Geodesic
Mathematical modelling of three-dimensional stress-strain state of homogeneous and composite cylindrical axisymmetric shells
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 1, pp. 27-37.

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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. 
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Arseniy G. Gorynin; Gleb L. Gorynin; Sergey K. Golushko. Mathematical modelling of three-dimensional stress-strain state of homogeneous and composite cylindrical axisymmetric shells. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 17 (2024) no. 1, pp. 27-37. http://geodesic.mathdoc.fr/item/JSFU_2024_17_1_a3/

[1] G.L.Gorynin, Yu.V.Nemirovsky, Spatial tasks of bending and torsion of layered structures, Asymptotic splitting method, Novosibirsk, 2004 (in Russian)

[2] G.L.Gorynin, Y.V.Nemirovskii, “Deformation of laminated anisotropic bars in the three-dimensional statement 1. Transverse-longitudinal bending and edge compatibility condition”, Mechanics of Composite Materials, 45 (2009), 257–280 | DOI

[3] S.Golushko, G.Gorynin, A.Gorynin, “A new beam element for the analysis of laminated composites based on the asymptotic splitting method”, Journal of Physics: Conference Series, 1666 (2020), 012066 | DOI

[4] S.Golushko, G G.orynin, A.Gorynin, “Method of asymptotic splitting in dynamical problems of the spatial theory of elasticity”, Differential Equations and Mathematical Modeling, Itogi Nauki i Tekhniki. Seriya Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 188, 2020, 43–53 (in Russian) | DOI | MR

[5] M.S.Alnaes, J.Blechta, J.Hake, A.Johansson, B.Kehlet, A.Logg, C.Richardson, J.Ring, M.E.Rognes, G.N.Wells, “The FEniCS Project Version 1.5”, Archive of Numerical Software, 3 (2015) | DOI

[6] G.Dhondt, The Finite Element Method for Three-Dimensional Thermomechanical Applications, Wiley, 2004 | Zbl

[7] A.N.Andreev, Yu.V.Nemirovskii, Multi layered anisotropic shells and plates. Bending, stability and vibration, Nauka Publ, Novosibirsk, 2001 (in Russian)

[8] J.Kierzenka, L.F.Shampine, “A BVP Solver Based on Residual Control and the Maltab PSE”, ACM Trans. Math. Softw., 27:3 (2001), 299–316 | DOI | MR | Zbl