analysis (FEA)
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It is one of the techniques to study the behavior of an
Airframe structure by performing:
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Stress Analysis
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Frequency Analysis
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Buckling Analysis
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Flutter Analysis
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Missiles and their influence
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Multidisciplinary design Optimization
Stress Analysis
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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.
Forces acting on the wing
Leading edge
Tip chord
Trailing Edge
Root chord
Stress distributions along the wing
Minimum Stress at tip chord
Maximum Stress at root chord
Finite Element Analysis (FEA)

It is one of the techniques to study the behavior of an
Airframe structure by performing:
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Stress Analysis
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Frequency Analysis
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Buckling Analysis
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Flutter Analysis
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Missiles and their influence
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Multidisciplinary design Optimization
Frequency Analysis
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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:
[ K ]{x}  [M ]{x}
where

{x}
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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.
Mode shapes of the Wing
Structural model
26.5’’
Shear Elements
108’’
Quadrilateral
Elements
Rod Element
48’’
Mode 1: Bending mode (9.73 Hz)
Wing Mode Shapes
Structural model
26.5’’
Shear Elements
108’’
Quadrilateral
Elements
Rod Element
48’’
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.
..
.
M x + C x + Kx = A(t) = Aerodynamic forces
This interaction helps in accurately capturing the various
aerodynamic effects such as angle of attack/deflections/ shocks.
Structure
Flow Field
Occurrence of Shocks
Shock on the wing
Wing Model
Tip chord
Leading edge
Trailing Edge
Root chord
Shock transmission on the wing
0.06
0.04
0.02
0
-0.02
-0.04
1
0
0.8
0.2
0.6
0.4
0.4
0.6
0.2
0.8
0
1
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 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
Before Buckling
F = compressive load
After Buckling
Buckling Phenomena in a Sensorcraft
AFRL/VA Sensorcraft Concept
Finite Element Model
Buckling Phenomenon
1562 grid pts
3013 elements
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
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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
Missiles and their influence
Wing Tip
Missile
Under wing
Missile
Influence of a Missile
Missile Influence
Structural dynamic effect
The natural frequency of the
wing reduces due to increased
mass
  k /m
This shows that frequency is
inversely proportional to mass.
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.
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
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Optimization is required for:
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Improved performance
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High reliability
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Manufacturability
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Higher strength
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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
• Sensitivity analysis measures the
impact of changing a key parameter
in system response.
1.62E-02
9.58E-02
2.91E-03
-3.35E-03
-1.04E-02
• 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
-1.71E-02
-2.37E-02
-3.04E-02
-3.07E-02
-3.74E-02
-4.37E-02
Sensitivity analysis plot
Optimization of design variables
(Thickness)
1.6
Initial value
Optimum value
1.4
Thickness
1.2
4.23E-01
4.08 E-01
3.74 E-01
7.05E-01
1
7.05 E-01
0.8
2.71 E-01
0.6
2.37 E-01
2.03 E-01
0.4
1.68 E-01
0.2
1.34 E-01
0
1.00 E-01
Rib1
Rib2 Rib3
Rib4 Rib5 Rib6
Rib7 Rib8 Rib9
Design Variables
Optimum Thickness Distribution
Simulation Based Design
Physical Modeling
Simulations
Design Optimization
Manufacturing Schemes
Database Generation
Rapid Access/Decision Making
Cost functions
Design variables
Performance limits
Forging
Extrusion
Rolling
Sheet Drawing
Simulations
Experiments
Forging Process
Forging Illustration
3-D view of a Mechanical part :Case study
Forging Simulation
Top die
Billet
Bottom die
Conventional approach
(Peanut Shaped Billet)
Challenges in Process Simulation
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Modeling of forging dies
Collection of material flow-data
Thermal expansion
Heat conductivity
Flow stresses
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Appropriate boundary conditions.
Nonlinear material behavior
Optimal forging process parameters
Press velocity
Die and Billet temperature
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Die Shape Optimization
Preforming Stages
Preform Shapes
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Infinite paths to reach the final shape
Optimal Design Objectives
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Design for manufacturability
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Reduce material waste, i.e. achieve a net shape forging process by
optimizing material utilization and scrap minimization.
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Eliminate surface defects, i.e. laps and voids.
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Eliminate internal defects, i.e. shear cracks and poor
microstructure.
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Minimize effective strain and strain-rate variance in workpiece.
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Design optimal process parameters such as forming rate (die
velocity) and initial workpiece and die temperatures.
Preform Design Engineering
Preform Design Methods:
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Empirical guidelines based on designer’s experience
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Computer aided design/geometric mapping
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Backward Deformation Optimization Method (BDOM)
Current Design Methods:
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Backward tracing method
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Numerical optimization method
Preform Design of the billet
Trimming the scrap
Reducing the scrap
Section After Die fill
Backward Simulation – Preform Design
Optimization Approach
Scrap Comparison for different
initial billets
12 % Scrap
Peanut Shape
5 % Scrap
Preform Shape
Crankshaft (Ford Motor Company)
Crankshaft Forging - Initial Stage
Top Die
Billet
Bottom die
Crankshaft undergoing deformation
Forging Challenges
Incomplete die fill
Computational Engineering
Visualize complex
dynamics in multiphysics behavior
Understand
system response
Visualization
Visualize product
quality (shape,
defects)
Modeling
Identify design
limits
Database
Development
&
Rapid access
High fidelity simulations
for certification
Defect detection
Imaging
Features
extraction
Manufacturing
process
Simulation
Based
Design
Design under
competing
goals