H. Millwater, K. Griffin, D. Wieland Southwest Research Institute A. West, H. Smith, M. Holly

1. Probabilistic Analysis of an Advanced Fighter/Attack Aircraft Composite Wing Structure H. Millwater, K. Griffin, D. Wieland Southwest Research Institute A. West, H. Smith, M. Holly The Boeing Co. R. Holzwarth Air Force Research Laboratory

2. Objective Assess the benefits of applying probabilistic design technology to a state-of-the-art composite wing design

3. Background • Aircraft structure is a composite wing designed under an advanced lightweight aircraft structures development program. • Represents state-of-the-art in aircraft design • Has high quality computational models available • Has experimental component test data available

4. Structural Example

5. Evident Failure Surrounding Nugget Edges Remain Connected Comparison with Test Structures • Purpose: compute probability distribution of failure load and compare with experimental results • Two test temperatures: -65 F and 75 F • Three specimens at each temperature • Pull-off load increased until failure

6. Computational Model • Nonlinear composite analysis using BLADEM/THELMA (Boeing) • Probabilistic analysis computed using NESSUS (SwRI)

7. Random Variable Statistics TNORM = Truncated Normal Dist. at  3 

8. Failure Model • Structure is assumed failed when failure index >= 1.0 S3, T - Material Strengths

9. Comparison of Computational and Experimental Results • Failure due to pull-off load • (75 degrees; 3 test structures)

10. Probabilistic Sensitivity Factors (75)

11. Comparison of Computational and Experimental Results • Failurelocations and mean failure load agree. • Amount of variation in pull-off load is several times that from test • Expected reason: • Computational results were developed using material property data collected over several years. • Test structures were manufactured as one structure then sectioned. • Variations in material properties and geometries likely to be significantly less than that used in computation. • Computational results expected to be more accurate of fleet. • Use of test results as indicative of fleet may be unconservative.

12. Probabilistic Analysis of a Composite Wing • Failure: pull-off load in bonded joint of spar/wing • Severe down bending load (ultimate load) • 20 independent random variables - material properties • Geometrically Nonlinear NASTRAN analysis of wing - local analysis of composite joint • Failure probability and sensitivities computed Spar 3 Location of Load Extraction

13. NASTRANNon-linear Global ALAFS Model BLADEM_POSTExtraction of Failure Index from Results Force Post-ProcessorExtract Free-Body Forces for Sub-model Region BLADEMDetailed Blade Model Prob. Distrib. BLADEM_PREPreprocessor to Create BLADEM Input File l l l l sl fl fr sr WING-BLADE ANALYSIS Methodogy

14. Computational Procedure • Link NESSUS, PATRAN, NASTRAN, THELMA

15. Structural Deformation At Nominal Values Post-buckled Wing Skin

16. Highly stressed region l l l l sl fl fr sr Joint STRESSES

17. Random Variables

18. System Reliability Results • Consider failure of the joint as failure in any location or ply, i.e., adhesive, nugget, flanges or skin • Results indicate failure governed entirely by failure in 1st ply of left flange.

19. * * Probabilistic Sensitivity Results

20. Probabilistic Redesign • Probability of Failure was too high from original design • Several redesigns were explored deterministically • Effective redesigns were: • Increase nugget radius (from prob. sensitivities) • Remove ply from right flange • Soften E2 modulus of cloth (from prob. sensitivities)

21. Probabilistic Redesign Pf ~ 10-30 Probability Density Function after Redesign

22. Probabilistic Redesign Conclusions • A many order of magnitude improvement in safety was obtained with a small amount of effort • Probabilistic sensitivity factors indicated 2 of the 3 elements to change - nugget radius and E2 of the cloth • The effect of E2 would have been difficult to ascertain without the sensitivity analysis • Exploratory analyses were performed determinstically (quickly) to indicate a promising design

23. Summary and Conclusions Test Structures • Computed distribution of probability of failure loads were compared with test results. • Failure region and mean failure load agree. • Computed scatter was several times that of test. • Expected reason - test structures do not exhibit realistic amount of variation that would be seen in fleet. • Computational results expected to be more representative of fleet. • Use of test results as indicative of fleet may be unconservative. • Test procedures may need to be modified in order to represent better the variation seen in production.

24. Summary and Conclusions Wing/Joint Analysis • Probabilistic analysis of a state-of-the-art composite wing is practical using standard probabilistic and structural analysis tools. • Probability of failure of a post-buckled wing/joint subjected to a severe down bending load was determined • Combined probabilistic analysis (NESSUS) with geometrically nonlinear NASTRAN analysis with local composite THELMA analysis

25. Summary and Conclusions • Wing/joint structure was redesigned by modifying three variables: nugget radius, removing ply from right flange and reducing E2 material property. • Probabilistic sensitivities give valuable insight into the redesign. • Redesigned structure’s probability of failure was reduced by many orders of magnitude