Optimization of Thick-Walled Viscoelastic Hollow Polymer Cylinders by Artificial Heterogeneity Creation: Theoretical Aspects

A theoretical solution of the problem of thick-walled shell optimization by varying the mechanical characteristics of the material over the thickness of the structure is proposed, taking into account its rheological properties. The optimization technique is considered by the example of a cylindrical shell made of high-density polyethylene with hydroxyapatite subjected to internal pressure. Radial heterogeneity can be created by centrifugation during the curing of the polymer mixed with the additive. The nonlinear Maxwell–Gurevich equation is used as the law describing polymer creep. The relationship of the change in the additive content along with the radius r, at which the structure is equally stressed following the four classical criteria of fracture, is determined in an elastic formulation. Moreover, it is shown that a cylinder with equal stress at the beginning of the creep process ceases to be equally stressed during creep. Finally, an algorithm for defining the relationship of the additive mass content on coordinate r, at which the structure is equally stressed at the end of the creep process, is proposed. The developed algorithm, implemented in the MATLAB software, allows modeling both equally stressed and equally strength structures.