growing surface, 3D material, axial symmetry, Lame parameters

The article provides a solution to a boundary value problem that simulates the processes of synthesis of a 3D material under conditions of axial symmetry. A method for solving the stated boundary value problem has been developed. The condition of thin-walledness allows us to study the finite displacements of the cylinder points under the condition of small deformations. This, in particular, makes it possible to solve the problem with exact boundary conditions on a moving surface. The features of the behavior of the main characteristics, which depend on the pressure on the inner surface of the cylinder, the interference on the build-up surface, and the speed of its propagation, are discussed. The distributions of circumferential and radial stresses are obtained. The results obtained can be used in modeling the processes of synthesis of 3D woven materials.

Stadnik Nikita Eduardovich, Researcher, Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences, 101, korp. 1, pr. Vernadskogo, Moscow, 119526, Russian Federation.