Advances in aircraft and spacecraft science

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A multilevel framework for decomposition-based reliability shape and size optimization

  • Tamijani, Ali Y. (Department of Aerospace Engineering, Embry-Riddle Aeronautical University) ;
  • Mulani, Sameer B. (Department of Aerospace Engineering and Mechanics, University of Alabama) ;
  • Kapania, Rakesh K. (Department of Aerospace and Ocean Engineering, Virginia Tech)
  • Received : 2016.11.10
  • Accepted : 2017.02.06
  • Published : 2017.07.25
⟨ Previous Next ⟩

Abstract

A method for decoupling reliability based design optimization problem into a set of deterministic optimization and performing a reliability analysis is described. The inner reliability analysis and the outer optimization are performed separately in a sequential manner. Since the outer optimizer must perform a large number of iterations to find the optimized shape and size of structure, the computational cost is very high. Therefore, during the course of this research, new multilevel reliability optimization methods are developed that divide the design domain into two sub-spaces to be employed in an iterative procedure: one of the shape design variables, and the other of the size design variables. In each iteration, the probability constraints are converted into equivalent deterministic constraints using reliability analysis and then implemented in the deterministic optimization problem. The framework is first tested on a short column with cross-sectional properties as design variables, the applied loads and the yield stress as random variables. In addition, two cases of curvilinearly stiffened panels subjected to uniform shear and compression in-plane loads, and two cases of curvilinearly stiffened panels subjected to shear and compression loads that vary in linear and quadratic manner are presented.

Keywords

References

  1. Adams, B.M., Bohnhoff, W., Dalbey, K., Eddy, J., Eldred, M., Gay, D., Haskell, K., Hough, P.D. and Swiler, L. (2009), Dakota, a Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis: Version 5.0 User's Manual, Sandia National Laboratories, Tech. Rep. SAND2010-2183.
  2. Agarwal, H. and Renaud, J.E. (2006), "New decoupled framework for reliability-based design optimization", AIAA J. 44(7), 1524-1531. https://doi.org/10.2514/1.13510
  3. Agarwal, H., Renaud, J.E., Lee, J.C. and Watson, L.T. (2004), "A unilevel method for reliability based design optimization", Proceedings of the 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference.
  4. Ba-Abbad, M.A., Nikolaidis, E. and Kapania, R.K. (2006), "New approach for system reliability-based design optimization", AIAA J., 44(5), 1087-1096. https://doi.org/10.2514/1.17237
  5. Chen, X., Hasselman, T.K. and Neill, D.J. (1997), "Reliability based structural design optimization for practical applications", Proceedings of the 38th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference.
  6. Cheng, G.D., Xu, L. and Jiang, L. (2006), "A sequential approximate programming strategy for reliabilitybased structural optimization", Comput. Struct., 84(21), 1353-1367. https://doi.org/10.1016/j.compstruc.2006.03.006
  7. Choi, S.K., Grandhi, R.V. and Canfield, R.A. (2006), Reliability-Based Structural Design, Springer-Verlag London.
  8. Du, X.P. and Chen, W. (2004), "Sequential optimization and reliability assessment method for efficient probabilistic design", J. Mech. Des., 126(2), 225-233. https://doi.org/10.1115/1.1649968
  9. Elishakoff, I. (2001), Interrelation Between Safety Factors and Reliability, NASA/CR-2001-211309.
  10. Hansen, L.U. and Horst, P. (2008), "Multilevel optimization in aircraft structural design evaluation", Comput. Struct., 86(1-2), 104-118. https://doi.org/10.1016/j.compstruc.2007.05.021
  11. Hasofer, A.M. and Lind, N.C. (1974), "Exact and invariant second-moment code format", J. Eng. Mech. Div., 100(1), 111-121.
  12. Kapania, R.K., Mulani, S.B., Tamijani, A., Sunny, M. and Joshi, P. (2013), "EBF3PanelOpt: A computational design environment for panels fabricated by additive manufacturing", Proceedings of the 51st AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition Proceedings.
  13. Kirjner-Neto, C., Polak, E. and Der Kiureghian, A. (1998), "An outer approximations approach to reliability-based optimal design of structures", J. Optim. Theor. Appl., 98(1), 1-16. https://doi.org/10.1023/A:1022647728419
  14. Kuschel, N. and Rackwitz, R. (1997), "Two basic problems in reliability-based structural optimization", Math. Meth. Operat. Res., 46(3), 309-333. https://doi.org/10.1007/BF01194859
  15. Li, F., Wu, T., Badiru, A., Hu, M.Q. and Soni, S. (2013), "A single-loop deterministic method for reliabilitybased design optimization", Eng. Optim., 45(4), 435-458. https://doi.org/10.1080/0305215X.2012.685071
  16. Lopez, R.H., Torii, A.J., Miguel, L.F.F. and De Cursi, J.E.S. (2015), "An approach for the global reliability based optimization of the size and shape of truss structures", Mech. Ind., 16(6), 603. https://doi.org/10.1051/meca/2015029
  17. Marler, R.T. and Arora, J.S. (2010), "The weighted sum method for multi-objective optimization: New insights", Struct. Multidiscipl. Optim., 41(6), 853-862. https://doi.org/10.1007/s00158-009-0460-7
  18. Mohaghegh, M. (2005), "Evolution of structures design philosophy and criteria", J. Aircr., 42(4), 814-831. https://doi.org/10.2514/1.11717
  19. Montemurro, M., Catapano, A. and Doroszewski, D. (2016), "A multi-scale approach for the simultaneous shape and material optimisation of sandwich panels with cellular core", Compos. Part B: Eng., 91, 458-472. https://doi.org/10.1016/j.compositesb.2016.01.030
  20. Mulani, S.B., Slemp, W.C.H. and Kapania, R.K. (2013), "EBF3PanelOpt: An optimization framework for curvilinear blade-stiffened panels", Thin Wall Struct., 63, 13-26. https://doi.org/10.1016/j.tws.2012.09.008
  21. Niu, M.C.Y. (2011), Airframe Stress Analysis and Sizing, Adaso/Adastra Engineering Center.
  22. Qu, X. and Haftka, R.T. (2004), "Reliability-based design optimization using probabilistic sufficiency factor", Struct. Multidiscipl. Optim., 27(5), 314-325. https://doi.org/10.1007/s00158-004-0390-3
  23. Shan, S.Q. and Wang, G.G. (2008), "Reliable design space and complete single-loop reliability-based design optimization", Reliab. Eng. Syst. Safe., 93(8), 1218-1230. https://doi.org/10.1016/j.ress.2007.07.006
  24. Tamijani, A.Y., Mulani, S.B. and Kapania, R.K. (2014), "A framework combining meshfree analysis and adaptive kriging for optimization of stiffened panels", Struct. Multidiscipl. Optim., 49(4), 577-594. https://doi.org/10.1007/s00158-013-0993-7
  25. Wang, X., Kennedy, D. and Williams, F. (1997), "A two level decomposition method for shape optimization of structures", J. Numer. Meth. Eng., 40(1), 75-88. https://doi.org/10.1002/(SICI)1097-0207(19970115)40:1<75::AID-NME51>3.0.CO;2-G
  26. Wu, Y.T., Shin, Y., Sues, R. and Cesare, M. (2001), "Safety-factor based approach for probability-based design optimization", Proceedings of the 19th AIAA Applied Aerodynamics Conference.
  27. Yao, W., Chen, X.Q., Luo, W.C., Van Tooren, M. and Guo, J. (2011), "Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles", Prog. Aerosp. Sci., 47(6), 450-479. https://doi.org/10.1016/j.paerosci.2011.05.001
  28. Yi, P., Cheng, G.D. and Jiang, L. (2008), "A sequential approximate programming strategy for performancemeasure-based probabilistic structural design optimization", Struct. Saf., 30(2), 91-109. https://doi.org/10.1016/j.strusafe.2006.08.003

Cited by

  1. Multistage Reliability-Based Design Optimization and Application to Aircraft Conceptual Design vol.55, pp.5, 2017, https://doi.org/10.2514/1.c032099
  2. Fast Precision Margin with the First-Order Reliability Method vol.57, pp.11, 2017, https://doi.org/10.2514/1.j058345
  3. An approach for the reliability-based design optimization of shape memory alloy structure vol.49, pp.2, 2017, https://doi.org/10.1080/15397734.2019.1665541