Skip to main content

Multi-objective optimal design of stiffened laminated composite cylindrical shell with piezoelectric actuators

Abstract

The stiffeners and piezoelectric actuators are used in many aerospace structures as an auxiliary layer with laminated composites. A question then arises as to whether we can estimate the percentage of these materials in an efficient design. Due to the high computational cost, it is not easy to answer through numerical solutions. The objective of this paper is concurrently to maximize the buckling load and minimize the weight of the cylindrical shell. To reach this aim, a multi-objective optimization problem is developed based on the closed-form solutions of thermal/mechanical buckling and weight of the piezolaminated shell with eccentric/concentric stiffener. The Non-dominated Sorting Genetic Algorithm II (NSGA-II) is used for solving multi-criteria optimization. Shannon’s entropy-based TOPSIS decision-making algorithm is employed to select the best design from Pareto fronts. To illustrate the potential of lightweight optimal design in structural stability, the obtained optimal and conventional designs are compared.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

References

  1. Vosoughi, A., Darabi, A., Anjabin, N., Topal, U.: A mixed finite element and improved genetic algorithm method for maximizing buckling load of stiffened laminated composite plates. Aerosp. Sci. Technol. 70, 378–387 (2017)

    Article  Google Scholar 

  2. Wang, Y., Wang, F., Jia, S., Yue, Z.: Experimental and numerical studies on the stability behavior of composite panels stiffened by tilting hat-stringers. Compos. Struct. 174, 187–195 (2017)

    Article  Google Scholar 

  3. Patel, S., Sheikh, A.: Buckling response of laminated composite stiffened plates subjected to partial in-plane edge loading. Int. J. Comput. Methods Eng. Sci. Mech. 17(5–6), 322–338 (2016)

    MathSciNet  Article  Google Scholar 

  4. Huang, L., Sheikh, A.H., Ng, C.-T., Griffith, M.C.: An efficient finite element model for buckling analysis of grid stiffened laminated composite plates. Compos. Struct. 122, 41–50 (2015)

    Article  Google Scholar 

  5. Abramovich, H., Weller, T.: Repeated buckling and postbuckling behavior of laminated stringer-stiffened composite panels with and without damage. Int. J. Struct. Stab. Dyn. 10(04), 807–825 (2010)

    MATH  Article  Google Scholar 

  6. Bohlooly, M., Kouchakzadeh, M.A., Mirzavand, B., Noghabi, M.: Buckling and postbuckling of advanced grid stiffened truncated conical shells with laminated composite skins. Thin-Walled Struct. (2019). https://doi.org/10.1016/j.tws.2019.106528 (in press)

    Article  Google Scholar 

  7. Datchanamourty, B., Blandford, G.E.: Uncoupled/coupled buckling response of piezothermoelastic composite plates. J. Therm. Stress. 40(10), 1303–1319 (2017)

    Article  Google Scholar 

  8. Bohlooly, M., Mirzavand, B.: Thermomechanical buckling of hybrid cross-ply laminated rectangular plates. Adv. Compos. Mater. 26(5), 407–426 (2017)

    Article  Google Scholar 

  9. Bohlooly, M., Mirzavand, B.: Closed form solutions for buckling and postbuckling analysis of imperfect laminated composite plates with piezoelectric actuators. Compos. B Eng. 72, 21–29 (2015)

    Article  Google Scholar 

  10. Bohlooly, M., Mirzavand, B.: A closed-form solution for thermal buckling of cross-ply piezolaminated plates. Int. J. Struct. Stab. Dyn. 16(03), 1450112 (2016)

    MathSciNet  MATH  Article  Google Scholar 

  11. Mirzavand, B., Rezapour, P., Bohlooly, M.: Thermal buckling of shallow/nonshallow piezoelectric-composite cylindrical shells. Mech. Adv. Mater. Struct. 23(10), 1236–1243 (2016)

    Article  Google Scholar 

  12. Mirzavand, B., Bohlooly, M.: Thermal buckling of piezolaminated plates subjected to different loading conditions. J. Therm. Stress. 38(10), 1138–1162 (2015)

    Article  Google Scholar 

  13. Bohlooly, M., Mirzavand, B.: Postbuckling and deflection response of imperfect piezo-composite plates resting on elastic foundations under in-plane and lateral compression and electro-thermal loading. Mech. Adv. Mater. Struct. 25(3), 192–201 (2017)

    Article  Google Scholar 

  14. Shen, H.-S.: Postbuckling analysis of axially loaded piezolaminated cylindrical panels with temperature dependent properties. Compos. Struct. 79(3), 390–403 (2007)

    Article  Google Scholar 

  15. Mirzavand, B., Bohlooly, M.: Higher-order stability analysis of imperfect laminated piezo-composite plates on elastic foundations under electro-thermo-mechanical loads. J. Solid Mech. 11(3), 550–569 (2019)

    Google Scholar 

  16. Fard, K.M., Bohlooly, M.: Postbuckling of piezolaminated cylindrical shells with eccentrically/concentrically stiffeners surrounded by nonlinear elastic foundations. Compos. Struct. 171, 360–369 (2017)

    Article  Google Scholar 

  17. Bohlooly, M., Malekzadeh Fard, K.: Buckling and postbuckling of concentrically stiffened piezo-composite plates on elastic foundations. J. Appl. Comput. Mech. 5(1), 128–140 (2019)

    Google Scholar 

  18. Rao, G.V., Narayanaswami, R.: Optimum design of cantilever columns in the post buckling region with constraint on axial load—an optimality criterion approach. Comput. Struct. 12(6), 843–848 (1980)

    MATH  Article  Google Scholar 

  19. Ruiqiang, Q.: Weight optimization of stiffened cylinders under axial compression. Comput. Struct. 21(5), 945–952 (1985)

    MATH  Article  Google Scholar 

  20. Sun, G., Hansen, J.: Optimal design of laminated-composite circular-cylindrical shells subjected to combined loads. J. Appl. Mech. 55(1), 136–142 (1988)

    MATH  Article  Google Scholar 

  21. Lanzi, L., Giavotto, V.: Post-buckling optimization of composite stiffened panels: computations and experiments. Compos. Struct. 73(2), 208–220 (2006)

    Article  Google Scholar 

  22. Król, M., Krużelecki, J., Trybuła, D.: Optimal stabilization of the post-buckling path for cylindrical shells under external pressure. Eng Optim. 41(1), 59–72 (2009)

    Article  Google Scholar 

  23. Bisagni, C., Lanzi, L.: Post-buckling optimisation of composite stiffened panels using neural networks. Compos. Struct. 58(2), 237–247 (2002)

    Article  Google Scholar 

  24. Falzon, B., Faggiani, A.: The use of a genetic algorithm to improve the postbuckling strength of stiffened composite panels susceptible to secondary instabilities. Compos. Struct. 94(3), 883–895 (2012)

    Article  Google Scholar 

  25. Foryś, P.: Optimization of cylindrical shells stiffened by rings under external pressure including their post-buckling behaviour. Thin-Walled Struct. 95, 231–243 (2015)

    Article  Google Scholar 

  26. Wang, C., Xu, Y., Du, J.: Study on the thermal buckling and post-buckling of metallic sub-stiffening structure and its optimization. Mater. Struct. 49(11), 4867–4879 (2016)

    Article  Google Scholar 

  27. Mo, Y., Ge, D., He, B.: Experiment and optimization of the hat-stringer-stiffened composite panels under axial compression. Compos. Part B: Eng. 84, 285–293 (2016)

    Article  Google Scholar 

  28. Wang, D., Abdalla, M.M., Zhang, W.: Buckling optimization design of curved stiffeners for grid-stiffened composite structures. Compos. Struct. 159, 656–666 (2017)

    Article  Google Scholar 

  29. Reitinger, R., Ramm, E.: Buckling and imperfection sensitivity in the optimization of shell structures. Thin-Walled Struct. 23(1–4), 159–177 (1995)

    Article  Google Scholar 

  30. Hao, P., Wang, B., Li, G., Meng, Z., Wang, L.: Hybrid framework for reliability-based design optimization of imperfect stiffened shells. AIAA J. 53(10), 2878–2889 (2015)

    Article  Google Scholar 

  31. Hao, P., Wang, B., Tian, K., Li, G., Sun, Y., Zhou, C.: Fast procedure for non-uniform optimum design of stiffened shells under buckling constraint. Struct. Multidiscip. Optim. 55(4), 1503–1516 (2017)

    MathSciNet  Article  Google Scholar 

  32. Wang, B., Tian, K., Zhou, C., Hao, P., Zheng, Y., Ma, Y., Wang, J.: Grid-pattern optimization framework of novel hierarchical stiffened shells allowing for imperfection sensitivity. Aerosp. Sci. Technol. 62, 114–121 (2017)

    Article  Google Scholar 

  33. Topal, U., Uzman, Ü.: Multiobjective optimization of angle-ply laminated plates for maximum buckling load. Finite Elem. Anal. Des. 46(3), 273–279 (2010)

    Article  Google Scholar 

  34. Hwang, S.-F., Hsu, Y.-C., Chen, Y.: A genetic algorithm for the optimization of fiber angles in composite laminates. J. Mech. Sci. Technol. 28(8), 3163–3169 (2014)

    Article  Google Scholar 

  35. Zhao, W., Kapania, R.K.: Buckling analysis of unitized curvilinearly stiffened composite panels. Compos. Struct. 135, 365–382 (2016)

    Article  Google Scholar 

  36. Wang, D., Abdalla, M.M., Wang, Z.-P., Su, Z.: Streamline stiffener path optimization (SSPO) for embedded stiffener layout design of non-uniform curved grid-stiffened composite (NCGC) structures. Comput. Methods Appl. Mech. Eng. 344, 1021–1050 (2019)

    MathSciNet  Article  Google Scholar 

  37. Fischer, X., Nadeau, J.-P.: Research in Interactive Design Vol. 3: Virtual, Interactive and Integrated Product Design and Manufacturing for Industrial Innovation. Springer, Berlin (2011)

    Book  Google Scholar 

  38. Legardeur, J., Merlo, C., Fischer, X.: An integrated information system for product design assistance based on artificial intelligence and collaborative tools. Int. J. Prod. Lifecycle Manag. 1(3), 211–229 (2006)

    Article  Google Scholar 

  39. Ordaz-Hernandez, K., Fischer, X., Bennis, F.: Granular modelling for virtual prototyping in interactive design. Virtual Phys. Prototyp. 2(2), 111–126 (2007)

    Article  Google Scholar 

  40. Brush, D.O., Almroth, B.O., Hutchinson, J.: Buckling of bars, plates, and shells. J. Appl. Mech. 42, 911 (1975)

    MATH  Article  Google Scholar 

  41. Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press, Boca Raton (2004)

    MATH  Book  Google Scholar 

  42. Bohlooly, M., Mirzavand, B., Fard, K.M.: An analytical approach for postbuckling of eccentrically or concentrically stiffened composite double curved panel on nonlinear elastic foundation. Appl. Math. Model. 62, 415–435 (2018)

    MathSciNet  Article  Google Scholar 

  43. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  44. Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength Pareto evolutionary algorithm. TIK Rep. 103, 1 (2001). https://doi.org/10.3929/ethz-a-004284029

    Article  Google Scholar 

  45. Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)

    Article  Google Scholar 

  46. Tzeng, G.-H., Huang, J.-J.: Multiple Attribute Decision Making: Methods and Applications. CRC Press, Boca Raton (2011)

    MATH  Book  Google Scholar 

  47. Yoon, K.P., Hwang, C.-L.: Multiple Attribute Decision Making: An Introduction, vol. 104. Sage, Thousand Oaks (1995)

    Book  Google Scholar 

  48. Deng, H., Yeh, C.-H., Willis, R.J.: Inter-company comparison using modified TOPSIS with objective weights. Comput. Oper. Res. 27(10), 963–973 (2000)

    MATH  Article  Google Scholar 

  49. Khodaygan, S., Golmohammadi, A.: Multi-criteria optimization of the part build orientation (PBO) through a combined meta-modeling/NSGAII/TOPSIS method for additive manufacturing processes. Int. J. Interact. Des. Manuf. 12(3), 1071–1085 (2018)

    Article  Google Scholar 

  50. Khodaygan, S.: An interactive method for computer-aided optimal process tolerance design based on automated decision making. Int. J. Interact. Des. Manuf. 13(1), 349–364 (2019)

    Article  Google Scholar 

  51. Khodaygan, S.: Meta-model based multi-objective optimisation method for computer-aided tolerance design of compliant assemblies. Int. J. Comput. Integr. Manuf. 32(1), 27–42 (2019)

    Article  Google Scholar 

  52. Shen, H.-S.: Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments. Part I: Axially-loaded shells. Compos. Struct. 93(8), 2096–2108 (2011)

    Article  Google Scholar 

  53. Shen, H.-S.: Thermal postbuckling behavior of anisotropic laminated cylindrical shells with temperature-dependent properties. AIAA J. 46(1), 185–193 (2008)

    Article  Google Scholar 

  54. Xu, C., Wu, M.-Z., Hamdaoui, M.: Mixed integer multi-objective optimization of composite structures with frequency-dependent interleaved viscoelastic damping layers. Comput. Struct. 172, 81–92 (2016)

    Article  Google Scholar 

  55. Vo-Duy, T., Duong-Gia, D., Ho-Huu, V., Vu-Do, H., Nguyen-Thoi, T.: Multi-objective optimization of laminated composite beam structures using NSGA-II algorithm. Compos. Struct. 168, 498–509 (2017)

    Article  Google Scholar 

  56. Vosoughi, A., Nikoo, M.: Maximum fundamental frequency and thermal buckling temperature of laminated composite plates by a new hybrid multi-objective optimization technique. Thin-Walled Struct. 95, 408–415 (2015)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Saeed Khodaygan.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Khodaygan, S., Bohlooly, M. Multi-objective optimal design of stiffened laminated composite cylindrical shell with piezoelectric actuators. Int J Interact Des Manuf 14, 595–611 (2020). https://doi.org/10.1007/s12008-020-00644-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12008-020-00644-1

Keywords

  • Stiffened laminated composite
  • Piezoelectric actuators
  • Pareto fronts
  • NSGA-II
  • Shannon’s entropy based TOPSIS