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Uncertainty Analysis in Aircraft Structures

This study presents a comprehensive methodology aimed at enhancing the predictive capabilities of aircraft structure performance through uncertainty analysis. By utilizing uncertain input variables and advanced sampling techniques, the approach minimizes computational expense while enabling robust probabilistic assessments. The Wing Box Model serves as the primary case study, allowing for better understanding of structural responses. The methodology aims to reduce prototype production and experimental needs, ultimately improving cost-effectiveness. Future work will expand this analysis to incorporate additional uncertainties across various structural components.

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Uncertainty Analysis in Aircraft Structures

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  1. Uncertainty Analysis in Aircraft Structures Air Frame Finite Element Modeling for Uncertainty Analysis and Large-Scale Numerical Simulation Validation Jason Gruenwald University of Illinois-Urbana/Champaign Dr. Mark Brandyberry MSSC, CSAR

  2. Goal • Create a Methodology • Better Predicts Performance of aircraft structure • Using uncertain input variables • Minimizes computation expense (number of runs) • Need to be able to answer probabilistic questions • 99% confident satisfies requirement rather than use safety factor • Predictive Analysis: • Reduce experiments needed • Reduce the number of Prototypes built • Increase Cost effectiveness

  3. Uncertainty Analysis • Variation of the structure’s response due to collective variation of input parameters • i.e. Aircraft wing • Better understand change in response • Apply methodology used for Computational Fluid Dynamics in rockets

  4. Overview of Methodology Determine Input Uncertainties and probability distributions Create Sample Sets using sampling method Create Surrogate Model Simulate a few specific sample sets Create Clusters of Similar Predictions Predict output trends quickly Cumulative Probabilities of Output Variables Interpolate results over entire range

  5. Wing Box Model • Modeled in ABAQUS • Solid Mechanics Finite Element Program • Chosen for simplicity • Short Simulation time • Material assumptions: • Entire model is 7075-T6 Al • Behaves linearly

  6. Input Parameters & Sample Sets • Young’s Modulus • 10400 ksi ± 5% • Normal Distribution • Poisson’s Ratio • 0.33 ± 5% • Normal Distribution • Load Reference Case • FALSTAFF Spectrum • Assumed loads change in phase • Latin Hypercube Sampling • Samples values from extremes • 50 sample sets

  7. Set Prediction 1 1.327 2 0.779 3 0.746 48 1.223 49 0.921 50 1.06 Surrogate Model Wing Box Cluster 1 Cluster 2 Cluster 9 Cluster 10

  8. Clusters and Simulation Front Spar Max Stress Prediction 1.00 Prediction Cluster 10 Cluster 4 Cumulative Probability 0.50 Cluster 3 Cluster 1 0.00 0 60000 120000 Max Stress (psi)

  9. Cumulative Probability Maximum Stress (psi) Interpolation ABAQUS Sims Results Tensile Yield Tensile Yield Ultimate Yield Ultimate Yield

  10. Conclusion • Cluster Methodology accurately predicts performance • Engineers ability to answer probabilistic questions • Minimal computational expense • Predictive Analysis: • Reduce the number of Prototypes built • Reduce experiments needed • Cost effective

  11. Future Work • Investigate techniques to validate computational model • Compare uncertain simulation with uncertain experiments • Multiple points of comparison • Weighted comparisons • Multi-Attribute Decision Tree Methods • Incorporate other uncertainties • i.e. Geometric tolerances, Friction, Boundary Conditions Uncertainties • Apply to entire aircraft wing

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