Construction should be taking into account the influence of time factor on the stability of the structures. In the paper hereditary creep and homogenization theories are used to determine stresses in the layered elastic creeping array with a vertical shaft. Volterra correspondence principle was applied. As a result, the reduction of a time-dependent elastic creeping problem to a corresponding elastic problem became possible. The method proposes a way to determine average (effective) elastic creeping properties and homogenized stress field from known properties of the layers’ components. Creep kernels are of a convolution type and are taken in the exponential form. The problem of heterogeneous elastic creeping environment is reduced to a problem of homogeneous transversely isotropic medium. Different boundary conditions on the cylindrical shaft’s surface were considered. An analytical solution was obtained. These explicit expressions can be useful for the necessary calculations in the construction practice.
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