1. Sdm 2000 H. Millwater, K. Griffin, D. Wieland Southwest Research Institute A. West, H. Smith, M. Holly The Boeing Co. R. Holzwarth Air Force Research Laboratory Probabilistic Analysis of an Advanced Fighter/Attack Aircraft Composite Wing Structure

2. Sdm 2000 Assess the benefits of applying probabilistic design technology to a state-of-the-art composite wing design Objective

3. Sdm 2000 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 Background

4. Sdm 2000 Structural Example

5. Sdm 2000 n 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 Edges Remain Connected Evident Failure Surrounding Nugget Comparison with Test Structures

6. Sdm 2000 Computational Model n Nonlinear composite analysis using BLADEM/THELMA (Boeing) n Probabilistic analysis computed using NESSUS (SwRI)

7. Sdm 2000 Random Variable Statistics TNORM = Truncated Normal Dist. at  3 

8. Sdm 2000 Failure Model n Structure is assumed failed when failure index >= 1.0 S3, T - Material Strengths

9. Sdm 2000 n Failure due to pull-off load (75 degrees; 3 test structures) Comparison of Computational and Experimental Results

10. Sdm 2000 Probabilistic Sensitivity Factors (75  )

11. Sdm 2000 Comparison of Computational and Experimental Results n Failure locations and mean failure load agree. n Amount of variation in pull-off load is several times that from test n 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. Sdm 2000 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 Probabilistic Analysis of a Composite Wing Spar 3 Location of Load Extraction

13. Sdm 2000 WING-BLADE ANALYSIS Methodogy NASTRAN Non-linear Global ALAFS Model BLADEM Detailed Blade Model BLADEM_POST Extraction of Failure Index from Results BLADEM_PRE Preprocessor to Create BLADEM Input File Force Post-Processor Extract Free-Body Forces for Sub-model Region Prob. Distrib. l sl l fl l fr l sr

14. Sdm 2000 Computational Procedure n Link NESSUS, PATRAN, NASTRAN, THELMA

15. Sdm 2000 Structural Deformation At Nominal Values Post-buckled Wing Skin

16. Sdm 2000 Joint STRESSES Highly stressed region l sl l fl l fr l sr

17. Sdm 2000 Random Variables

18. Sdm 2000 System Reliability Results n Consider failure of the joint as failure in any location or ply, i.e., adhesive, nugget, flanges or skin n Results indicate failure governed entirely by failure in 1st ply of left flange.

19. Sdm 2000 Probabilistic Sensitivity Results * *

20. Sdm 2000 n Probability of Failure was too high from original design n 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) Probabilistic Redesign

21. Sdm 2000 Probabilistic Redesign Probability Density Function after Redesign Pf ~ 10 -30

22. Sdm 2000 Probabilistic Redesign Conclusions n A many order of magnitude improvement in safety was obtained with a small amount of effort n 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 n Exploratory analyses were performed determinstically (quickly) to indicate a promising design

23. Sdm 2000 Summary and Conclusions n Computed distribution of probability of failure loads were compared with test results. n Failure region and mean failure load agree. n Computed scatter was several times that of test. n Expected reason - test structures do not exhibit realistic amount of variation that would be seen in fleet. n Computational results expected to be more representative of fleet. n Use of test results as indicative of fleet may be unconservative. n Test procedures may need to be modified in order to represent better the variation seen in production. Test Structures

24. Sdm 2000 Summary and Conclusions n Probabilistic analysis of a state-of-the-art composite wing is practical using standard probabilistic and structural analysis tools. n 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 n Wing/Joint Analysis

25. Sdm 2000 Summary and Conclusions n Wing/joint structure was redesigned by modifying three variables: nugget radius, removing ply from right flange and reducing E2 material property. n Probabilistic sensitivities give valuable insight into the redesign. n Redesigned structure’s probability of failure was reduced by many orders of magnitude