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

Optimal design problems arising in mechanics of growing composite viscoelastic and elastic solids subjected to aging are considered. The growth means a continuous mass influx to the body surface. Due to this process, the size of the body increases in time. The mass influx with pretensioning causes the rise of stresses in the growing body. The purpose of the current study is to propose a new class of the optimal design problems for the growing viscoelastic composite solids subjected to aging, and to solve the mechanical design problems of this new type. In the current paper, we analyze the optimal preload distribution in the winding process for cylindrical solids. The proposed approach and the obtained new solutions are of a special interest and importance for the optimization of winding of composite pressure vessels.