Combined Global / Local Variability and Uncertainty in the ...depts.washington.edu/amtas/events/jams_05may/Livne-JAMS.pdf · joints/attachments stiffness and damping, actuator nonlinearities

The Joint Advanced Materials and Structures Center of Excellence

Combined Global / Local Variability and Uncertainty Combined Global / Local Variability and Uncertainty in the in the AeroservoelasticityAeroservoelasticity of Composite Aircraftof Composite Aircraft

Eli LivneEli LivneDepartment of Aeronautics and AstronauticsDepartment of Aeronautics and Astronautics

May 24,2005 2The Joint Advanced Materials and Structures Center of Excellence

Aeroservoelastic Global / Local Variability and Uncertainty in Composite Aircraft

Variation (over time) of local structural characteristics might lead to a major impact on the global aeroservoelastic integrity of flight vehicle components.Sources in composite structures: damage, delamination, environmental effects, joint/attachment changes, etc.

Nonlinear structural behavior: delaminated composite components, changes in joints/attachments stiffness and damping, actuator nonlinearities nonlinear aeroelastic behavior such as Limit Cycle Oscillations (LCO) of control surfaces with stability, vibrations, and fatigue consequences.Modification of control laws later in an airplane’s service can affect dynamic loads and fatigue life.

Uncertainty Propagation: Uncertain Inputs, Uncertain System

V.J.Romero, Sandia National Lab, AIAA Paper 2001-1653

uncertain systemuncertain response

uncertain excitation

•

•

•

•

Motivation and Key Issues



• Motivation and Key Issues– Local structural variations in composite airframes due to damage, material changes

over time, and nonlinear mechanisms can affect global aeroelastic and aeroservoelastic stability and response.

• Objectives– Develop computational tools (validated by experiments) for local/global linear/nonlinear

analysis of integrated structures/ aerodynamics / control systems subject to multiple local variations/ damage.

– Establish a collaborative expertise base for future response to FAA, NTSB, and industry needs, R&D, training,and education.

– Develop a better understanding of effects of local structural and material variations in composites on overall Aeroservoelastic integrity.

• Approach– Use sensitivity analysis and techniques from structural / aeroelastic optimization (the

capability to run many simulations efficiently) as well as reliability analysis to create the desired analysis / simulation capabilities for the linear and nonlinear cases.

– Work with realistic structural / aeroelastic models using industry-standard tools. – Build a structural dynamic / aeroelastic testing capability and carry out experiments. – Integrate aeroelasticity work with work on damage mechanisms and material behavior

in composite airframes.



Boeing Control Surface Freeplay Effort - Plan

• Develop nonlinear flutter analysis for control surfaces – Nonlinearities

• Control surface freeplay• Coulomb friction (about control surface hinge line)• Add composite structures structural nonlinearities

– Unsteady aerodynamic terms converted to time domain with RFA for• Linear or nonlinear aerodynamics• Time domain solutions (state space formulation and/or time integration)

– Solution Methods• Describing function• Multiple-time-scale• Direct time integration

• Obtain limit cycle amplitude and frequency at different flight conditions

• Apply to test problems and compare with test data– 3DOF typical section with control surface freeplay– Elevator with freeplay– Elevator tab limit cycle oscillation

• Incorporate the nonlinear freeplay capability in the standard Boeing flutter process



Approach



FAA Sponsored Project Information

• Principal Investigators & Researchers• Prof. Eli Livne• Dr. Luciano Demasi• Dr. Andrey Styuart (25%)• Mr. Levent Coskuner, PhD student

• FAA Technical Monitor• Peter Shyprykevich

• Other FAA Personnel Involved• Dr. Larry Ilcewicz• Mr. Gerry Lakin

• Industry Participation– Boeing Commercial, Seattle

• Mr. Carl Niedermeyer• Dr. Kumar Bhatia• Mr. James Gordon



Part I

Aeroservoelastic Sensitivity and Uncertainty in Composite Aircraft

Sensitivity analysis

Local structural variation and global system’s behavior



Integrated ASE System ModelPlant = Composite Structure+Aerodynamics

CONTROL LAWS

-

GUST FILTER

SENSOR BLOCKACTUATOR BLOCK PLANT

HW

{ }CMDu

{ }EXTF

{ }SENy{ }PILOTu

{ }CTRLu

{ }

{ }{ }{ }{ }

P

ACTASE

SEN

G

xx

xxx

ì üï ïï ïï ïï ïï ïï ï= í ýï ïï ïï ïï ïï ïï ïî þ

ASEMODEL



Analysis / Sensitivity / Approximation Capability• Behavior Functions:

• Static&Dynamic Stresses and Strains, Deformations, Aeroservoelastic poles, Gust Response: RMS values of stresses, strains, deformations, and control activity

• Analysis - Current:– Static Response

– Natural Modes and Frequencies

– Frequency Response

– ASE Poles (open- and closed-loop)

– Aircraft Trim / Maneuver

– Gust Response

• Analysis – Planned Addition:– Buckling

– Damage Tolerance / Fatigue



Computationally-Efficient Approximations of Behavior Functions based on Analysis and Analytic Sensitivities at a Reference Design

( )0 0( )ff f DV DV

DV¶= + -

¶

00

0

1 11( )

ff fDV DV

DV

æ ö¶ ÷ç ÷= + -ç ÷ç ÷çè ø¶

Direct Taylor Series:

Reciprocal Taylor Series:

( )f x

x

Move LimitsFor acceptable

accuracy of approximation

Direct

Reciprocal

Exact

00

&( )

ffDV¶

¶

DV



Aeroelastic State Space Equations

[ ]

[ ] [ ]

[ ] [ ] [ ] [ ][ ] [ ] [ ]

1 1 1 1

[0] 0 [0]

0 00 0 0

GLAG LAG

P

r rGr

I

M K M C M A M AA

B AA

- - - -

é ùê úê úé ù é ù é ùé ù é ù é ù é ù é ù- -ê úë û ë û ë û ë û ë ûë û ë û ë û= ê úê úê úê úé ùê úë ûë û

i i ijl s w= +®{ } { } [ ]( )( ) ( ) 0p i p ix t A x t I Al fé ù é ù= ® - =ë û ë û&

[Ap] depends on mass, stiffness, damping, Mach Number, dynamic pressure (qD)

Open loop flutter poles

s

jwstable unstable

qDqD

Flutterpoint



Sensitivities &Approximations of Flutter Poles on a Test Wing (Control System in the Loop)

Variable Local Structure:Modulus of Elasticity (E) of certain skin panels

Variable Local Structure:Modulus of Elasticity (E) of certain skin panels

STRCT/AERO

CONTROL

Active Aileron

Variation of the Real (damping) And Imaginary (frequency) Parts of a Typical Pole

Delta E

σ

ω



Vertical Tail / Rudder FEMVertical Tail / Rudder FEM

• 767-size vertical tail / rudder structure • Fixed at root• Rudder actuated at 5 pivot points

along hinge line• All composite structure:

Graphite/Epoxy and E-Glass/Epoxy• 11 Property cards:

2 skin cards; 4 web cards;2 caps cards; 2 vertical stiffener cards1 actuator card

• 232 Nodes• 1851 Elements:

1308 Membranes; 503 Bars;35 Rigid Links; 5 Rotary Actuators



Vertical Tail / Rudder Skin Thickness VariablesVertical Tail / Rudder Skin Thickness Variables

DV1 [0°]DV7 [90°]DV13 [+45°]DV19 [-45°]

DV2 [0°]DV8 [90°]DV14 [+45°]DV20 [-45°]

DV3 [0°]DV9 [90°]DV15 [+45°]DV21 [-45°]

DV4 [0°]DV10 [90°]DV16 [+45°]DV22 [-45°]

DV5 [0°]DV11 [90°]DV17 [+45°]DV23 [-45°]

DV6 [0°]DV12 [90°]DV18 [+45°]DV24 [-45°]

DV = thickness of ply angle groups1

2



Design Load & Stress ConstraintsDesign Load & Stress Constraints

1515°° yaw at 250 MPHyaw at 250 MPH

Evaluate TsiEvaluate Tsi--Wu Failure Criteria Wu Failure Criteria for all layers at all pointsfor all layers at all points(Factor of Safety = 1.5)(Factor of Safety = 1.5)

Stress Sample Points(12 points x 4 layers x 2 sides = 96)



Optimized Weight ConvergenceOptimized Weight Convergence



Variation of thickness variables during convergence to a minimum weight design



Natural Modes of the Optimized Structure

Index Freq. (Hz)

1 8.38732 23.3303 31.23594 36.59905 38.73506 40.87907 46.80858 56.74149 60.322710 67.105311 77.134812 78.691713 82.190414 95.256315 99.946616 100.931617 107.034918 110.799419 121.247920 124.8834

Mode 1 Mode 2 Mode 3 Mode 4

Mode 5Mode 6 Mode 7 Mode 8

Mode 9 Mode 10 Mode 11 Mode 12



Effect of Local Material Property Change on Aeroelastic Poles

Change in elastic Change in elastic modulus (E) of composite modulus (E) of composite

skin panels at root skin panels at root (all layers [0/90/+45/-45];

both sides)

-30 -20 -10 0 10 20 30-11.22

-11.2

-11.18

-11.16pole = 1, comp = open-loop

%∆E

RE

AL

( λA

SE)

-30 -20 -10 0 10 20 30378.8

379

379.2

379.4

379.6

379.8

%∆E

IMA

G ( λ

AS

E)



Effect of Local Structural Change on Aeroelastic Poles

Change in rudder Change in rudder mass (moisture mass (moisture

absorption?)absorption?)

-30 -20 -10 0 10 20 30-5.5

-5

-4.5

-4

-3.5

-3pole = 3, comp = open-loop

%∆ρR

EA

L ( λ

AS

E)

-30 -20 -10 0 10 20 30335

340

345

350

355

360

%∆ρ

IMA

G ( λ

AS

E)



Part II

Control Surface Limit Cycle Oscillations

Nonlinear structural effects in actuator / composite control surface assemblies

Methods development

Validation



Comparison of Benchmark Linear Analysis Results

• Effect of torsional stiffness of control surface on its hinge on linear flutter:

• Vf (flutter speed) • and • ωf (flutter frequency) • vs Kβ (ωβ) (torsional stiffness of control • surface on its hinge)

• Boeing ATLAS results • vs Tang&Dowell (Duke University)

No Freeplay –Linear Results

Freeplay δ±

Kβ

Fig.Ref. Dowell&Tang



Boeing LCO Prediction Methods Correlation

• Torsional control surface spring Amplitude of control surface limit-cycle

oscillations as a function of speed

βδ



Boeing Control Surface Freeplay Effort – Status

• Nonlinear flutter solution for typical section model with freeplay– Direct time integration solution of 3DOF problem

• Duplicated Conner’s state-space model including aerodynamics• Easy5 nonlinear model completed for time integration solutions• Comparisons with Conner’s results – very good• Analyzed linear and nonlinear models for nominal Kβ only

– Describing function/harmonic balance solution of 3DOF problem• Implementation and checkout of method in ATLAS completed

– State space formulation (time domain)– Second order equations of motion (frequency or time domain)– RFA used to convert aerodynamics to time domain if required

• Limit cycle amplitudes have been compared with – Results from direct time integration (Easy5 model) solution – Published results in open literature (Conner, Tang, and Dowell)– Comparisons look reasonable (some issues need further study)



Nonlinear Stability Analysis – Status (continued)

• Jim Gordon’s version of Conner’s 3DOF typical section model• Duplicated Conner’s state-space model including aerodynamics• Comparisons with Conner’s results

– Linear stability analysis (flutter speed and frequency) – very good– Time history responses for nonlinear equations with freeplay – very good– Analyses conducted for nominal Kβ only

• Jim Gordon’s ATLAS version of Tang/Conner 3DOF model• Used AF1 in 2D mode (obtained similar results with or without RFA ) • Comparisons with Tang’s results

– Linear stability analysis (flutter speed and frequency vs Kβ) – good– Describing function analysis comparisons: good for β, fair for α and h

• Need time history analyses with this model for consistent comparisons• Some issues need further study (e.g., differences in Vf and ωβ vs Kβ)



Part III

Modal Test System for Structural Dynamic and Aeroelastic Model

TestsStructural dynamic tests of composite components: effects of different types of damage, and changes in material properties, joints / attachments.

Nonlinear behavior of representative composite structures.

Extension to flutter tests at the UWAL Kirsten Wind Tunnel.



Modal Test System - Status

• Two competitive systems identified

• Final round of spec / cost development about to end

• Consultation with Boeing structural dynamic and flight test experts

• Decision – within the next month



A Look Forward

• Benefit to Aviation• a. Technology for design optimization of composite aircraft - accounting for

variation in airframe characteristics early in the design process of a new vehicle, and leading to designs that will be robust with respect to such changes but not over-conservative.

• b. The capability to guide structural and control system modifications of existing airplanes to minimize or totally eliminate adverse effects on the reliability, fatigue, and damage tolerance of the airframe.

• c. The capability to quantify the reliability of composite airframes accounting for material degradation and local damage, to update reliability estimates based on scheduled maintenance checks, and to guide maintenance decisions based on this information.

• d. Better understanding of control surface limit cycle oscillations sources in composite airframes and resulting engineering-based maintenance guides.

• e. A university center of expertise for commercial aircraft aeroservoelasticity– meeting FAA & NTSB needs, and contributing to research, education, and training.



A Look ForwardNext StepsLink sensitivity / approximation analysis to models of local damage and

local structural variation

Develop probabilistics / reliability analysis for structurally linear and nonlinear composite aircraft.

Extend nonlinear aeroelastic modeling / simulations to 3D real systems and link models of structural uncertainty of structure and attachments to variation in nonlinear global aeroelastic behavior

Add control system variability and nonlinearity

Build structural dynamic / flutter test system and use in a series of tests to support damaged / uncertain composite structures simulations andflutter predictions

Documents

Combined Global / Local Variability and Uncertainty in the ...depts.washington.edu/amtas/events/jams_05may/Livne-JAMS.pdf · joints/attachments stiffness and damping, actuator nonlinearities