A STATISTICAL METHOD OF IDENTIFYING GENERAL BUCKLING MODES ON THE CHINOOK HELICOPTER FUSELAGE

1
A STATISTICAL METHOD OF IDENTIFYING GENERAL
BUCKLING MODES ON THE CHINOOK HELICOPTER FUSELAGE

• Brandon Wegge The Boeing Company
• Lance Proctor MSC.Software

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Identifying Global Buckling Modes

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

3
Introduction

• Local buckling is characterized by a small
  portion of the structure buckling
• Skin wrinkling
• Tertiary struts
• Not necessarily catastrophic

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Introduction

• Global buckling is characterized by the entire
  structure (or a large portion of the structure)
  undergoing buckling.
• Often catastrophic.

5
Introduction

• Helicopter fuselage
• Lightweight Skin
• tertiary load path
• buckling expected and allowed
• Structural Space Frame
• primary load path
• buckling could be catastophic

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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

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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

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Theory

• Statistical Methods on Buckling Eigenvectors and
  Interpretation
• Mean (0.0ltmeanlt1.0)
• local mode, low mean / global mode, higher mean
• Standard deviation (0.0ltstddevlt1.0)
• 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

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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

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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.

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Test Case

• Stiffened Panel,
• First 100 Modes
• (longitudinal compression)

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Test Case
Mode 21, (mixed/ local)
Mode 1, (local)
Mode 57, (second bending)
Mode 42, (1st torsion)
Mode 15, (1st global)
Buckling Modes 1, 15, 21, 42, and 57 (in
ascending order left to right)
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Test Case Results
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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.

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Identifying Fuselage Modes
Area of Interest
Frame Configuration of Fuselage
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Identifying Fuselage Modes
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
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Identifying Fuselage Modes
Critical Load Condition Running Load of Vertical
Bending Moment
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Identifying Fuselage Modes
Fine Grid Model
Model Used for Proof of Concept
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Identifying Fuselage Modes
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Identifying Fuselage Modes
701
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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

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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.

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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.

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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.