General Problems of Diffraction in the Theory of Design: Nonlinear Shells and Plates Locally Interacting with Temperature Fields

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


This chapter is devoted to diffraction problems of plates/shells designed in a nonlinear way and interacting locally with temperature fields. In Section 4.1, a definition of the problem at hand is given and we emphasize the novel way required to study the structural members comprehensively, and the need to involve different PDEs in different parts of the mechanical objects under consideration is also emphasized.


  1. 1.
    Volmir, A. S. (1972). The Nonlinear Dynamics of Plates and Shells. Moscow (in Russian): Nauka.Google Scholar
  2. 2.
    Ladyzhenskaya, O. A. (1973). The Boundary Value Problems of Mathematical Physics. Berlin: Springer.Google Scholar
  3. 3.
    Ladyzhenskaya, O. A. (1969). The Mathematical Theory of Viscous Incompressible Flow. New York: Gordon and Breach.zbMATHGoogle Scholar
  4. 4.
    Mikhlin, S. G. (1970). Variational Methods in Mathematical Physics. Oxford: Pergamon.zbMATHGoogle Scholar
  5. 5.
    Grigolyuk, E. I., & Chulkov, P. P. (1973). Stability and Vibration of Three-Layer Shells. Moscow: Mashinostroyeniye.Google Scholar
  6. 6.
    Lions, J.-L. (1969). Some Problems of Solving Non-Linear Boundary Value Problems. Paris: Dunod-Gauthier-Villars.Google Scholar
  7. 7.
    Galimov, K. Z. (1975). Introduction to Nonlinear Theory of Thin Shells. Kazan (in Russian): Kazan University.Google Scholar

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

Personalised recommendations