Airframe Structural Modeling and Design...

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

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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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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