Abstract
Aeroelastic phenomena are most often either ignored or roughly approximated when uncertainties are considered in the design optimization process of structures subject to aerodynamic loading, affecting the quality of the optimization results. Therefore, a design methodology is proposed that combines reliability-based design optimization and high-fidelity aeroelastic simulations for the analysis and design of aeroelastic structures. To account for uncertainties in design and operating conditions, a first-order reliability method (FORM) is employed to approximate the system reliability. To limit model uncertainties while accounting for the effects of given uncertainties, a high-fidelity nonlinear aeroelastic simulation method is used. The structure is modelled by a finite element method, and the aerodynamic loads are predicted by a finite volume discretization of a nonlinear Euler flow. The usefulness of the employed reliability analysis in both describing the effects of uncertainties on a particular design and as a design tool in the optimization process is illustrated. Though computationally more expensive than a deterministic optimum, due to the necessity of solving additional optimization problems for reliability analysis within each step of the broader design optimization procedure, a reliability-based optimum is shown to be an improved design. Conventional deterministic aeroelastic tailoring, which exploits the aeroelastic nature of the structure to enhance performance, is shown to often produce designs that are sensitive to variations in system or operational parameters.
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Allen, M.; Maute, K. 2003: Shape Optimization of Aeroelastic Structures under Uncertainties. 16th AIAA Computational Fluid Dynamics Conference, June 23–26, Orlando, FL
Box, G. 1988: Signal-to-Noise Rations, Performance Criteria, and Transformations. Technometrics 30(1), pp. 141–149
Cai, X.-C.; Farhat, C.; Sarkis, M. 1998: A Minimum Overlap Restricted Additive Schwarz Preconditioner and Applications in 3D Flow Simulations. The Tenth International Conference on Domain Decomposition Methods for Partial Differential Equations, ed. by Mandel, X.-C.C.J.; Farhat, C.
Cesare, M.; Sues, R. 1999: ProFES Probabilistic Finite Element System – Bringing Probabilistic Mechanics to the Desktop. AIAA-99-1607, 40th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, April 12–15, 1999/St. Louis, MO
Chandu, S.; Grandhi, R. 1995: General Purpose Procedure for Reliability Based Structural Optimization under Parametric Uncertainties. Adv Eng Softw 23, pp. 7–14
Chen, W.; Allen, J.; Mistree, F.; Tsui, K. 1996: A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors. ASME J Mech Des 118, pp. 478–485
Cornell, C. 1969: A Probability-Based Structural Code. J Am Concrete Inst 66(12), pp. 974–985
Das, I.; Dennis, J. 1997: A Closer Look at Drawbacks of Minimizing Weighted Sums of Objectives for Pareto Set Generation in Multicriteria Optimization Problems. Struct Optim 14, pp. 63–69
DeLaurentis, D.; Mavris, D. 2000: Uncertainty Modeling and Management in Multidisciplinary Analysis and Synthesis. 38th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV
Enevoldsen, I.; Sorensen, J. 1994a: Reliability-Based Optimization in Structural Engineering. Struct Saf 15, pp. 169–196
Enevoldsen, I.; Sorensen, J. 1994b. Reliability-Based Optimization as an Information Tool. Mech Struct Mach 22(1), pp. 117–135
Engelund, S.; Rackwitz, R. 1993: A Benchmark Study on Importance Sampling Techniques in Structural Reliability. Struct Saf 12, pp. 255–276
Farhat, C.; Lesoinne, M.; Maman, N. 1995: Mixed Explicit/Implicit Time Integration of Coupled Aeroelastic Problems: Three–Field Formulation, Geometric Conservation and Distributed Solution. Int J Numer Methods Fluids 21, pp. 807–835
Farhat, C.; Degand, C.; Koobus, B.; Lesoinne, M. 1998a: Torsional Springs for Two-Dimensional Dynamic Unstructured Fluid Meshes. Comput Methods Appl Mech Eng 163, pp. 231–245
Farhat, C.; Lesoinne, M.; LeTallec, P. 1998b: Load and Motion Transfer Algorithms for Fluid/Structure Interaction Problems with Non-Matching Discrete Interfaces: Momentum and Energy Conservation, Optimal Discretization and Application to Aeroelasticity. Comput Methods Appl Mech Eng 157, pp. 95–114
Frangopol, D.; Corotis, R. 1996: Reliability-Based Structural System Optimization: State-of-the-Art verse State-of-the-Practice. Analysis and Computation: Proceedings of the Twelfth Conference held in Conjunction with Structures Congress XIV, ed. by Cheng, pp. 67–78
Ghattas, O.; Li, X. 1998: Domain Decomposition Methods for Sensitivity Analysis of a Nonlinear Aeroelastic Problem. Int J Comput Fluid Dyn 11, pp. 113–130
Gill, P.; Saunders, M.; Murray, W. 1997: SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization. Report no 97-2m Department of Mathematics, University of California, San Diego
Grandhi, R.; Wang, L. 1998: Reliability-Based Structural Optimization Using Improved Two-Point Adaptive Nonlinear Approximations. Finite Elem Anal Des, pp. 35–48
Hasofer, A.; Lind, N. 1974: Exact and Invariant Second-Moment Code Format, J Eng Mech 100, pp. 111–121
Hohenbichler, M.; Rackwitz, R. 1986: Sensitivities and Importance Measures in Structural Reliability. Civ Eng Syst 3, pp. 203–209
Hou, G.-W.; Satyanarayana, A. 2000: Analytical Sensitivity Analysis of a Statical Aeroelastic Wing. AIAA 2000–4824, 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, September 6–8, 2000/Long Beach, CA
Imai, K.; Frangopol, D.M. 2000a: Geometrically Nonlinear Finite Element Reliability Analysis of Structural Systems. I: Theory. Comput Struct 77(6), pp. 677–691
Imai, K.; Frangopol, D.M. 2000b: Response Prediction of Geometrically Nonlinear Structures. J Struct Eng 126(11), pp. 1348–1355
Kahn, H. 1956: Use of Different Monte Carlo Sampling Techniques. Proc. Symp. on Monte Carlo Methods, New York, pp. 149–190
Kalos, M.; Whitlock, P. 1986: Monte Carlo Methods (Volume I: Basics). New York: John Wiley & Sons
Karamchandani, A.; Cornell, C. 1992: Sensitivity Estimation within First and Second Order Reliability Methods. Struct Saf 11(2), pp. 95–107
Kim, S-H.; Ra, K-W. 2000: Adaptive Importance Sampling Method for the Stochastic Finite Element Analysis. 8th ASCE Joint Specialty Conference on Probabilistic Mechanics and Structural Reliability, South Bend, IN
Li, W.; Huyse, L.; Padula, S. 2002: Robust Airfoil Optimization to Achieve Consistent Drag Reduction over a Range of Mach Numbers. Struct Multidisc Optim 24, pp. 38–50
Luo, X.; Grandhi, R.V. 1997: ASTROS for Reliability-Based Multidisciplinary Structural Analysis and Optimization. Comput Struct 62, pp. 737–745
Madsen, H.; Krenk, S.; Lind, N. 1986: Methods of Structural Safety. Prentice-Hall, Inc., Englewook Cliffs, NJ, USA
Martins, J.; Alonso, J. 2002: High-Fidelity Aero-Structural Design Optimization of a Supersonic Business Jet. AIAA 2002-1483, 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, April 22–25, 2002, Denver, CO
Maute, K.; Nikbay, M.; Farhat, C. 2000: Analytically Based Sensitivity Analysis and Optimization of Nonlinear Aeroelastic Systems. AIAA 2000–4825, 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, September 6–8, 2000, Long Beach, CA
Maute, K.; Nikbay, M.; Farhat, C. 2001: Coupled Analytical Sensitivity Analysis and Optimization of Three-Dimensional Nonlinear Aeroelastic Systems. AIAA J 39(11), pp. 2051–2061
Maute, K.; Nikbay, M.; Farhat, C. 2003: Sensitivity Analysis and Design Optimization of Three-Dimensional Nonlinear Aeroelastic Systems by the Adjoint Method. Int J Numer Methods Eng 56, pp. 911–933
Mavris, D.; Macsotai, N.; Roth, B. 1998: A Probabilistic Design Methodology for Commercial Aircraft Engine Cycle Selection. 3rd World Aviation Congress and Exposition, Anaheim, CA, SAE-985510
Mavris, D.; DeLaurentis, D. 1998: A Stochastic Design Approach for Aircraft Affordability. 21st ICAS Congress of the International Council on the Aeronautical Sciences, Melbourne, Australia
Melchers, R. 1990: Radial Importance Sampling for Structural Reliability. J Eng Mech 116(1), pp. 189–203
Meric, R. 1985: Coupled Optimization in Steady-State Thermoelasticity. J Therm Stresses 8, pp. 333–347
Meric, R. 1986: Material and Load Optimization of Thermoelastic Solids. Part I: Sensitivity Analysis. Part II: Numerical results. J Therm Stresses 9, pp. 359–372, 373–388
Meric, R. 1990: Optimal Cross-Sectional Shape for MHD Channel Flows. Int J Numer Methods Eng 30, pp. 919–929
Messac, A.; Ismail-Yahaya, A. 2002: Multiobjective Robust Design using Physical Programming. Struct Multidisc Optim 23, pp. 357–371
Michaleris, P.; Tortorelli, D.A.; Vidal, C.A. 1995: Analysis and Optimization of Weakly Coupled Thermoelastoplastic Systems with Application to Weldment Design. Int J Numer Methods Eng 38, pp. 1259–1285
Militello, C.; Felippa, C. 1991: The First ANDES Elements: 9-dof Plate Bending Triangles. Comput Methods Appl Mech Eng 91, pp. 217–246
Møller, H.; Lund, E. 2000: Shape Sensitivity Analysis of Strongly Coupled Fluid–Structure Interaction Problems. AIAA 2000–4823, 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, September 6–8, 2000, Long Beach, CA
Padmanabhan, D.; Batill, S. 2000: An Iterative Concurrent Subspace Robust Design Framework, AIAA 2000-4841, 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, September 6–8, Long Beach, CA
Parkinson, A.; Sorensen, C.; Pourhassan, N. 1993: A General Approach for Robust Optimality. Trans ASME 115, pp. 74–80
Pettit, C.; Grandhi, R. 2000: Multidisciplinary Optimization of Aerospace Structures with High Reliability. 8th ASCE Joint Specialty Conference on Probabilistic Mechanics and Structural Reliability, South Bend, IN
Pettit, C.; Grandhi, R. 2001: Reliability Optimization of Aerospace Structures for Gust Response and Aileron Effectiveness. 8th International Conference on Structural Safety and Reliability, June 2001, Newport Beach, CA
Riha, D.S.; Thacker, B.H.; Millwater, H.R.; Wu, Y.-T.; Enright, M.P. 2000: Probabilistic Engineering Analysis Using the NESSUS Software. AIAA 2000-1512, 41st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, Atlanta, GA
Roe, P. 1981: Approximate Riemann Solvers, Parameter Vectors and Difference Schemes. J Computat Phys 43, pp. 357–372
Rubinstein, R. 1981: Simulation of the Monte Carlo Method. New York: Wiley
Schittkowski, K. 1985: NLPQL: A FORTRAN Subroutine for Solving Constrained Nonlinear Programming Problems. Ann Oper Res 5, pp. 485–500
Shinozuka, M. 1983: Basic Analysis of Structural Safety. J Am Concrete Inst 109, pp. 721–740
Sobieszczanski-Sobieski, J. 1990: Sensitivity of Complex, Internally Coupled Systems. AIAA J 28, pp. 153–160
Su, J.; Renaud, J. 1997: Automatic Differentiation in Robust Optimization. AIAA J 35(6), pp. 1072
Sunderasan, S.; Ishii, K.; Houser, D. 1993: A Robust Optimization Procedure with Variation on Design Variables and Constraints. Adv Des Autom 65(1), pp. 379–386
Taguchi, G.; Wu, Y. 1979: Introduction to Off-Line Quality Control. Quality Control Associate
Taguchi, G. 1986a: Introduction to Quality Engineering. Krauss International Publications
Taguchi, G. 1986b: Systems of Experimental Design. Krauss International Publications Vol. 1 & 2
Taguchi, G. 1993: Taguchi on Robust Technology Development. ASME Press
Tortorelli, D.; Subramani, G.; Lu, S.; Haber, R. 1991: Sensitivity Analysis for Coupled Thermoelastic Systems. Int J Solids Struct 27, pp. 1477–1497
Wu, Y.-T.; Millwater, H.; Cruse, T. 1990: Advanced Probabilistic Structural Analysis Method for Implicit Performance Functions. AIAA J 12, pp. 255–276
Wu, Y.-T. 1992: Reliability Technology – 1992 28, New York: The American Society of Mechanical Engineers
Wu, Y.-T. et al. 2000: Probabilistic methods for design assessment of reliability with inspection (DARWIN). 41st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, Atlanta, GA
Yang, J.; Nikolaidis, E. 1991: Design of Aircraft Wings Subjected to Gust Loads: A Safety Index Based Approach. AIAA J 29(5), pp. 804–812
Yu, X.; Choi, K.; Chang, K. 1997a: A Mixed Design Approach for Probabilistic Structural Durability. J Struct Optim 14(2)–(3), pp. 81–90
Yu, X.; Choi, K.; Chang, K. 1997b: Reliability and Durability Based Design Sensitivity Analysis and Optimization. Tech. Rep. R97-01, Center for Computer Aided Design University of Iowa
Yu, X.; Chang, K.; Choi, K. 1998: Probabilistic Structural Durability Prediction. AIAA J 36(4), pp. 628–637
Zink, P.; Mavris, D.; Love, M.: Karpel, M. 1998: Robust Design for Aeroelastically Tailored/Active Aeroelastic Wing. 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St. Louis, MO
Zink, P.; Raveh, D.; Mavris, D. 2000: Robust Structural Design for Active Aeroelastic Wing with Aerodynamic Uncertainties. 41st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, Atlanta, GA
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Allen, M., Maute, K. Reliability-based design optimization of aeroelastic structures. Struct Multidisc Optim 27, 228–242 (2004). https://doi.org/10.1007/s00158-004-0384-1
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DOI: https://doi.org/10.1007/s00158-004-0384-1