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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Angheluta-Bauer, Luiza / Chen, Xi / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi / Yang, Xu

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Volume 20, Issue 3-4


The Optimal Design of a Functionally Graded Corrugated Cylindrical Shell under Axisymmetric Loading

I. I. Andrianov / J. Awrejcewicz
  • Corresponding author
  • Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowski St., Lodz PL-90-924, Poland
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/ A.A. Diskovsky
  • Department of Economic and Law Security, Dnipropetrovsk State University of Internal Affairs, 23 Gagarina Str., Dnipro UA-49005, Ukraine
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Published Online: 2019-03-13 | DOI: https://doi.org/10.1515/ijnsns-2018-0156


Optimization of parameters of the corrugated shell aims to achieve its minimum weight while keeping maximum stiffness ability. How an introduction of functionally graded corrugations resulted in improved efficiency of this thin-walled structure is demonstrated. The corrugations are graded varying their pitch. The effect of variation in pitch is studied. Homogenization approach gives explicit expressions to calculate the equivalent shell properties. Then well-elaborate methods of optimal design theory are used. The illustrative examples for hydrostatic load demonstrate a high efficiency of the used method.

Keywords: cylindrical shell; corrugations; optimization; design; homogenization

MSC 2010: 65Kxx; 74Kxx; 74Qxx


  • [1]

    I. Dayyani, A. D. Shaw, E. I. Saavedra Flores and M. I. Friswell, The mechanics of composite corrugated structures: A review with applications in morphing aircraft, Comp. Struct. 133 (2015), 358–380.CrossrefGoogle Scholar

  • [2]

    S. Rawat, A. Narayanan, T. Nagendiran and A. K. Upadhyay, Collapse behavior and energy absorption in elliptical tubes with functionally graded corrugations, Proc. Eng. 173 (2017), 1374–1381.CrossrefGoogle Scholar

  • [3]

    F. Guinea, M. I. Katsnelson and M. A. H. Vozmediano, Midgap states and charge inhomogeneities in corrugated graphene, Phys. Rev. B 77 (7) (2008), 075422.CrossrefWeb of ScienceGoogle Scholar

  • [4]

    I. V. Andrianov, J. Awrejcewicz and A. A. Diskovsky, Sensitivity analysis in design of constructions made of functionally graded materials, Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sc. 227 (1) (2013), 19–28.CrossrefGoogle Scholar

  • [5]

    I. V. Andrianov, J. Awrejcewicz and A. A. Diskovsky, Optimal design of a functionally graded corrugated rods subjected to longitudinal deformation, Arch. Appl. Mech. 85 (2015), 303–314.CrossrefWeb of ScienceGoogle Scholar

  • [6]

    I. V. Andrianov, A. A. Diskovsky and E. Syerko, Optimal design of a circular diaphragm using the homogenization approach, Math. Mech. Sol. 22 (3) (2017), 283–303.CrossrefGoogle Scholar

  • [7]

    I. V. Andrianov, J. Awrejcewicz and A. A. Diskovsky, Optimal design of a functionally graded corrugated cylindrical shell subjected to axisymmetric loading, Arch. Appl. Mech. 88 (2018), 1027–1039.CrossrefWeb of ScienceGoogle Scholar

  • [8]

    A. G. Kolpakov, Design of corrugated plates with extreme stiffnesses, J. Appl. Mech. Tech. Phys. 58 (3) (2017), 495–502.Web of ScienceCrossrefGoogle Scholar

  • [9]

    Y. S. Tian and T. J. Lu, Optimal design of compression corrugated panels, Thin-Wall. Struct. 43 (1) (2005), 477–498.CrossrefGoogle Scholar

  • [10]

    T. Flatscher, T. Daxner, D. H. Pahr and F. G. Rammerstorfer, Optimization of corrugated paperboard under local and global buckling constraints, Lect. Notes Appl. Comput. Mech. 55 (2011), 329–346.CrossrefGoogle Scholar

  • [11]

    N. V. Banichuk and B. L. Karihaloo, On the solution of optimization problems with non-smooth extremals, Int. J. Sol. Struct. 13 (8) (1977), 725–733.CrossrefGoogle Scholar

  • [12]

    A. F. Arkhangelskii and V. I. Gorbachev, Effective characteristics of corrugated plates, Mech. Sol. 42 (2007), 447–462.Web of ScienceCrossrefGoogle Scholar

  • [13]

    A. G. Kolpakov and S. I. Rakin, Calculation of the effective stiffness of the corrugated plate by solving the problem on the plate cross-section, J. Appl. Mech. Tech. Phys. 57 (4) (2016), 757–767.CrossrefGoogle Scholar

  • [14]

    E. Syerko, A. A. Diskovsky, I. V. Andrianov, S. Comas-Cardona and C. Binetruy, Corrugated beams mechanical behavior modeling by the homogenization method, Int. J. Sol. Struct. 50 (2013), 928–936.CrossrefGoogle Scholar

  • [15]

    Y. Zheng, V. L. Berdichevsky and W. Yu, An equivalent classical plate model of corrugated structures, Int. J. Sol. Struct. 51 (11) (2014), 2073–2083.CrossrefGoogle Scholar

  • [16]

    D. Briassoulis, Equivalent orthotropic properties of corrugated sheets, Comput. Struct. 23 (1986), 129–138.CrossrefGoogle Scholar

  • [17]

    Y. Xia, M. I. Friswell and E. I. Saavedra Flores, Equivalent models of corrugated panels, Int. J. Sol. Struct. 49 (13) (2012), 1453–1462.CrossrefGoogle Scholar

  • [18]

    I. V. Andrianov, A. A. Diskovsky and E.G. Kholod, Homogenization method in the theory of corrugated plates, Tech. Mech. 18 (1998), 123–133.Google Scholar

  • [19]

    S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, McGraw-Hill, New York, 1959.Google Scholar

  • [20]

    M. V. Pryjmak, Periodic functions with variable period, arXiv:1006.2792v1 [math.GM].Google Scholar

  • [21]

    A. Bensoussan, J.-L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam, 1978.Google Scholar

About the article

Received: 2018-05-31

Accepted: 2019-02-20

Published Online: 2019-03-13

Published in Print: 2019-05-26

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 20, Issue 3-4, Pages 387–398, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2018-0156.

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