Skip to main content
Search
Search
Quick Search anywhere
Quick Search fdjslkfh
Advanced search
Cart
Join AIAA Institution Login
Skip main navigation
AIAA Journal logo
Skip to article control options
No AccessRegular Article

High-Fidelity Aerostructural Gradient Computation Techniques with Application to a Realistic Wing Sizing

Published Online:10 Oct 2018https://doi.org/10.2514/1.J056736

Abstract

Aerostructural optimization is a keystone process to concurrently improve aerodynamic performance and reduce the structural mass of an aircraft. However, gradient-based multidisciplinary design optimization is efficient only if the computation of gradients is fast and accurate. To this end, two high-fidelity aerostructural gradient computation techniques are proposed for strongly coupled aeroelastic systems. In the specific context of this work, the focus is on design variables affecting structural stiffness only. Scalar objective functions like aerodynamic performance criteria are considered as well as a field of structural grid forces. The most intrusive technique includes well-established direct and adjoint formulations that require substantial implementation effort. In contrast, an alternative uncoupled nonintrusive approach is proposed that is easier to implement and yet capable of providing accurate gradient approximations. The accuracy of these methods is first demonstrated on the ONERA M6 wing test case. Their efficiency and applicability are then illustrated via a mass minimization problem applied to the Common Research Model. Both methods lead to very similar optimal designs, and the detailed analysis of results promotes the nonintrusive approach as a promising gradient computation alternative.

References

  • [1] Adelman H. M. and Haftka R. T., “Sensitivity Analysis of Discrete Structural Systems,” AIAA Journal, Vol. 24, No. 5, 1986, pp. 823–832. doi:https://doi.org/10.2514/3.48671 AIAJAH 0001-1452 LinkGoogle Scholar

  • [2] Hicks R. M. and Szelazek C. A., “Airfoil Design by Numerical Optimization Using a Minicomputer,” NASA TM 78502, 1978. Google Scholar

  • [3] Barthelemy J.-F. M. and Bergen F., “Shape Sensitivity Analysis of Wing Static Aeroelastic Characteristics,” NASA TP 2808, 1988. LinkGoogle Scholar

  • [4] Shirk M. H., Hertz T. J. and Weisshaar T. A., “Aeroelastic Tailoring–Theory, Practice, and Promise,” Journal of Aircraft, Vol. 23, No. 1, 1986, pp. 6–18. doi:https://doi.org/10.2514/3.45260 LinkGoogle Scholar

  • [5] Grossman B., Gurdal Z., Strauch G. J., Eppard W. M. and Haftka R. T., “Integrated Aerodynamic/Structural Design of a Sailplane Wing,” Journal of Aircraft, Vol. 25, No. 9, 1988, pp. 855–860. doi:https://doi.org/10.2514/3.45670 LinkGoogle Scholar

  • [6] Chittick I. R. and Martins J. R. R. A., “An Asymmetric Suboptimization Approach to Aerostructural Optimization,” Optimization and Engineering, Vol. 10, No. 1, 2009, pp. 133–152. doi:https://doi.org/10.1007/s11081-008-9046-2 CrossrefGoogle Scholar

  • [7] Hutchison M., Unger E., Mason W., Grossman B. and Haftka R., “Variable-Complexity Aerodynamic Optimization of an HSCT Wing Using Structural Wing-Weight Equations,” Journal of Aircraft, Vol. 31, No. 1, 1994, pp. 110–116. doi:https://doi.org/10.2514/3.46462 LinkGoogle Scholar

  • [8] McQuade P. D., Eberhardt S. and Livne E., “CFD-Based Aerodynamic Approximation Concepts Optimization of a Two-Dimensional Scramjet Vehicle,” Journal of Aircraft, Vol. 32, No. 2, 1995, pp. 262–269. doi:https://doi.org/10.2514/3.46711 LinkGoogle Scholar

  • [9] Knoll D. and Keyes D., “Jacobian-Free Newton-Krylov Methods: A Survey of Approaches and Applications,” Journal of Computational Physics, Vol. 193, No. 2, 2004, pp. 357–397. doi:https://doi.org/10.1016/j.jcp.2003.08.010 JCTPAH 0021-9991 CrossrefGoogle Scholar

  • [10] Zhang Z. J. and Zingg D. W., “Efficient Monolithic Solution Algorithm for High-Fidelity Aerostructural Analysis and Optimization,” AIAA Journal, Vol. 56, No. 3, 2018, pp. 1251–1265. doi:https://doi.org/10.2514/1.J056163 AIAJAH 0001-1452 LinkGoogle Scholar

  • [11] Sobieszczanski-Sobieski J., Bloebaum C. L. and Hajela P., “Sensitivity of Control-Augmented Structure Obtained by a System Decomposition Method,” AIAA Journal, Vol. 29, No. 2, 1991, pp. 264–270. doi:https://doi.org/10.2514/3.10573 AIAJAH 0001-1452 LinkGoogle Scholar

  • [12] Martins J. R. R. A., Sturdza P. and Alonso J. J., “The Complex-Step Derivative Approximation,” ACM Transactions on Mathematical Software, Vol. 29, No. 3, 2003, pp. 245–262. doi:https://doi.org/10.1145/838250 ACMSCU 0098-3500 CrossrefGoogle Scholar

  • [13] Sobieszczanski-Sobieski J., “Sensitivity of Complex, Internally Coupled Systems,” AIAA Journal, Vol. 28, No. 1, 1990, pp. 153–160. doi:https://doi.org/10.2514/3.10366 AIAJAH 0001-1452 LinkGoogle Scholar

  • [14] Maute K., Nikbay M. and Farhat C., “Coupled Analytical Sensitivity Analysis and Optimization of Three-Dimensional Nonlinear Aeroelastic Systems,” AIAA Journal, Vol. 39, No. 11, 2001, pp. 2051–2061. doi:https://doi.org/10.2514/2.1227 AIAJAH 0001-1452 LinkGoogle Scholar

  • [15] Jameson A., “Aerodynamic Design via Control Theory,” Journal of Scientific Computing, Vol. 3, No. 3, 1988, pp. 233–260. doi:https://doi.org/10.1007/BF01061285 JSCOEB 0885-7474 CrossrefGoogle Scholar

  • [16] Reuther J., Jameson A., Farmer J., Martinelli L. and Saunders D., “Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation,” 34th Aerospace Sciences Meeting and Exhibit, AIAA Paper 1996-0094, Jan. 1996. doi:https://doi.org/10.2514/6.1996-94 LinkGoogle Scholar

  • [17] Maute K., Nikbay M. and Farhat C., “Analytically Based Sensitivity Analysis and Optimization of Nonlinear Aeroelastic Systems,” 8th Symposium on Multidisciplinary Analysis and Optimization, AIAA Paper 2000-4825, Sept. 2000. doi:https://doi.org/10.2514/6.2000-4825 LinkGoogle Scholar

  • [18] Jameson A., “Efficient Aerodynamic Shape Optimization,” 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2004-4369, Aug.–Sept. 2004. doi:https://doi.org/10.2514/6.2004-4369 LinkGoogle Scholar

  • [19] Gauger N. R., “Adjoint Approaches in Aerodynamic Shape Optimization and MDO Context,” European Conference on Computational Fluid Dynamics ECCOMAS CFD, edited by Wesseling P., Oñnate E. and Periaux J., TU Delft, The Netherlands, 2006. Google Scholar

  • [20] Salah El Din I., Carrier G. and Mouton S., “Discrete Adjoint Method in elsA (Part 2): Application to Aerodynamic Design Optimisation,” 7th ONERA-DLR Aerospace Symposium, Toulouse, 2006. Google Scholar

  • [21] Mavriplis D., “Discrete Adjoint-Based Approach for Optimization Problems on Three-Dimensional Unstructured Meshes,” AIAA Journal, Vol. 45, No. 4, 2007, pp. 741–750. doi:https://doi.org/10.2514/1.22743 AIAJAH 0001-1452 LinkGoogle Scholar

  • [22] Bücker M., Corliss G., Hovland P., Naumann U. and Norris B., Automatic Differentiation: Applications, Theory, and Implementations, Lecture Notes in Computational Science and Engineering, Springer–Verlag, Berlin, 2006. CrossrefGoogle Scholar

  • [23] Hascoët L., “Adjoints by Automatic Differentiation,” Advanced Data Assimilation for Geosciences, Oxford Univ. Press, 2014, Paper 978-0-19-872384-4. CrossrefGoogle Scholar

  • [24] Kenway G. K. W., Kennedy G. J. and Martins J. R. R. A., “Scalable Parallel Approach for High-Fidelity Steady-State Aeroelastic Analysis and Adjoint Derivative Computations,” AIAA Journal, Vol. 52, No. 5, 2014, pp. 935–951. doi:https://doi.org/10.2514/1.J052255 AIAJAH 0001-1452 LinkGoogle Scholar

  • [25] Sanchez R. and Palacios R., “Computing Derivatives in Nonlinear Aeroelasticity Using Algorithm Differentiation,” Proceedings of 17th International Forum on Aeroelasticity and Structural Dynamics (IFASD 2017), Politecnico di Milano, Milano, Italy, 2017, pp. 1634–1641. Google Scholar

  • [26] Marcelet M., Peter J. and Carrier G., “Sensitivity Analysis of a Strongly Coupled System Using the Discrete Direct and Adjoint Approach,” European Journal of Computational Mechanics, Vol. 17, No. 8, 2008, pp. 1077–1106. doi:https://doi.org/10.3166/remn.17.1077-1106 CrossrefGoogle Scholar

  • [27] Ghazlane I., Carrier G. and Dumont A., “Aerostructural Adjoint Method for Flexible Wing Optimization,” 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA Paper 2012-1924, April 2012. doi:https://doi.org/10.2514/6.2012-1924 LinkGoogle Scholar

  • [28] Viti A., Druot T. and Dumont A., “Aero-Structural Approach Coupled with Direct Operative Cost Optimization for New Aircraft Concept in Preliminary Design,” 17th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2016-3512, 2016. doi:https://doi.org/10.2514/6.2016-3512 LinkGoogle Scholar

  • [29] Jameson A., “Aerodynamic-Structural Design Studies of Low-Sweep Transonic Wings,” Journal of Aircraft, Vol. 47, No. 2, 2010, pp. 505–514. doi:https://doi.org/10.2514/1.42775 LinkGoogle Scholar

  • [30] Brezillon J., Ronzheimer A., Haar D., Abu-Zurayk M., Lummer M., Krüger W. and Natterer F. J., “Development and Application of Multi-Disciplinary Optimization Capabilities Based on High-Fidelity Methods,” 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA Paper 2012-1757, April 2012.doi:https://doi.org/10.2514/6.2012-1757 Google Scholar

  • [31] Blondeau C., Achard T., Girodroux-Lavigne P. and Ohayon R., “Recent Achievements Towards Aero-Structure Gradient Computation Using High-Fidelity CFD-CSM in the Onera elsA Software,” Proceedings of 15th International Forum on Aeroelasticity and Structural Dynamics (IFASD 2015), Central Aerohydrodynamic Inst., TSAGI, Russian Federation, 2015, pp. 672–691. Google Scholar

  • [32] Cambier L., Heib S. and Plot S., “The Onera else A CFD Software: Input from Research and Feedback from Industry,” Mechanics & Industry, Vol. 14, 2013, pp. 159–174. doi:https://doi.org/10.1051/meca/2013056 CrossrefGoogle Scholar

  • [33] Akgün M. A., Haftka R. T., Wu K. C., Walsh J. L. and Garcelon J. H., “Efficient Structural Optimization for Multiple Load Cases Using Adjoint Sensitivities,” AIAA Journal, Vol. 39, No. 3, 2001, pp. 511–516. doi:https://doi.org/10.2514/3.14760 AIAJAH 0001-1452 LinkGoogle Scholar

  • [34] Raspanti C., Bandoni J. and Biegler L., “New Strategies for Flexibility Analysis and Design Under Uncertainty,” Computers & Chemical Engineering, Vol. 24, No. 9, 2000, pp. 2193–2209. doi:https://doi.org/10.1016/S0098-1354(00)00591-3 CrossrefGoogle Scholar

  • [35] Poon N. M. K. and Martins J. R. R. A., “An Adaptive Approach to Constraint Aggregation Using Adjoint Sensitivity Analysis,” Structural and Multidisciplinary Optimization, Vol. 34, No. 1, 2007, pp. 61–73. doi:https://doi.org/10.1007/s00158-006-0061-7 SMOTB4 1615-1488 CrossrefGoogle Scholar

  • [36] Abu-Zurayk M., Ilić C., Schuster A. and Liepelt R., “Effect of Gradient Approximations on Aero-Structural Gradient-Based Wing Optimization,” Proceedings of EUROGEN 2017, ECCOMAS Thematic Conference, Springer International Publ., 2019. doi:https://doi.org/10.1007/978-3-319-89890-2 Google Scholar

  • [37] Lambe A. B., Martins J. R. R. A. and Kennedy G. J., “An Evaluation of Constraint Aggregation Strategies for Wing Box Mass Minimization,” Structural and Multidisciplinary Optimization, Vol. 55, No. 1, 2017, pp. 257–277. doi:https://doi.org/10.1007/s00158-016-1495-1 SMOTB4 1615-1488 CrossrefGoogle Scholar

  • [38] Achard T., Blondeau C. and Ohayon R., “An Uncoupled Approach to Compute Aero-Structure Gradients Using High-Fidelity CFD-CSM,” 17th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2016-4121, 2016. doi:https://doi.org/10.2514/6.2016-4121 LinkGoogle Scholar

  • [39] Vanderplaats G. N. and Salajegheh E., “New Approximation Method for Stress Constraints in Structural Synthesis,” AIAA Journal, Vol. 27, No. 3, 1989, pp. 352–358. doi:https://doi.org/10.2514/3.10119 AIAJAH 0001-1452 LinkGoogle Scholar

  • [40] Schmitt V. and Charpin F., “Pressure Distributions on the ONERA M6 Wing at Transonic Mach Numbers,” Experimental Data Base for Computer Program Assessment, AGARD Advisory Rept. AR-138, Neuilly sur Seine, France, 1979. Google Scholar

  • [41] Vassberg J. C., DeHann M. A., Rivers S. M. and Wahls R. A., “Development of a Common Research Model for Applied CFD Validation Studies,” 26th AIAA Applied Aerodynamics Conference, AIAA Paper 2008-6919, Aug. 2008. doi:https://doi.org/10.2514/6.2008-6919 LinkGoogle Scholar

  • [42] Blondeau C. and Salah El Din I., “A Bi-Level High Fidelity Aero-Structural Integrated Design Methodology—A Focus on the Structural Sizing Process,” Proceedings of 3rd Aircraft Structural Design Conference, Royal Aeronautical Soc. (RAeS), 2012, pp. 176–189. Google Scholar

  • [43] Vanderplaats G. N., “An Efficient Feasible Directions Algorithm for Design Synthesis,” AIAA Journal, Vol. 22, No. 11, 1984, pp. 1633–1640. doi:https://doi.org/10.2514/3.8829 AIAJAH 0001-1452 LinkGoogle Scholar

Previous article
Next article