Abstract:
This paper deals with the development of a method for solving the problems of isotropic and anisotropic viscoelastic bodies based on the separation of spatial and temporal variables. In contrast to the classical method of separation of variables implying the transformation of systems of partial differential equations, a specific scheme of transformation of the constitutive equations for a viscoelastic body is proposed. As a result of these transformations, the elastic body equations are obtained, in which some known time functions are used in terms of the material constants of elasticity.
First, the constitutive equations of a linear viscoelastic body are considered. Using identical transformations, the equivalence of the constitutive equations for a viscoelastic medium and a comparative elastic medium is proved if the stresses are set at the boundary. In the same manner, the equivalence of viscoelastic and elastic media is proved if the displacements are specified at the boundary. Finally, a relation is identified between the parameters of the comparative elastic media for these two cases, and their mutual converse is justified. The real-problem example is solved and presented at the end of the paper.
Keywords:time-efficient moduli, identity of constitutive equations, interchangeability of constitutive equations of elasticity and viscoelasticity, the first and second boundary-value problems.
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