Application of Genetic Algorithms to the Shape Optimization of the Nonlinearly Elastic Corrugated Membranes

  • Mikhail KaryakinEmail author
  • Taisiya Sigaeva
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 15)


Corrugated membranes are extremely important structural parts of a great number of devices, highly sensitive pressure sensors in particular. In engineering of corrugated shapes different factors could be taken into account as crucial. Among them – membrane’s work without buckling, buckling for the prescribed load, flatness of the membrane characteristic – dependence of the applied pressure on the liquid or gas volume, a lack of the plastic deformation and so on. In this paper an approach to different problems of optimization and design using genetic algorithm is proposed. To model elastic behavior of the membrane the non-linear equations based on the Kirchhoff-Love hypothesis and not imposed constrains on the shallowness of the membrane’s shape are used. Several multi-parameter families of the axially symmetric “design”, i.e. functions of the shape that describe the dependence of the middle surface prominence on the membrane radius, are considered. These designs were obtained due to special modifications of spherical dome, conical membrane and their integration. The value of the linear section length of the membrane characteristic served as an optimality criterion. The paper presents modified genetic algorithm, describes refinement mechanism of its settings and observes examples of the designs, which are optimal in the specified shape classes.


Genetic algorithm Corrugated membrane Nonlinear shell theory Shape optimization 


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This research was supported by the Federal target program “Scientific and pedagogical cadre of the innovated Russia during 2009–2013” (state contract P–361).


  1. 1.
    Back, T.: Evolutionary algorithms in heory and practice: evolution strategies, evolutionary programming, genetic algorithms. Oxford University Press, NY (1996)Google Scholar
  2. 2.
    Banichuk, N.V., Ivanova, S.Yu., Makeev, E.V.: Some problems of optimizing shell shape and thickness distribution on the basis of a genetic algorithm. Mech. Solids, 42(6), 956–964 (2007)CrossRefGoogle Scholar
  3. 3.
    Bletzinger, K.-U.: Form Finding and Optimization of Membranes and Minimal Surfaces. Tech. University of Denmark, Lyngby (1998)Google Scholar
  4. 4.
    Delfour, M.C., Zolesio, J.P.: Shapes and Geometries: Analysis, Differential Calculus and Optimization. SIAM, Philadelphia (2001)Google Scholar
  5. 5.
    Getman, I.P., Karyakin, M.I., Ustinov, U.A.: Nonlinear behavior analysis of circular membranes with arbitrary radius profile. J. Appl. Math. Mech. 74(6), 917–927 (2010)CrossRefGoogle Scholar
  6. 6.
    Gosling, P.D., Lewis, W.J.: Form-finding of prestressed membranes using a curved quadrilateral finite element for surface definition. Comput. Struct. 61(5), 871–883 (1996)CrossRefGoogle Scholar
  7. 7.
    Holland, J.H.: Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor MI (1975)Google Scholar
  8. 8.
    Lassila, T.: Optimal damping of a membrane and topological shape optimization. Struct. Multidisc. Optim. 38(1), 3438–3452 (2009)CrossRefGoogle Scholar
  9. 9.
    Rowe, J., Whitley, D., Barbulescu, L., Watson, J.P.: Properties of Gray and binary representations. Evol. Comput. 12, 47–76 (2004)CrossRefGoogle Scholar
  10. 10.
    Vorovich, I.I.: Nonlinear Theory of Shallow Shells. Springer, NY (1999)Google Scholar
  11. 11.
    Yuen, C.C., Aatmeeyata Gupta, S.K., Ray, A.K.: Multi-objective optimization of membrane separation modules using genetic algorithm. J. Membrane Sci. 176, 177–196 (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Southern Federal UniversityRostov-on-DonRussia
  2. 2.Southern Mathematical InstituteVladikavkazRussia

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