# Coupled Thermoelasticity Problem for Multilayer Composite Shells of Revolution. I. Theoretical Aspects of the Problem

## Abstract

On the basis of a general integral form of the variational principle of the least possible dissipation of energy of the nonequilibrium thermodynamics, we deduce a nonclassical nonsteady heat-conduction equation for multilayer polyreinforced shells of any shape. A method for the determination of the integral heat conductivities of reinforced layers is developed and the effective constitutive equations for the description of its thermoelastic behavior are proposed. A nonclassical model of deformation of the multilayer shell and a nonlinear model of distribution of the heat flux along the thickness of the layer are formulated. This allows us to take into account the transverse shear strains and guarantee the conditions of thermomechanical contact of the layers and the conditions of thermomechanical loading on the face surfaces of the shell. We construct a closed system of differential equations with the corresponding initial and boundary conditions for a coupled problem of thermoelastic deformation of layered composite shells and plates.

- Authors:

- Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Division of RAS (Russian Federation)
- Kuzbass State Technical University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771552

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 229; Journal Issue: 2; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; 42 ENGINEERING; BOUNDARY CONDITIONS; DEFORMATION; DIFFERENTIAL EQUATIONS; HEAT FLUX; HEATING LOAD; NONLINEAR PROBLEMS; SHEAR; STRAINS; SURFACES; THERMAL CONDUCTION; THERMODYNAMICS; THERMOELASTICITY; VARIATIONAL METHODS

### Citation Formats

```
Nemirovskii, Yu. V., and Babin, A. I.
```*Coupled Thermoelasticity Problem for Multilayer Composite Shells of Revolution. I. Theoretical Aspects of the Problem*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3672-9.

```
Nemirovskii, Yu. V., & Babin, A. I.
```*Coupled Thermoelasticity Problem for Multilayer Composite Shells of Revolution. I. Theoretical Aspects of the Problem*. United States. doi:10.1007/S10958-018-3672-9.

```
Nemirovskii, Yu. V., and Babin, A. I. Thu .
"Coupled Thermoelasticity Problem for Multilayer Composite Shells of Revolution. I. Theoretical Aspects of the Problem". United States. doi:10.1007/S10958-018-3672-9.
```

```
@article{osti_22771552,
```

title = {Coupled Thermoelasticity Problem for Multilayer Composite Shells of Revolution. I. Theoretical Aspects of the Problem},

author = {Nemirovskii, Yu. V. and Babin, A. I.},

abstractNote = {On the basis of a general integral form of the variational principle of the least possible dissipation of energy of the nonequilibrium thermodynamics, we deduce a nonclassical nonsteady heat-conduction equation for multilayer polyreinforced shells of any shape. A method for the determination of the integral heat conductivities of reinforced layers is developed and the effective constitutive equations for the description of its thermoelastic behavior are proposed. A nonclassical model of deformation of the multilayer shell and a nonlinear model of distribution of the heat flux along the thickness of the layer are formulated. This allows us to take into account the transverse shear strains and guarantee the conditions of thermomechanical contact of the layers and the conditions of thermomechanical loading on the face surfaces of the shell. We construct a closed system of differential equations with the corresponding initial and boundary conditions for a coupled problem of thermoelastic deformation of layered composite shells and plates.},

doi = {10.1007/S10958-018-3672-9},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 2,

volume = 229,

place = {United States},

year = {2018},

month = {2}

}