Airframe Structural Modeling and. Design Optimization. Ramana V. Grandhi.
Distinguished Professor. Department of Mechanical and Materials Engineering.
Airframe Structural Modeling and Design 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
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
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-anderror 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.
[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)
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.
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:
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:
[ K ]{x} = λ[ M ]{x} where
λ {x}
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
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
ν = 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
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 • 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 2.37 E-01
0.6
2.03 E-01
0.4
1.68 E-01 1.34 E-01
0.2 0
1.00 E-01 Rib1
Rib2
Rib3
Rib4
Rib5
Rib6
Rib7
Design Variables
Rib8
Rib9
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
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
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.
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
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
