Evolution of Stresses and Deformations in Hollow Cylinder with Variable Material Composition: Mathematical Modeling and Optimization⁎

The present paper is aimed at modelling and optimization of stress-strain state for a multilayered structure, which is represented by a hollow hyperelastic cylinder. Two cases are considered. In the first case the structure is assembled by a finite number of hollow cylinders (discrete assembling process). The second case is a limit for the discrete processes, when a number of layers increases indefinitely with a fixed total thickness of the whole structure. It is convenient to use the non-Euclidean approach to investigate so obtained continuous structure. The optimization for stress intensity have been performed over the control function of inner pressure. The distributions of Ricci invariant that characterize measure of non-Euclidity are obtained for the uncontrolled and optimized processes. The proposed approach can be used to determine the optimal strategies for synthesis of 3D-details by DLP stereolithography.