Investigation of nonlinear deformation and stability of a composite cylindrical shell under combined loading with torque, edge transversal force and internal pressure

The paper presents a finite element formulation for solving stability problems of the composite cylindrical shells taking into account momentness and nonlinearity of their subcritical stress-strain state. The nonlinear problem of strength and stability was solved by the finite element methods and the Newton-Kantorovich linearization. Critical loads were determined in the process of solving the geometrically nonlinear problem using the Sylvester criterion. Finite elements of the composite cylindrical shells with natural curvature previously developed on the basis of Timoshenko’s hypothesis were used. Their rigid motions were explicitly identified in the movement approximation. Stability of a circular cylindrical shell made of the polymer composite material was studied under combined loading with torque, transverse force and internal pressure. Interaction curves of the external loads were obtained. Influence was determined of monolayers laying methods, nonlinearity of deformation and internal pressure on the critical loads of the shell buckling and the weight efficiency of composite shells in comparison with the metal ones.

References

[1] Vasilyev V.V. Mekhanika konstruktsiy iz kompozitnykh materialov [Mechanics of structures from composite materials]. Moscow, Mashinostroenie Publ., 1988. 272 p. (In Russ.).

[2] Vasiliev V.V., Morozov E.V. Advanced mechanics of composite materials and structures. Elsevier, 2018. 900 p.

[3] Vanin G.A., Semenyuk N.P., Emelyanov R.F. Ustoychivost obolochek iz armirovannykh materialov [Stability of shells of reinforced materials]. Kiev, Naukova Dumka Publ., 1978. 211 p. (In Russ.).

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

[5] Bakulin V.N., Gusev E.L, Markov V.G. Metody optimalnogo proektirovaniya i rascheta kompozitsionnykh konstruktsiy T. 1. [Methods for optimal design and calculation of composite structures. Vol. 1.]. Moscow, Fizmatlit Publ., 2008. 256 p. (In Russ.).

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

[7] Kabanov V.V., Zheleznov L.P. Calculation of cylindrical shells by the finite-element method. Prikladnaya mekhanika, 1985, vol. 21, no. 9, pp. 35–38. (In Russ.). (Eng. version: Sov. Appl. Mech., 1985, vol. 21, no. 9, pp. 851–856, doi: https://doi.org/10.1007/BF00886970)

[8] Zheleznov L.P., Kabanov V.V. Nonlinear deformation and stability of noncircular cylindrical shells under internal pressure and axial compression. Prikladnaya mekhanika i tekhnicheskaya fizika, 2002, vol. 43, no. 4, pp. 155–160. (In Russ.). (Eng. version: J. Appl. Mech. Tech. Phy., 2002, vol. 43, no. 4, pp. 617–621, doi: https://doi.org/10.1023/A:1016066001346)

[9] Zheleznov L.P., Seryeznov A.N. Research on nonlinear deformation and stability of an aircraft fuselage composite section under transverse bending. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie [BMSTU Journal of Mechanical Engineering], 2021, no. 10, pp. 106–116, doi: http://dx.doi.org/10.18698/0536-1044-2021-10-106-116 (in Russ.).

[10] 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. Izvestiya vysshikh uchebnykh zavedeniy. 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)

[11] Zheleznov L.P., Seryeznov A.N. Nonlinear deformation and stability of the aircraft fuselage composite section under pure bending. Izvestiya vysshikh uchebnykh zavedeniy. Aviatsionnaya tekhnika, 2021, no. 3, pp. 22–30. (In Russ.). (Eng. version: Russ. Aeronaut., 2021, vol. 64, no. 3, pp. 385–393, doi: https://doi.org/10.3103/S106879982103003X)

[12] Postnov V.A., Kharkhurim I.Ya. Metod konechnykh elementov v raschetakh sudovykh konstruktsiy [Finite element method in calculations of ship structures]. Leningrad, Sudostroenie Publ., 1974. 341 p. (In Russ.).

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

[14] Wilkinson J.H., Reinsch C. Handbook for automatic computation. Vol. II. Linear algebra. Springer, 2012. 441 p. (Russ. ed.: Spravochnik algoritmov na yazyke Algol. Lineynaya algebra. Moscow, Mashinostroenie Publ., 1976. 390 p.)

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