Mathematical modelling of three-dimensional stress-strain state of homogeneous and composite cylindrical axisymmetric shells

Arseniy G. Gorynin^a, Gleb L. Gorynin^b, Sergey K. Golushko<sup>ca

a</sup> Novosibirsk State University, Novosibirsk, Russian Federation
^b Surgut State University, Surgut, Russian Federation
^c Federal Research Center for Information and Computational Technologies, Novosibirsk, Russian Federation

Abstract: Application of the asymptotic splitting method for solving static problems of deformation of homogeneous isotropic and composite cylindrical shells is considered in this paper. The problem of deformation of a composite cylindrical shell subjected to internal axisymmetric load is studied. The solution is constructed by expanding components of the stress tensor and the displacement vector in powers of differential operators acting along the cylinder axis. As this takes place, a small parameter is the ratio of shell thickness to its length. A governing differential system of equations describing the deformation of a cylindrical shell is obtained. It is shown that developed mathematical model allows one to compute all components of the stress tensor for both thick-walled and thin-walled cylindrical shells. The obtained analytic and numerical solutions are compared with the finite element solution of the 2D axisymmetric problem.

Keywords: cylindrical shell, stress-strain state, method of asymptotic splitting, linear theory of elasticity, axisymmetric problem, finite element method.

UDC: 539.3

Received: 10.03.2023
Received in revised form: 15.06.2023
Accepted: 04.09.2023

Language: English