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Generatrix shape optimization of stiffened shells for low imperfection sensitivity

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Abstract

According to previous studies, stiffened shells with convex hyperbolic generatrix shape are less sensitive to imperfections. In this study, the effects of generatrix shape on the performances of elastic and plastic buckling in stiffened shells are investigated. Then, a more general description of generatrix shape is proposed, which can simply be expressed as a convex B-spline curve (controlled by four key points). An optimization framework of stiffened shells with a convex B-spline generatrix is established, with optimization objective being measured in terms of nominal collapse load, which can be expressed as a weighted sum of geometrically imperfect shells. The effectiveness of the proposed framework is demonstrated by a detailed comparison of the optimum designs for the B-spline and hyperbolic generatrix shapes. The decrease of imperfection sensitivity allows for a significant weight saving, which is particularly important in the development of future heavy-lift launch vehicles.

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References

  1. Weingarten V I, Seide P, Peterson J P. Buckling of thin-walled circular cylinders. NASA SP-8007, 1968

    Google Scholar 

  2. Arbocz J, Starnes J H. Future directions and challenges in shell stability analysis. Thin-Walled Struct, 2002, 40: 729–754

    Article  Google Scholar 

  3. Hühne C, Rolfes R, Breitbach E, et al. Robust design of composite cylindrical shells under axial compression-simulation and validation. Thin-Walled Struct, 2008, 46: 947–962

    Article  Google Scholar 

  4. Wang B, Hao P, Li G, et al. Determination of realistic worst imperfection for cylindrical shells using optimization algorithm. Struct Multidiscip Optim, 2013, 48: 777–794

    Article  Google Scholar 

  5. Hilburger M W, Starnes J H. Effects of imperfections of the buckling response of composite shells. Thin-Walled Struct, 2004, 42: 369–397

    Article  Google Scholar 

  6. Leriche R, Haftka R T. Optimization of laminate stacking sequence for buckling load maximization by genetic algorithm. AIAA J, 1993, 31: 951–956

    Article  Google Scholar 

  7. Bushnell D, Bushnell W D. Minimum-weight design of a stiffened panel via PANDA2 and evaluation of the optimized panel via STAGS. Comput Struct, 1994, 50: 569–602

    Article  Google Scholar 

  8. Venkataraman S, Lamberti L, Haftka R T. Challenges in comparing numerical solutions for optimum weights of stiffened shells. J Spacecraft Rockets, 2003, 40: 183–192

    Article  Google Scholar 

  9. Wu H, Yan Y, Yan W, et al. Adaptive approximation-based optimization of composite advanced grid-stiffened cylinder. Chin J Aeronaut, 2010, 23: 423–429

    Article  Google Scholar 

  10. Vescovini R, Bisagni C. Buckling analysis and optimization of stiffened composite flat and curved panels. AIAA J, 2012, 50: 904–915

    Article  Google Scholar 

  11. Hao P, Wang B, Li G. Surrogate-based optimum design for stiffened shells with adaptive sampling. AIAA J, 2012, 50: 2389–2407

    Article  Google Scholar 

  12. Obrecht H, Rosenthal B, Fuchs P, et al. Buckling, postbuckling and imperfection-sensitivity: Old questions and some new answers. Comp Mech, 2006, 37: 498–506

    Article  MATH  Google Scholar 

  13. Reitinger R, Ramm E. Maximizing structural efficiency including buckling and imperfection sensitivity. In: Proceedings of 5th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. Panama City Beach, 1994. 1228–1238

    Google Scholar 

  14. Gao H, Ji B, Jäger I L, et al. Materials become insensitive to flaws at nanoscale: Lessons from nature. Proc Natl Acad Sci USA, 2003, 100: 5597–5600

    Article  Google Scholar 

  15. Wang B, Hao P, Li G, et al. Optimum design of hierarchical stiffened shells for low imperfection sensitivity. Acta Mech Sin, 2014, 30: 391–402

    Article  Google Scholar 

  16. Hrinda G A. Effects of shell-buckling knockdown factors in large cylindrical shells. In: Proceedings of 5th International Conference on High Performance Structures and Materials. Tallinn, Estonia, 2010

    Google Scholar 

  17. Hao P, Wang B, Li G, et al. Surrogate-based optimization of stiffened shells including load-carrying capacity and imperfection sensitivity. Thin-Walled Struct, 2013, 72: 164–174

    Article  Google Scholar 

  18. Tomás A, Tovar J P. The influence of initial geometric imperfections on the buckling load of single and double curvature concrete shells. Comput Struct, 2012, 96: 34–45

    Article  Google Scholar 

  19. Yang H, Zhan M, Liu Y L, et al. Some advanced plastic processing technologies and their numerical simulation. J Mat Process Technol, 2004, 151: 63–69

    Article  Google Scholar 

  20. Li C, Yang H, Zhan M, et al. Effects of process parameters on numerical control bending process for large diameter thin-walled aluminum alloy tubes. Trans Nonferrous Met Soc China, 2009, 19: 668–673

    Article  Google Scholar 

  21. Lanzi L. A numerical and experimental investigation on composite stiffened panels into post-buckling. Thin-walled Struct, 2004, 42: 1645–1664

    Article  Google Scholar 

  22. Lanzi L, Giavotto V. Post-buckling optimization of composite stiffened panels: Computations and experiments. Compos Struct, 2006, 73: 208–220

    Article  Google Scholar 

  23. Hao P, Wang B, Li G, et al. Worst Multiple Perturbation Load Approach of stiffened shells with and without cutouts for improved knockdown factors. Thin-Walled Struct, 2014, 82: 321–330

    Article  Google Scholar 

  24. Dyn N, Levin D, Rippa S. Numerical procedures for surface fitting of scattered data by radial functions. SIAM J Sci Stat Comput, 1986, 7: 639–659

    Article  MathSciNet  MATH  Google Scholar 

  25. Jin R, Chen W, Simpson T W. Comparative studies of metamodelling techniques under multiple modelling criteria. Struct Multidiscip Optim, 2001 23: 1–13

    Article  Google Scholar 

  26. Vitali R, Park O, Haftka R T, et al. Structural optimization of a hat-stiffened panel using response surfaces. J Aircraft, 2002, 39: 158–166

    Article  Google Scholar 

  27. Rikards R, Abramovich H, Kalnins K, et al. Surrogate modeling in design optimization of stiffened composite shells. Compos Struct, 2006, 73: 244–251

    Article  Google Scholar 

  28. MarÍn L, Trias D, Badalló P, et al. Optimization of composite stiffened panels under mechanical and hygrothermal loads using neural networks and genetic algorithms. Compos Struct, 2012, 94: 3321–3326

    Article  Google Scholar 

  29. Mazzolani F M, Mandara A, Di Lauro G. Plastic buckling of axially loaded aluminium cylinders: A new design approach. In: Proceedings of 4th International Conference on Coupled Instabilities in Metal Structures. Rome, Italy, 2004

    Google Scholar 

  30. Teng J G, Song C Y. Numerical models for nonlinear analysis of elastic shells with eigenmode-affine imperfections. Int J Solids Struct, 2001, 38: 3263–3280

    Article  MATH  Google Scholar 

  31. Anonymous. General rules-supplementary rules for the strength and stability of shell structures. Eurocode 3, 1999

  32. Mulani S B, Slemp W C H, Kapania R K. EBF3PanelOpt: An optimization framework for curvilinear blade-stiffened panels. Thinwalled Struct, 2013, 63: 13–26

    Google Scholar 

  33. Panda S, Padhy N P. Comparison of particle swarm optimization and genetic algorithm for FACTS-based controller design. Appl Soft Comput, 2008, 8: 1418–1427

    Article  Google Scholar 

  34. Reiko T. Distributed genetic algorithms. In: Proceedings of 3rd ICGA. San Francisco, 1989

    Google Scholar 

  35. Wong C C, Dean T A, Lin J. A review of spinning, shear forming and flow forming processes. Int J Mach Tools Manuf, 2003, 43: 1419–1435

    Article  Google Scholar 

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116023, China

    Bo Wang, Peng Hao & Gang Li

  2. Beijing Institute of Astronautical Systems Engineering, Beijing, 100076, China

    XiaoJun Wang, XiaoHan Tang & Yu Luan

Authors
  1. Bo Wang
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  2. Peng Hao
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  3. Gang Li
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  4. XiaoJun Wang
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  5. XiaoHan Tang
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  6. Yu Luan
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Correspondence to Peng Hao.

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Wang, B., Hao, P., Li, G. et al. Generatrix shape optimization of stiffened shells for low imperfection sensitivity. Sci. China Technol. Sci. 57, 2012–2019 (2014). https://doi.org/10.1007/s11431-014-5654-6

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  • DOI: https://doi.org/10.1007/s11431-014-5654-6

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