Nonlinear deformation and stability of a composite non-circular cylindrical shell exposed to torsion

The paper solves the problem of stability of the non-circular cylindrical shells made of the composite material taking into account the moment and nonlinearity of their subcritical stress-strain state. The geometrically nonlinear stability problem is solved using the finite element methods and the Newton-Kantorovich linearization. Critical loads are determined in the process of solving the nonlinear problem using the Sylvester criterion. The paper uses finite elements of the composite cylindrical shells with natural curvature developed on the basis of the Timoshenko hypothesis. Their displacements approximation explicitly identifies the rigid displacements thereof, which significantly affects the solution convergence. The paper studies stability of an oval cantilever-fixed cylindrical shell made of a polymer composite material exposed to torsion. It identifies the influence of monolayer laying methods, deformation nonlinearity and out-of-roundness parameter on the critical loads in the shell stability loss and weight efficiency of the composite shells.
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References

[1] Boyko D.V., Zheleznov L.P., Nonlinear deformation and stability of oval cylindrical shells under pure bending and internal pressure. PMTF, 2006, vol. 47, no. 3, pp. 119–125. (In Russ.). (Eng. version: J. Appl. Mech. Tech. Phys., 2006, vol. 47, no. 3, pp. 406–411, doi: https://doi.org/10.1007/s10808-006-0070-8)

[2] Zheleznov L.P., Kabanov V.V. Investigation of nonlinear deformation and stability of non-circular cylindrical shells under pure bending. Izvestiya RAN. Mekhanika tverdogo tela, 2004, no. 3, pp. 144–151. (In Russ.).

[3] Boyko D.V., Zheleznov L.P., Kabanov V.V. Nonlinear deformation and stability of oval cylindrical shells under combined loading. PMTF, 2008, vol. 49, no. 1, pp. 134–138. (In Russ.). (Eng. version: J. Appl. Mech. Tech. Phys., 2008, vol. 49, no. 1, pp. 109–113, doi: https://doi.org/10.1007/s10808-008-0016-4)

[4] Vasilyev V.V. Mekhanika konstruktsiy iz kompozitnykh materialov [Structural mechanics of composite materials]. Moscow, Mashinostroenie Publ., 1988. 272 p. (In Russ.).

[5] Vasiliev V.V., Morozov E.V. Advanced mechanics of composite materials and structures. Amsterdam, Elsevier, 2013. 832 p.

[6] Alfutov N.A., Zinovyev P.A., Popov B.G. Raschet mnogosloynykh plastin i obolochek iz kompozitsionnykh materialov [Calculation of multilayer plates and shells made of composite materials]. Moscow, Mashinostroenie Publ., 1984. 263 p. (In Russ.).

[7] Karmishin A.V., Lyaskovets V.A., Myachenkov V.I. et al. Statika i dinamika obolochechnykh konstruktsiy [Statics and dynamics of shell structures]. Moscow, Mashinostroenie Publ., 1975. 376 p. (In Russ.).

[8] Kantorovich L.V., Akilov G.P. Funktsionalnyy analiz v normirovannykh prostranstvakh [Functional analysis in normalized spaces]. Moscow, Fizmatgiz Publ., 1959. 684 p. (In Russ.).

[9] Kabanov V.V., Zheleznov L.P. On calculation of cylinder shell using infinite elements method. Prikladnaya mekhanika, 1985, vol. 21, no. 9, pp. 35–38. (In Russ.).

[10] Zheleznov L.P., Kabanov V.V. Nonlinear deformation and stability of noncircular cylindrical shells under internal pressure and axial compression. PMTF, 2002, vol. 43, no. 4, pp. 161–169. (In Russ.). (Eng. version: J. Appl. Mech. Tech. Phys., 2002, vol. 43, no. 4, pp. 617–621.)

[11] Boyko D.V., Zheleznov L.P., Kabanov V.V. Nonlinear deformation and stability of discrete-reinforced elliptical cylindrical composite shells under torsion and internal pressure. Aviatsionnaya tekhnika, 2018, no. 2, pp. 27–34. (In Russ.). (Eng. version: Russ. Aeronaut., 2018, vol. 61, no. 2, pp. 175–182, doi: https://doi.org/10.3103/S1068799818020046)

[12] Zheleznov L.P. Investigation of nonlinear deformation and stability of a composite cylindrical shell under combined loading with torque, edge transversal force and internal pressure. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [BMSTU Journal of Mechanical Engineering], 2023, no. 10, pp. 114–125, doi: http://dx.doi.org/10.18698/0536-1044-2023-10-114-125 (in Russ.).

[13] Zheleznov L.P. Nonlinear deformation and stability of anisogrid circular cylindrical shells under pure bending. Polet [Flight], 2023, no. 1–2, pp. 3–15. (In Russ.).

[14] Kabanov V.V. Ustoychivost neodnorodnykh tsilindricheskikh obolochek [Stability of inhomogeneous cylindrical shells]. Moscow, Mashinostroenie Publ., 1982. 253 p. (In Russ.).