Study of nonlinear deformation and stability of the non-circular composite cylindrical shell exposed to loading with the bending moment

The problem of stability of the non-circular cylindrical shells made of composite material is solved, taking into account torque and nonlinearity in their subcritical stress-strain state. The geometrically nonlinear stability problem is solved by the finite element methods and the Newton–Kantorovich linearization. Critical loads are determined in solving the nonlinear problem using the Sylvester criterion. Finite elements of the composite cylindrical shells with natural curvature, previously developed on the basis of the Timoshenko hypothesis, are used, in which motion approximation their rigid movements are explicitly identified significantly effecting the solution convergence. Stability of the oval cylindrical shell made of the polymer composite material exposed to loading with the bending moment is studied. Influence is established of methods of laying monolayers, nonlinearity of deformation and ovality parameter on the shell critical buckling loads and weight efficiency of the composite shells.
EDN: YTOYLN, https://elibrary/ytoyln

References

[1] 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. 161–169. (In Russ.). (Eng. version: J. Appl. Mech. Tech. Phys., 2002, vol. 43, no. 4, pp. 617–621.)

[2] Zheleznov L.P., Kabanov V.V. Investigation of nonlinear deformation and stability of non-circular cylindrical shells under pure bending. Izvestiya AN. MTT, 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. Prikladnaya mekhanika i tekhnicheskaya fizika, 2008, vol. 49, no. 1, pp. 134–138. (In Russ.). (Eng. version: J. Appl. Mech. Tech. Phys., 2002, vol. 43, no. 4, pp. 617–621.)

[4] Vasilyev V.V. Mekhanika konstruktsiy iz kompozitnykh materialov [Mechanics of structures and composites]. Moscow, Mashinostroenie Publ., 1988. 272 p. (In Russ.).

[5] Vasiliev V.V., Morozov E.V. Advanced mechanics of composite materials and structures. Elsevier, 2018. 882 p.

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

[7] Karmishin A.V., Lyaskovets V.A., Myachenkov V.I. et al. Statika i dinamika tonkostennykh obolochechnykh konstruktsiy [Statics and dynamics of thin-walled 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 normalised spaces]. Moscow, Fizmatgiz Publ., 1959. 684 p. (In Russ.).

[9] Kabanov V.V., Zheleznov L.P. To the calculation of a cylindrical shell by the finite element method. Prikladnaya mekhanika, 1985, vol. 21, no. 9, pp. 35–38. (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. Aviatsionnaya tekhnika, 2018, no. 2, pp. 27–34. (In Russ.). (Eng. version: Russ. Aeronaut., 2018, vol. 61, no. 2, 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. 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] Kabanov V.V. Ustoychivost neodnorodnykh tsilindricheskikh obolochek [Stability of non-uniform cylindrical shells]. Moscow, Mashinostroenie Publ., 1982. 253 p. (In Russ.).