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**Equilibrium of a plate and a tube made of a stratified composite material with viscoelastic components.**
*(English.
Russian original)*
Zbl 0657.73043

Mosc. Univ. Mech. Bull. 42, No. 6, 20-24 (1987); translation from Vestn. Mosk. Univ., Ser. I 1987, No. 6, 78-82 (1987).

Using an averaging method, the quasi-static problem for an inhomogeneous viscoelastic medium is reduced to a series of problems of homogeneous anisotropic viscoelasticity. In the lowest approximation, the tensorial relaxation kernel of the reduced problem is a linear combination (with constant coefficients) of certain scalar viscoelastic operators. Solution of the reduced problem may be constructed from the analytical solution of the associated anisotropic elasticity problem (the latter problem is obtained by substituting the elastic moduli for the viscoelastic operators).

The present paper deals with the case when the solution of the associated elasticity problem can only be found numerically or experimentally but not analytically.

The forcing functions (inhomogeneous terms in the governing field equations) are separated into products of time-dependent and space- dependent functions. For each component of the forcing function, the solution is obtained numerically or experimentally and an analytical form of approximation solution is then constructed. These analytical solutions are finally combined to form the solution corresponding to the actual forcing function. The method is applied to two specific example problems and the resulting zeroth approximate viscoelastic solutions are compared to the elasticity solutions.

The paper is tensely written and uses certain results from recent Russian works that may not be easily accessible.

The present paper deals with the case when the solution of the associated elasticity problem can only be found numerically or experimentally but not analytically.

The forcing functions (inhomogeneous terms in the governing field equations) are separated into products of time-dependent and space- dependent functions. For each component of the forcing function, the solution is obtained numerically or experimentally and an analytical form of approximation solution is then constructed. These analytical solutions are finally combined to form the solution corresponding to the actual forcing function. The method is applied to two specific example problems and the resulting zeroth approximate viscoelastic solutions are compared to the elasticity solutions.

The paper is tensely written and uses certain results from recent Russian works that may not be easily accessible.

Reviewer: Yin Wanlee

### MSC:

74E30 | Composite and mixture properties |

74D05 | Linear constitutive equations for materials with memory |

74D10 | Nonlinear constitutive equations for materials with memory |

74K20 | Plates |

74K15 | Membranes |