The Exact Solution Of The Three-Dimensional Boundary Value Problem For A Rotating Viscoelastic Disk

Summary In this paper, the author’s previously proposed method for the exact solution of quasi-static problems of the linear isotropic theory of viscoelasticity is improved using a three-dimensional boundary value problem of a rotating disk as an example. The two creep functions used in the constitutive relations are assumed to be independent; the viscoelastic Poisson’s ratio is assumed to vary with time. Both a solid disk and a disk with a central circular hole are considered. For arbitrary creep functions, an exact solution to the problem under consideration is presented in the form of analytical formulas for the stress, strain, and displacement components. The solution is formulated as a theorem and is of independent interest as an exact solution to this problem. At the same time, the obtained solution can be used in testing various numerical methods.