Optimal design problems in mechanics of growing composite solids, Part I: Preload optimization: Fid-Bau Portal

Optimal design problems in mechanics of growing composite solids, Part I: Preload optimization

Drozdov, A.D. / Kalamkarov, A.L.

A new class of the optimal design problems arising in mechanics of growing viscoelastic composite bodies subjected to aging is proposed. In the current paper, the problem of the optimal pretensioning in fabrication of composite pressure vessels by winding layers of a ribbon is considered. In this problem, an explicit solution (the dependence of the optimal preload intensity xi versus the polar radius r) for a nonaging material and an asymptotic analytical solution for an aging material of the ribbon is derived. A numerical analysis enables to study the influence of the rheological characteristics of material on the optimal pretensioning and to formulate the following recommendations: for a thick initial pressure vessel, the optimal preload intensity xi is practically independent of the radius r as well as of the internal pressure P; for a thin initial pressure vessel and sufficiently small internal pressure P, the optimal preload intensity xi monotonously decreases with the growth of the radius r and tends to a constant value in the region far enough from initial body; the rate of decrease is maximum for a nonaging material, and diminishes with the growth of the rate of aging. For a fixed time of the winding process, the increase of the rate of aging implies the increase of the optimal preload intensity xi at any point of the growing cylindrical body; and for a thin initial pressure vessels and sufficiently large internal pressure P, the optimal preload intensity xi monotonously increases with the growth of the radius r.