Experimental and theoretical study of elastoplastic buckling of cylindrical shells filled with bulk material under the action of a transverse force

V. G. Bazhenov   ; E. G. Gonik   ; A. I. Kibets   ; M. V. Petrov   ; T. G. Fedorova   ; I. A. Frolova

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 159 (2017) no. 3, pp. 282-295

Résumé

The process of elastoplastic deformation, loss of stability and supercritical behavior of cantilevered thin-walled cylindrical shells of medium length loaded at the end face by transverse force, has been numerically and experimentally investigated. The defining system of equations has been formulated in the Lagrange variables in a three-dimensional dynamic formulation. The elastic-plastic deformation has been described by the relations of the theory of flow. Geometric nonlinearity (large deformations) has been taken into account by recalculating the geometry of the shell at each instant of time. The numerical solution of the problem is based on the finite element method and an explicit finite-difference time-integration scheme of the “cross” type. The effect of geometric parameters and loose filler on shell buckling has been studied. It has been shown numerically and experimentally that the bulk filler in the problem under consideration raises the value of the critical load, but its effect on the form of stability loss is insignificant.

Détail

Keywords: cylindrical shell, aggregate, plastic deformation, buckling, experiment
Mots-clés : calculation.

Bibliographie

[1] Lundquist E. E., Strength Tests of Thin-Walled Duralumin Cylinders in Combined Transverse Shear and Bending, NACA TN523, 1935, 28 pp.

[2] Darevsky V. M., “Stability of the cantilevered cylindrical shell under bending by transverse force with torsion and internal pressure”, Calculation of Spatial Structures, 5, 1959, 431–449 (In Russian)

[3] Turkin K. D., “General stability of a reinforced cylindrical shell under transverse bending”, Calculation of Spatial Structures, 5, 1959, 450–474 (In Russian)

[4] Ilgamov M. A., “Experimental study of the stability of a cantilevered cylindrical shell under the action of transverse force and internal pressure”, Issled. Teor. Plastin Obolochek, 2, Kazan, Izd. Kazan. Univ., 1964, 186–191 (In Russian)

[5] Konoplev Yu. G., “Experimental study of the stability of a cylindrical shell under the effect of an arbitrary number of local axial forces”, Issled. Teor. Plastin Obolochek, 6–7, Izd. Kazan. Univ., Kazan, 1970, 481–484 (In Russian)

[6] Mossakovsky V. I., Menevich L. I., Miltsyn A. M., Modeling of the Bearing Capacity of Cylindrical Shells, Naukova Dumka, Kiev, 1977, 141 pp. (In Russian)

[7] Sachenkov A. V., “On the local stability of shells”, Izv. Kazan. Fil. Akad. Nauk SSSR, Ser. Fiz.-Mat. Tekh. Nauk, 1960, no. 14, 35–42 (In Russian)

[8] Guryanov N. G., “Closed cylindrical shell under the action of concentrated force”, Issled. Teor. Plastin Obolochek, 4, Izd. Kazan. Univ., Kazan, 1966, 55–64 (In Russian)

[9] Zhigalko Yu. P., “Calculation of thin elastic cylindrical shells for local loads”, Issled. Teor. Plastin Obolochek, 4, Izd. Kazan. Univ., Kazan, 1966, 3–41 (In Russian)

[10] Sobolev Yu. V., Wegner A. G., Adler A. G., Aleshin N. N., “On calculation of the bearing capacity of steel cylindrical shells under local loading”, Izv. Vyssh. Uchebn. Zaved., Stroit. Arkhit., 1986, no. 12, 1–5 (In Russian)

[11] Manevich A. I., Ponomarenko E. A., Prokopalo E. F., “Stability of orthotropic cylindrical shells under bending by transverse force. Part 1. Theory”, Strength Mater., 45:1 (2013), 73–81 | DOI

[12] Manevich A. I., Ponomarenko E. A., Prokopalo E. F., “Stability of orthotropic cylindrical shells under bending by a transverse force. Part 2. Experiment”, Strength Mater., 45:2 (2013), 205–209 | DOI

[13] Boyko D. V., Zheleznov L. P., Kabanov V. V., “Investigation of nonlinear deformation and stability of oval cylindrical shells under combined loading by bending and twisting moments”, Izv. Vyssh. Uchebn. Zaved., Aviats. Tekh., 2007, no. 3, 3–7 (In Russian)

[14] Ilgamov M. A., Ivanov V. A., Gulin B. V., Strength, Stability, and Dynamics of Shells with Elastic Filler, Nauka, Moscow, 1977, 331 pp. (In Russian)

[15] Bazhenov V. G., Kibets A. I., Petrov M. V., Fedorova T. G., Shoshin D. V., “Theoretical and experimental study of stability loss and supercritical behavior of a thin-walled cylindrical shell under bending”, Probl. Prochn. Plast., 71 (2009), 77–83 (In Russian)

[16] Gonik E. G., Petrov M. V., Fedorova T. G., “Experimental study of the stability loss of cantilevered cylindrical thin-walled shells under transverse bending”, Probl. Prochn. Plast., 78:2 (2016), 228–235 (In Russian)

[17] Petrov M. V., Fedorova T. G., Gonik E. G., “Experimental study of the loss of stability of thin-walled shells under pure bending”, Vestn. Chuv. Gos. Pedagog. Univ. im. I. Y. Yakovleva, Ser. Mekh. Predelnogo Sost., 2015, no. 2, 119–125 (In Russian)

[18] Knebel K., Schweizerhof K., “Buckling of cylindrical shells containing granular solids ”, Thin-Walled Struct., 23:1–4 (1995), 295–312 | DOI

[19] Shagivaleev K. F., “Calculation of a closed cylindrical shell filled with bulk material, for a radial load”, Izv. Vyssh. Uchebn. Zaved., Stroit., 2003, no. 2, 20–23 (In Russian)

[20] Rotter J. M., Sadowski A. J., “Full plastic resistance of tubes under bending and axial force: exact treatment and approximations”, Structures, 10 (2016), 30–38 | DOI

[21] Bazhenov V. G., Gonik E. G., Kibets A. I., Petrov M. V., Fedorova T. G., “Stability and supercritical behavior of large size tankers for transportation of loose goods”, J. Mach. Manuf. Reliab., 44:5 (2015), 422–427 | DOI

[22] Chen L., Doerich C., Rotter J. M., “A study of cylindrical shells under global bending in the elastic-plastic range”, Steel Constr., 1:1 (2008), 59–65 | DOI

[23] Bazhenov V. G., Gonik E. G., Kibets A. I., Petrov M. V., Fedorova T. G., Frolova I. A., “Stability and supercritical behaviour of thin-walled cylindrical shell with discrete aggregate in bending”, Mater. Phys. Mech., 28:1–2 (2016), 16–20

[24] Rotter J. M., Sadowski A. J., Chen L., “Nonlinear stability of thin elastic cylinders of different length under global bending”, Int. J. Solids Struct., 51:15–16 (2014), 2826–2839 | DOI

[25] Volmir A. S., Stability of Deformable Systems, Nauka, Moscow, 1967, 984 pp. (In Russian)

[26] Grigolyuk E. I., Kabanov V. V., Stability of Shells, Nauka, Moscow, 1978, 360 pp. (In Russian) | MR

[27] Kabanov V. V., Stability of Inhomogeneous Cylindrical Shells, Mashinostroenie, Moscow, 1982, 256 pp. (In Russian) | MR

[28] Gudramovich V. S., “Peculiarities of nonlinear deformation and critical states of shell systems with geometric imperfections”, Prikl. Mekh., 42:12 (2006), 3–47 (In Russian)

[29] Sadowski A. J., Rotter J. M., “Solid or shell finite elements to model thick cylindrical tubes and shells under global bending”, Int. J. Mech. Sci., 74 (2013), 143–153 | DOI

[30] Zubchaninov V. G., Stability and Plasticity, v. 1, Stability, FIZMATLIT, Moscow, 2007, 448 pp. (In Russian)

[31] Shalashilin V. I., Kuznetsov E. B., The Method of Continuation of the Solution with Respect to the Parameter and the Best Parametrization, Ed. URSS, Moscow, 1999, 224 pp. (In Russian) | MR

[32] Bazhenov V. G., “Large deformations and limiting states of elastoplastic structures”, Elasticity and Inelasticity, Proc. Int. Sci. Symp. on the Problems of Mechanics of Deformable Bodies Dedicated to the 105th Anniversary of the Birth of A. A. Ilyushin, Mosk. Gos. Univ., Moscow, 2016, 136–140 (In Russian)

[33] Computer complex “Dynamics-3”, Attestation Passport of the Software Product No 325, Scientific and Technical Center for Nuclear and Radiation Safety, Apr. 18, 2013 (In Russian)

[34] GOST Russia Certificate of Conformity No RU.ME20.H00338 (In Russian)

[35] Rumshyskii L. Z., Mathematical Processing of Experimental Results, Nauka, Moscow, 1971, 192 pp. (In Russian)

[36] Pozdeev A. A., Trusov P. V., Nyashin Yu. I., Large elastoplastic Deformations: Theory, Algorithms, Applications, Nauka, Moscow, 1986., 232 pp. (In Russian) | MR

[37] Korobeinikov S. N., Nonlinear Deformation of Solids, In Russian, Izd. Sib. Otd. Ross. Akad. Nauk, Novosibirsk, 2000, 262 pp.

[38] Korobeinikov S. N., Shutov A. V., “Selection of the reference surface in the equations of plates and shells”, Vychisl. Tekh., 8:6 (2003), 38–59 (In Russian)

[39] Kachanov L. M., Fundamentals of the Theory of Plasticity, Nauka, Moscow, 1969, 420 pp. (In Russian)

[40] Kazakov D. A., Kapustin S. A., Korotkikh Yu. G., Modeling of the Processes of Deformation and Destruction of Materials and Structures, Izd. NNGU, Nizhny Novgorod, 1999, 226 pp. (In Russian)

[41] Bazhenov V. G., Gonik E. G., Kibets A. I., Shoshin D. V., “Stability and limit states of elastoplastic spherical shells under static and dynamic loading”, J. Appl. Mech. Tech. Phys., 55:1 (2014), 8–15 | DOI | MR

[42] Golovanov A. I., Tyuleneva O. N., Shigabutdinov A. F., Finite Element Method in Static and Dynamics of Thin-Walled Structures, FIZMATLIT, Moscow, 2006, 391 pp. (In Russian)

[43] Belytschko T., Liu W. K., Moran B., Nonlinear finite elements for continua and structures, John Wiley Sons, N.Y., 2000, 600 pp. | MR

[44] Bazhenov V. G., Zhestkov M. N., Zamyatin V. A., Kibets A. I., “Mathematical modeling of the development of a beyond-design accident within the reactor shell on fast neutrons”, Vestn. PNIPU Mekh., 2015, no. 3, 5–14 (In Russian)