A STATISTICAL METHOD OF IDENTIFYING GENERAL BUCKLING MODES ON THE CHINOOK HELICOPTER FUSELAGE Brandon Wegge – The Boeing Company Lance Proctor – MSC.Software.

A STATISTICAL METHOD OF IDENTIFYING GENERAL BUCKLING

MODES ON THE CHINOOK HELICOPTER FUSELAGE

Brandon Wegge – The Boeing Company

Lance Proctor – MSC.Software

Identifying Global Buckling Modes

• Introduction• Motivation• Statistical Approach to Identify Buckling• Test Case• Identifying Buckling modes for Chinook• Conclusions• Limitations

Introduction• Local buckling is characterized by a small

portion of the structure buckling– Skin wrinkling– Tertiary struts– Not necessarily catastrophic

Introduction• Global buckling is characterized by the

entire structure (or a large portion of the structure) undergoing buckling.

– Often catastrophic.

Introduction

• Helicopter fuselage– Lightweight Skin

• tertiary load path• buckling expected and allowed

– Structural Space Frame• primary load path• buckling could be catastophic

Motivation• Determine General Stability of Chinook Fuselage

– Identify “global” vs “local” modes• Too many tertiary skin buckling configurations at limit load

for quick ID of global modes

– Eventually use in design optimization for new projects

Theory

• Quantify “global” modes– Modal characteristics different between

dynamic modes and buckling modes• cannot use Modal Effective Mass

– Buckling Eigenvectors normalized to +/-1.0 for maximum displacement

• Statistical trends can be used to identify global modes for space frame structures with “reasonable” mesh distributions

Theory

• Statistical Methods on Buckling Eigenvectors and Interpretation– Mean (0.0<mean<1.0)

• local mode, low mean / global mode, higher mean

– Standard deviation (0.0<stddev<1.0)• local mode, low stddev / global mode, higher stddev

– Weighted Standard Deviation • Want modes with both higher mean and stddev• Drops modes with low mean or low stddev

Statistical Results Using Square of Eigenvector.Beam Grids Only.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Mode Number

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n ,1

1

ni

xix xn ,1

2)()1(

1

xx

Computational Strategy

• Convert Eigenvectors to BASIC C.S.– average in the same direction.

• Separate into Translational Components

– high rotation indicate local modes

• Make Eigenvectors positive.

– Absolute Value or Square each term

Computational Strategy• Reduce to a subset of “hard-points”

(optional)

• Compute statistics

– in each direction (X, Y, and Z)

– optionally, statistics on the magnitude

• Print results.

Test CaseStiffened Panel,First 100 Modes(longitudinal compression)

Test Case

Buckling Modes 1, 15, 21, 42, and 57 (in ascending order left to right)

Mode 1,(local)

Mode 15,(1st global)

Mode 21,(mixed/

local)

Mode 42,(1st torsion)

Mode 57,(second

bending)

Test Case ResultsStatistical Results Using Absolute Value of Eigenvector.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Mo d e N u m b e r

Statistical Results Using Square of Eigenvector.Beam Grids Only.

00.01

0.02

0.030.04

0.050.06

0.070.08

0.090.1

Mode Number

Statistical Results Using Square of Eigenvector.

0

0.02

0.04

0.06

0.08

0.1

Mode Number

Statistical Results Using Square of Eigenvector.Intersection Grids Only.

0

0.010.02

0.03

0.04

0.050.06

0.07

0.080.09

0.1

Mode Number

Test Case Conclusions• Squaring Eigenvector prior to statistics

isolates global modes more effectively• Limiting GRIDs to “hard points” identifies

global modes more clearly– More than two orders of magnitude separation

between “global” and “local” modes was observed when squaring eigenvector and using hard points for statistics.

Identifying Fuselage ModesArea of Interest

Frame Configuration of

Fuselage

In general instability, failure is not confined to the region between two adjacent frames or rings but may extend over a distance of several frame spacings… In panel instability, the transverse stiffeners provided by the frames on rings is sufficient to enforce nodes in the stringers at the frame support points… [Bruhn]

Identifying Fuselage Modes

Panel Instability

General Instability

Frame Frame FrameFrame

Skin

Panel Instability

General Instability

Frame Frame FrameFrame

Panel Instability

General Instability

Panel Instability

General Instability

Frame Frame FrameFrame

Skin

Identifying Fuselage Modes

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-10000000

-8000000

-6000000

-4000000

-2000000

0

2000000

4000000

20 120 220 320 420 520

Fuselage Station

Vertical

Ben

din

g M

omen

t

Critical Load Condition: Running Load of Vertical Bending Moment

Identifying Fuselage Modes

Fine Grid Model

Model Used for Proof of Concept

Identifying Fuselage Modes

M a x i m u m V e r t i c a l M o m e n t - F i r s t G e n e r a l E i g e n v a l u e

- 0 . 5 0

- 0 . 3 0

- 0 . 1 0

0 . 1 0

0 . 3 0

0 . 5 0

0 . 7 0

0 . 9 0

1 6 0 2 0 0 2 4 0 2 8 0 3 2 0 3 6 0 4 0 0 4 4 0

S t a t i o n

Eig

enve

cto

r

M a j o r F r a m e L o c a t i o n s

Identifying Fuselage Modes

0.00E+00

1.00E-06

2.00E-06

3.00E-06

4.00E-06

5.00E-06

6.00E-06

0 200 400 600 800 1000

Mode Number

Me

asu

re

701

Conclusions• A statistical method presented here

quickly identifies the nature of buckling modes for a space frame structure

• Validated on a simple test case.

– Using Eigenvector Square and “hard points” demonstrated better identification and separation of “local” vs “global” modes

Conclusions• Further validated on a model of the

Chinook helicopter.

– The first global mode of the Chinook helicopter was determined by manual sorting of the MSC.Nastran results (mode shape plots), then used to verify the statistical method. The two techniques yielded the same result.

Conclusions• The method showed time savings of three

days to one hour. – Before: mundane manipulation of large data (mode

plots)

– After: simple concise chart (single bar graph)

• Specifying the area of interest yields more conclusive results.

Limitations• Mesh Density/Continuity

– Should be used on a model with reasonably space nodes

– Highly refined regions can skew results

• Good Results for Space Frames and Stiffened Plates– Other models untested, but meeting mesh

density/continuity consideration above, the method should work fine.