On the non-classical mathematical models of coupled problems of thermo-elasticity for multi-layer shallow shells with initial imperfections

V. F. Kirichenko, J. Awrejcewicz, A. V. Kirichenko, A. V. Krysko, V. A. Krysko

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Mathematical modeling of evolutionary states of non-homogeneous multi-layer shallow shells with orthotropic initial imperfections belongs to one of the most important and necessary steps while constructing numerous technical devices, as well as aviation and ship structural members. In first part of the paper fundamental hypotheses are formulated which allow us to derive Hamilton-Ostrogradsky equations. The latter yield equations governing shell behavior within the applied hypotheses and modified Pelekh-Sheremetev conditions. The aim of second part of the paper is to formulate fundamental hypotheses in order to construct coupled boundary problems of thermo-elasticity which are used in non-classical mathematical models for multi-layer shallow shells with initial imperfections. In addition, a coupled problem for multi-layer shell taking into account a 3D heat transfer equation is formulated. Third part of the paper introduces necessary phase spaces for the second boundary value problem for evolutionary equations, defining the coupled problem of thermo-elasticity for a simply supported shallow shell. The theorem regarding uniqueness of the mentioned boundary value problem is proved. It is also proved that the approximate solution regarding the second boundary value problem defining condition for the thermo-mechanical evolution for rectangular shallow homogeneous and isotropic shells can be found using the Bubnov-Galerkin method.

Original languageEnglish
Pages (from-to)51-72
Number of pages22
JournalInternational Journal of Non-Linear Mechanics
Volume74
DOIs
Publication statusPublished - 1 Sep 2015
Externally publishedYes

Fingerprint

Shallow Shell
Coupled Problems
Thermoelasticity
Imperfections
Boundary value problems
Multilayer
Elasticity
Shell
Boundary Value Problem
Mathematical Model
Mathematical models
Defects
Necessary
Structural members
Aviation
Uniqueness Theorem
Galerkin methods
Boundary Problem
Galerkin Method
Ship

Keywords

  • General solutions
  • Non-classical theory
  • Non-linear boundary value problems
  • Shallow multi-layer shells

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

On the non-classical mathematical models of coupled problems of thermo-elasticity for multi-layer shallow shells with initial imperfections. / Kirichenko, V. F.; Awrejcewicz, J.; Kirichenko, A. V.; Krysko, A. V.; Krysko, V. A.

In: International Journal of Non-Linear Mechanics, Vol. 74, 01.09.2015, p. 51-72.

Research output: Contribution to journalArticle

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