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Probabilistic Design Methodology for Composite Aircraft Structures

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Probabilistic Design Methodology for Composite Aircraft Structures DOT/FAA/AR-99/2 Probabilistic Design Methodology Office of Aviation Research Washington, D.C. 20591 for Composite Aircraft Structures June 1999 Final Report This document is available to the U.S. public through the National Technical Information Service (NTIS), Springfield, Virginia 22161. U.S. Department of Transportation Federal Aviation Administration NOTICE This document is disseminated under the sponsorship of the U.S. Department of Transportation in the interest of information exchange. The United States Government assumes no liability for the contents or use thereof. The United States Government does not endorse products or manufacturers. Trade or manufacturer's names appear herein solely because they are considered essential to the objective of this report. This report is available at the Federal Aviation Administration William J. Hughes Technical Center's Full-Text Technical Reports page: www.tc.faa.gov/its/act141/reportpage.html in Adobe Acrobat portable document format (PDF). Technical Report Documentation Page 1. Report No. 2. Government Accession No. 3. Recipient's Catalog No. DOT/FAA/AR-99/2 4. Title and Subtitle 5. Report Date PROBABILISTIC DESIGN METHODOLOGY FOR COMPOSITE AIRCRAFT June 1999 STRUCTURES 6. Performing Organization Code 80378 7. Author(s) 8. Performing Organization Report No. M. W. Long and J. D. Narciso 2-51410/7R-001 9. Performing Organization Name and Address 10. Work Unit No. (TRAIS) Northrop Grumman Commercial Aircraft Division P.O. Box 655907 Dallas, TX 75265-5907 11. Contract or Grant No. FAA Grant No. 95G 0036 12. Sponsoring Agency Name and Address 13. Type of Report and Period Covered U.S. Department of Transportation Final Report Federal Aviation Administration September 1995-October 1997 Office of Aviation Research 14. Sponsoring Agency Code Washington, DC 20591 AIR-100 15. Supplementary Notes The Federal Aviation Administration William J. Hughes Technical Center COTR was Donald W. Oplinger. 16. Abstract Probabilistic structural analysis methods provide a means to quantify the inherent risk of a design and assess the sensitivities of design variables. This report is intended to introduce the subject of probabilistic analysis to engineers in the aerospace industry as well as act as a reference to guide those applying this technology. The current (deterministic) structural analysis approach is described, and its shortcomings are pointed out. The evolution of probabilistic analysis is presented, and the basic theory is discussed and explained via examples. Aerospace industry method development is described in detail, along with associated aerospace applications. An in-depth explanation of one industry method (Northrop Grumman) is given, along with an example run of their computer program. The report concludes with a consensus of potential benefits as well as potential issues of concern that must be addressed by those using these analysis methods. 17. Key Words 18. Distribution Statement Aircraft, Composites, Stress, Probabilistic methods This document is available to the public through the National Technical Information Service (NTIS) Springfield, Virginia 22161. 19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price Unclassified Unclassified 138 Form DOT F1700.7 (8-72) Reproduction of completed page authorized ACKNOWLEDGEMENTS The authors wish to extend thanks to Mr. Donald Oplinger and Mr. Peter Shyprykevich of the FAA and Dr. Michael Shiao formerly of Galaxy Scientific Corporation for performing a thorough review and providing helpful comments to improve the content and readability of this document. In addition, thanks to Mr. Rick Fucik of Northrop Grumman Commercial Aircraft Division, Mr. Joseph Soderquist of the FAA, and Dr. William Corley of the University of Texas at Arlington for providing overall direction and oversight for the effort. Finally, thanks to Dr. Kuo-Feng Chung of the University of Texas at Arlington for his research efforts to acquire and review the hundreds of technical reports, papers, and presentations that provided the majority of the content of chapters 2 through 4. iii/iv/ TABLE OF CONTENTS Page EXECUTIVE SUMMARY xi 1. INTRODUCTION 1-1 1.1 Current Deterministic Structural Design Approach 1-1 1.2 Need for a Different Approach 1-1 1.3 Philosophy of Probabilistic Analysis 1-2 1.4 General Concept 1-3 2. HISTORY OF PROBABILISTIC DESIGN 2-1 2.1 Probabilistic Methodology Development 2-1 2.2 History of the Safety Factor 2-2 2.3 Historical Aspect of Acceptable Probability of Failure 2-4 3. GENERAL THEORY AND APPROACH 3-1 3.1 Basic Approach 3-1 3.2 General Steps to Probabilistic Analysis 3-2 3.3 Step 1Identify Potential Failure Modes 3-2 3.4 Step 2Define Acceptable Probability of Failure 3-2 3.5 Step 3Develop Models for Stress and Strength 3-3 3.6 Step 4Statistically Characterize Design Variables 3-3 3.6.1 Random Variable Definition 3-3 3.6.2 Continuous Random Variable DefinitionThe Probability Density Function and Its Associated Cumulative Distribution Function (CDF) 3-4 3.6.2.1 Normal Distribution 3-5 3.6.2.2 Lognormal Distribution 3-6 3.6.2.3 Weibull Distribution 3-7 3.6.2.4 Beta Distribution 3-7 3.6.2.5 Uniform Distribution 3-8 3.6.3 Discrete Random Variables and Poisson Distribution 3-9 3.6.4 Considerations for Composite Material Properties and Sample Size for Material Testing 3-10 3.7 Step 5Structural Reliability Assessment 3-11 3.7.1 Single-Variable Failure Probability Determination 3-14 v 3.7.2 Two-Variable Probability of Failure Determination 3-15 3.7.2.1 Adjustment of PDF Parameters 3-15 3.7.2.2 First-Order Reliability Method 3-16 3.7.2.3 Lognormal-Lognormal Case 3-17 3.7.2.4 Other Two-Variable Cases 3-17 3.7.2.5 Two-Variable Example Problems 3-18 3.7.2.5.1 Scenario 1 (Normal-Normal Case) 3-19 3.7.2.5.2 Scenario 2 (Lognormal-Lognormal Case) 3-19 3.7.2.5.3 Scenario 3 (Lognormal-Normal Case) 3-20 3.7.2.5.4 Two-Variable Example Problem Summary 3-21 3.7.2.6 Probability of Failure With More Than Two Variables 3-22 3.7.3 Monte Carlo Simulation 3-22 3.7.3.1 Accuracy and Number of Required Trials 3-23 3.7.3.2 Generating Random Numbers From PDFs 3-24 3.7.3.3 Correlated Random Variables 3-25 3.7.3.4 Simulation Efficiency Improvement Approaches 3-25 3.7.3.5 Summary and General Discussion 3-25 3.7.3.6 Monte Carlo Example Problem 3-26 3.7.4 Response Surface Approximation Method 3-28 3.7.4.1 Step 1Analyze Structure at Chosen Values 3-29 3.7.4.2 Step 2Develop Regression Equation 3-30 3.7.4.3 Step 3Develop Response Variable PDF 3-30 3.7.4.4 Step 4Evaluate Probability of Failure 3-31 3.7.4.5 Response Surface Method Example Problem 3-31 3.7.5 Limit State Approximation 3-33 3.7.5.1 Most Probable Point Methods 3-33 3.7.5.1.1 Step 1Transform Variables 3-34 3.7.5.1.2 Step 2Identify Most Probable Point 3-35 3.7.5.1.3 Step 3Develop g-Function and Determine Failure Probability 3-35 3.7.6 General Discussion of Limit State Approximation Methods 3-36 3.7.7 Limit State Approximation Example Problem 3-36 vi 3.8 Step 6Determine System Probability of Failure 3-39 4. SUMMARY OF INDUSTRY EFFORTS: 1980 THROUGH 1996 4-1 4.1 Discussion and Explanation of Industry Efforts 4-1 4.2 Air Force 4-1 4.2.1 F-16 Risk Assessment 4-4 4.2.2 T-38 Risk Assessment 4-5 4.3 NASA Lewis 4-5 4.3.1 Integrate Probabilistic Analysis of Composite Structures (IPACS) 4-6 4.3.2 Integrated Composite Analyzer (ICAN) 4-8 4.3.3 Probabilistic Integrated Composite Analyzer (PICAN) 4-8 4.3.4 Adaptive Importance Sampling (AIS) 4-8 4.3.5 Probabilistic Fault Tree Analysis (PFTA) 4-8 4.3.6 Multifactor Interaction Equation (MFIE or TMFIE) 4-8 4.3.7 Parallel Virtual Machine (PVM) 4-9 4.3.8 Blade Assessment for Ice Impact (BLASIM) 4-9 4.3.9 Recent Work by NASA Lewis 4-9 4.4 Southwest Research Institute (SwRI) 4-9 4.4.1 Probabilistic Methods in NESSUS 4-11 4.4.2 Performance Functions in NESSUS 4-11 4.4.3 Recent Work 4-12 4.5 Jet Propulsion Laboratory (JPL) 4-13 4.5.1 PFA Methodology 4-13 4.5.2 NASA Marshall Conclusions and Recommendations 4-14 4.6 Rockwell International Corporation 4-15 4.6.1 SSME Turbopump Blade Application 4-15 4.6.2 Probabilistic Analysis Methodology Development Efforts 4-16 4.7 NYMA, Inc. 4-17 4.8 Aerospatiale 4-17 4.9 Pratt & Whitney 4-19 4.9.1 Methodology 4-20 4.9.2 Box-Behnken Experimental Design Procedure 4-21 4.9.3 Summary and Discussion of Pratt &Whitney Method 4-22 4.10 General Electric (GE) 4-23 vii 4.11 NASA Marshall Flight Center (MSFC) 4-23 4.11.1 Probabilistic Methods Documentation 4-23 4.11.2 Proposed First-Order Method 4-24 4.11.3 Recent Work at NASA Marshall 4-24 4.12 Thiokol Corporation 4-24 4.13 NASA Langley 4-25 4.14 Grumman Aerospace 4-27 4.15 The Central Aero-Hydrodynamic Institute (TsAGI) 4-27 4.15.1 General Input Requirements to the Software 4-27 4.15.2 ProDeCompoS Methodology 4-28 4.16 Nanchang Aircraft Manufacturing Group 4-29 4.17 Alpha STAR Corporation 4-30 5.
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