Lobachevskii Journal of Mathematics

, Volume 40, Issue 11, pp 1904–1914 | Cite as

Refined Equations of the Sandwich Shells Theory with Composite External Layers and a Transverse Soft Core at Average Bending

  • I. B. BadrievEmail author
  • V. N. PaimushinEmail author
  • M. A. ShihovEmail author


In the development of previously obtained results for the case of average bending, a refined geometrically nonlinear theory of static and dynamic deformation of sandwich plates and shells with a transversely soft core and external composite layers with low rigidity for transverse shears and transverse compression was constructed. It is based on the use of the refined Tymoshenko’s shear model for the carrier layers, taking into account lateral reduction, and for the transversally soft core, the simplified three-dimensional equations of the elasticity theory, which can be integrated along the transverse coordinate. The hypothesis of the similarity of the change laws of displacements across the thickness of the core during its static and dynamic deformation processes was adopted. When integrating the compiled equations of the elasticity theory to describe the stress-strain state, the two two-dimensional unknown functions are introduced that represent transverse shear stresses that are constant in thickness. Based on the generalized Lagrange and Ostrogradsky Hamilton variational principles for describing static and dynamic deformation processes with large indicators of the variability of the stress-strain state parameters, two-dimensional geometrically nonlinear equilibrium equations and general movements are constructed, which allow to reveal purely shear of buckling forms of the carrier layers during formation normal compressive stresses.

Keywords and phrases

sandwich plate sandwich shell transversally soft core carrier composite layer variability of a function average bending equilibrium equation motion equation stress-strain state buckling form 


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The research results were obtained with the financial support of the Russian Foundation for Basic Research (project no. 19-08-00073) and the Russian Science Foundation, project no. 19-19-00058 (Section 4) and project no. 16-11-10299 (Section 3).


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Kazan (Volga Region) Federal University, Institute of Computational Mathematics and Information TechnologiesKazanRussia
  2. 2.Kazan Tupolev National Research Technical University-KAI, Institute of Aviation, Land Vehicles and EnergeticsKazanRussia

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