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

2. 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

4. 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

6. 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

7. 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

8. 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

9. 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

10. 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.

11. Test Case Stiffened Panel, First 100 Modes (longitudinal compression)

12. 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 )

13. Test Case Results

14. 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.

15. Identifying Fuselage Modes Area of Interest Frame Configuration of Fuselage

16. 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

17. Fuselage Station Vertical Bending Moment Critical Load Condition: Running Load of Vertical Bending Moment

18. Identifying Fuselage Modes Fine Grid Model Model Used for Proof of Concept

19. Identifying Fuselage Modes

20. 701

21. 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

22. 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.

23. 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.

24. 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.