On Some Approaches to Numerical Solution of Linear and Nonlinear Boundary Value Problems of the Theory of Layered Anisotropic Shells

  • Ya. M. Grigorenko
Conference paper


Some approaches are presented to numerical solutions of boundary-value problems, describing the stressed-deformed state of layered shells with isotropic and anisotropic layers of variable stiffness - in linear and geometrically non-linear formulation on the basis of classical and improved, more accurate models under non-uniform mechanical and thermal actions.


Circumferential Direction Layered Shell Nonlinear Eigenvalue Problem Coordinate Surface Axisymmetric Deformation 
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  1. 1.
    Grigorenko Ya.M. Isotropic and anisotropic layered shells of revolution with variable thickness. Kiev: Naukova Dumka. 1973. (In Russian).Google Scholar
  2. 2.
    Grigorenko Ya.M., Vasilenko A.T. Theory of shells with variable stiffness. Kiev: Naukova Dumka. 1981. In Methods of analysis and design of shells, volume 4. (In Russian).Google Scholar
  3. 3.
    Guz A.N., Grigorenko Ya.M., Babich I.Yu. and others. Mechanics of structures elements. In “Mechanics of composite materials and structures elements”, volume 2. Kiev: Naukova Dumka. 1983. (In Russian).Google Scholar
  4. 4.
    Grigorenko Ya.M., Mukoyed A.P. Computer-aided solution of non-linear problems of shell theory. Kiev: Vyshcha Shkola. 1983. (In Russian).Google Scholar
  5. 5.
    Grigorenko Ya.M., Vasilenko A.T., Kryukov N.N.: Numerical solution of non-linear problems of axisymmetric deformation of layered anisotropic shells of revolution. Mekhanika compositn. materialov, 6 (1983), 1023–1028. (In Russian).Google Scholar
  6. 6.
    Bellman R., Kalaba R.: Quasilinearization and non-linear boundary-value problems, the Rand Corporation, New York. 1965.Google Scholar
  7. 7.
    Grigorenko Ya.M., Kokoshin S.S. On one approach to the solution of shell theory problems by finite elements method. Do-klady AN USSR. Series A. No 3 (1980), 48–53. (In Russian).Google Scholar
  8. 8.
    Bifurcation theory and nonlinear eigenvalue problems. Edited by I.B. Keller and S. Antman, New York University. 1969.Google Scholar
  9. 9.
    Grigorenko Ya.M., Kryukov N.N.: On non-axisymmetric deformation of flexible shells of revolution under axisymmetric load, Prikladnaya Mekhanika, 7 (1985), 56–62. (In Russian)Google Scholar
  10. 10.
    Grigorenko Ya.M. Solution of shell theory problems by numerical analysis method. - Prikladnaya Mekhanika 10, 1984, 3–22. (In Russian).MathSciNetGoogle Scholar

Copyright information

© Springer Japan 1986

Authors and Affiliations

  • Ya. M. Grigorenko
    • 1
  1. 1.Institute of Mechanics of the Academy of Sciences of the Ukrainian SSRKievUSSR

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