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.
Similar content being viewed by others
References
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)
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)
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)
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)
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)
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)
Datchanamourty, B., Blandford, G.E.: Uncoupled/coupled buckling response of piezothermoelastic composite plates. J. Therm. Stress. 40(10), 1303–1319 (2017)
Bohlooly, M., Mirzavand, B.: Thermomechanical buckling of hybrid cross-ply laminated rectangular plates. Adv. Compos. Mater. 26(5), 407–426 (2017)
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)
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)
Mirzavand, B., Rezapour, P., Bohlooly, M.: Thermal buckling of shallow/nonshallow piezoelectric-composite cylindrical shells. Mech. Adv. Mater. Struct. 23(10), 1236–1243 (2016)
Mirzavand, B., Bohlooly, M.: Thermal buckling of piezolaminated plates subjected to different loading conditions. J. Therm. Stress. 38(10), 1138–1162 (2015)
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)
Shen, H.-S.: Postbuckling analysis of axially loaded piezolaminated cylindrical panels with temperature dependent properties. Compos. Struct. 79(3), 390–403 (2007)
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)
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)
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)
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)
Ruiqiang, Q.: Weight optimization of stiffened cylinders under axial compression. Comput. Struct. 21(5), 945–952 (1985)
Sun, G., Hansen, J.: Optimal design of laminated-composite circular-cylindrical shells subjected to combined loads. J. Appl. Mech. 55(1), 136–142 (1988)
Lanzi, L., Giavotto, V.: Post-buckling optimization of composite stiffened panels: computations and experiments. Compos. Struct. 73(2), 208–220 (2006)
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)
Bisagni, C., Lanzi, L.: Post-buckling optimisation of composite stiffened panels using neural networks. Compos. Struct. 58(2), 237–247 (2002)
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)
Foryś, P.: Optimization of cylindrical shells stiffened by rings under external pressure including their post-buckling behaviour. Thin-Walled Struct. 95, 231–243 (2015)
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)
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)
Wang, D., Abdalla, M.M., Zhang, W.: Buckling optimization design of curved stiffeners for grid-stiffened composite structures. Compos. Struct. 159, 656–666 (2017)
Reitinger, R., Ramm, E.: Buckling and imperfection sensitivity in the optimization of shell structures. Thin-Walled Struct. 23(1–4), 159–177 (1995)
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)
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)
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)
Topal, U., Uzman, Ü.: Multiobjective optimization of angle-ply laminated plates for maximum buckling load. Finite Elem. Anal. Des. 46(3), 273–279 (2010)
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)
Zhao, W., Kapania, R.K.: Buckling analysis of unitized curvilinearly stiffened composite panels. Compos. Struct. 135, 365–382 (2016)
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)
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)
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)
Ordaz-Hernandez, K., Fischer, X., Bennis, F.: Granular modelling for virtual prototyping in interactive design. Virtual Phys. Prototyp. 2(2), 111–126 (2007)
Brush, D.O., Almroth, B.O., Hutchinson, J.: Buckling of bars, plates, and shells. J. Appl. Mech. 42, 911 (1975)
Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press, Boca Raton (2004)
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)
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)
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
Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)
Tzeng, G.-H., Huang, J.-J.: Multiple Attribute Decision Making: Methods and Applications. CRC Press, Boca Raton (2011)
Yoon, K.P., Hwang, C.-L.: Multiple Attribute Decision Making: An Introduction, vol. 104. Sage, Thousand Oaks (1995)
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)
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)
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)
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)
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)
Shen, H.-S.: Thermal postbuckling behavior of anisotropic laminated cylindrical shells with temperature-dependent properties. AIAA J. 46(1), 185–193 (2008)
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)
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)
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)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12008-020-00644-1