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Mathematical Models of Multilayer Flexible Orthotropic Shells Under a Temperature Field

  • Vadim A. Krysko
  • Jan AwrejcewiczEmail author
  • Maxim V. Zhigalov
  • Valeriy F. Kirichenko
  • Anton V. Krysko
Chapter
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 42)

Abstract

In this chapter we present methods and algorithms for the numerical investigation of shell stability “in the large” of the following multilayer mathematical models: the Timoshenko second order of approximation (Volmir, Flexible plates and shells, Defense Technical Information Center, Gainesville, 1967, [1]), the Sheremetev–Pelekh–Reddy–Levinson third order of approximation (Levinson, J Sound Vib, 74:81–87, 1981, [2]; Reddy, J Appl Mech, 51:745–752, 1984, [3]; Sheremetev, Pelekh, Eng J 4(3):504–510, 1964, [4]), the Grigolyuk–Kulikov model (Grigolyuk, Kulikov, Multilayer reinforced shells: calculation of pneumatic tyres, Mashinostroenie, Moscow, 1988, [5]), and their modifications. We also construct novel mathematical models including a modified asymptotically compatible model obtained with the help of a stationary variant of the “projectional conditions” of the shell’s motion and a model with \(\varepsilon \)-regularization. In the latter case, a theorem on the existence of a general solution is formulated and proved. First a comparative analysis of the computational results in the framework of our mathematical models focused on stability estimation “in the large” of shallow multilayer orthotropic shells within the models and the Kirchhoff–Love first-order approximation model has been carried out.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Vadim A. Krysko
    • 1
  • Jan Awrejcewicz
    • 2
    Email author
  • Maxim V. Zhigalov
    • 1
  • Valeriy F. Kirichenko
    • 1
  • Anton V. Krysko
    • 3
  1. 1.Department of Mathematics and ModelingSaratov State Technical UniversitySaratovRussia
  2. 2.Department of Automation, Biomechanics and MechatronicsLodz University of TechnologyLodzPoland
  3. 3.Department of Applied Mathematics and Systems AnalysisSaratov State Technical UniversitySaratovRussia

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