Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

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Bazhenov V. G., Linnik E. Y., Nagornykh E. V., Samsonova D. A. Numerical modeling of the processes of deformation and buckling of multilayer shells of revolution under combined quasi-static and dynamic axisymmetric loading with torsion. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2024, vol. 24, iss. 1, pp. 14-27. DOI: 10.18500/1816-9791-2024-24-1-14-27, EDN: DFKLFV

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
01.03.2024
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Language: 
Russian
Heading: 
Mechanics
Article type: 
Article
UDC: 
539.3
DOI: 
10.18500/1816-9791-2024-24-1-14-27
EDN: 
DFKLFV

Numerical modeling of the processes of deformation and buckling of multilayer shells of revolution under combined quasi-static and dynamic axisymmetric loading with torsion

Autors: 
Bazhenov Valentin G., National Research Lobachevsky State University of Nizhny Novgorod
Linnik Elena Yu., National Research Lobachevsky State University of Nizhny Novgorod
Nagornykh Elena V., National Research Lobachevsky State University of Nizhny Novgorod
Samsonova Daria A., National Research Lobachevsky State University of Nizhny Novgorod
Abstract: 

A two-dimensional formulation and method for numerical solution of problems of deformation and loss of stability of multilayer elastoplastic shells of rotation under quasi-static and dynamic axisymmetric loading with torsion have been developed. The defining system of equations is written in a Cartesian or cylindrical coordinate system. Modeling of the process of deformation of shell layers is carried out on the basis of hypotheses of solid mechanics or the theory of Timoshenko-type shells, taking into account geometric nonlinearities. Kinematic relations are written in speeds and formulated in the metric of the current state. The elastic-plastic properties of the shell are described by the generalized Hooke's law or the theory of plastic flow with nonlinear isotropic hardening. The variational equations of motion of the shell layers are derived from the three-dimensional balance equation of the virtual powers of the work of continuum mechanics, taking into account the accepted hypotheses of the theory of shells, either a plane deformed state or a generalized axisymmetric deformation with torsion. Modeling of the contact interaction of shell layers is based on the condition of rigid gluing or the condition of non-penetration along the normal and sliding along the tangential. To solve the governing system of equations, a finite-difference method and an explicit time integration scheme of the “cross” type are used. The method was tested on the problem of buckling of a three-layer cylindrical shell with elastoplastic load-bearing layers of aluminum alloy D16T and an elastic filler under quasi-static and dynamic loading by hydrostatic pressure, linearly increasing with time. The problem was solved in two versions: all three layers were modeled as a finite element of a continuous medium, or the load-bearing layers were modeled as shell elements, and the filler as elements of a continuous medium. The results of calculations using the two models are in good agreement with each other in terms of ultimate pressures and modes of buckling.

Key words: 
multilayer shells of revolution
elastoplastic shells
elastic filler
non-axisymmetric loss of stability
torsion
Timoshenko’s hypotheses
numerical modeling
contact interaction
axisymmetric loading
Acknowledgments: 
This work was supported by the Russian Science Foundation (project No. 22-29-00904, https://rscf.ru/project/22-29-00904/).
References: 
  1. Vol’mir A. S. Ustoychivost’ deformiruyemykh sistem [Stability of Deformable Systems]. Moscow, Nauka, 1967. 984 p. (in Russian).
  2. Novozhilov V. V. Teoriya tonkikh obolochek [Theory of Thin Shells]. Leningrad, Sudpromgiz, 1962. 432 p. (in Russian).
  3. Golovanov A. I., Tyuleneva O. N., Shigabutdinov A. F. Metod konechnykh elementov v statike i dinamike tonkostennykh konstruktsiy [Finite element method in statics and dynamics of thin-walled structures]. Moscow, Fizmatlit, 2006. 391 p. (in Russian). EDN: QJPXPV
  4. Paimushin V. N. On the forms of loss of stability of a cylindrical shell under an external side pressure. Journal of Applied Mathematics and Mechanics, 2016, vol. 80, iss. 1, pp. 65–72. https://doi.org/10.1016/j.jappmathmech.2016.05.010, EDN: YUZRSF
  5. Paimushin V. N. Relationships of the Timoshenko-type theory of thin shells with arbitrary displacements and strains. Journal of Applied Mechanics and Technical Physics, 2014, vol. 55, iss. 5, pp. 843–856. https://doi.org/10.1134/S0021894414050149, EDN: SEVBYD
  6. Dash A. P., Velmurugan R., Prasad M. S. R., Sikarwar R. S. Stability improvement of thin isotropic cylindrical shells with partially filled soft elastic core subjected to external pressure. Thin-Walled Structures, B, 2016, vol. 98, pp. 301–311. https://doi.org/10.1016/j.tws.2015.09.028
  7. Karam G. N., Gibson L. J. Elastic buckling of cylindrical shells with elastic cores—I. Analysis. International Journal of Solids and Structures, 1995, vol. 32, iss. 8–9, pp. 1259–1263. https://doi.org/10.1016/0020-7683(94)00147-O
  8. Karpov V. V., Bakusov P. A., Maslennikov A. M., Semenov A. A. Simulation models and research algorithms of thin shell structures deformation Part I. Shell deformation models. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2023, vol. 23, iss. 3, pp. 370–410 (in Russian). https://doi.org/10.18500/1816-9791-2023-23-3-370-410
  9. Bakulin V. N. Layer-by-layer analysis of the stress-strain state of three-layer shells with cutouts. Mechanics of Solids, 2019, vol. 54, iss. 3, pp. 448–460. https://doi.org/10.3103/S002565441906013X, EDN: GJAUZR
  10. Ivanov V. A., Paymushin V. N., Polyakova T. V. Investigation of stability loss forms of orthotropic threelayered cylindrical shell under torsion. Bulletin of Nizhny Novgorod University named after N. I. Lobachevsky. Mechanics, 2000, iss. 2 (2), pp. 136–146 (in Russian). EDN: HYICZX
  11. Lavrent’yev M. A., Ishlinskiy A. Yu. Dynamic forms of loss of stability of elastic systems. Doklady Akademii nauk, 1949, vol. 64, iss. 6, pp. 779–782 (in Russian).
  12. Farhat C., Wangc K. G., Main A., Kyriakides S., Lee L.-H., Ravi-Chandar K., Belytschko T. Dynamic implosion of underwater cylindrical shells: Experiments and Computations. International Journal of Solids and Structures, 2013, vol. 50, iss. 19, pp. 2943–2961. https://doi.org/10.1016/j.ijsolstr.2013.05.006
  13. Giezen J. J., Babcock C. D., Singer J. Plastic buckling of cylindrical shells under biaxial loading. Experimental Mechanics, 1990, vol. 33, pp. 337–343. https://doi.org/10.1007/BF02325990
  14. Carvelli V., Panzeri N., Poggi C. Buckling strength of GFRP under-water vehicles. Composites: Part B, 2001, vol. 32, pp. 89–101. https://doi.org/10.1016/S1359-8368(00)00063-9
  15. Ghazijahani T. G., Showkati H. Experiments on conical shell reducers under uniform external pressure. Journal of Constructional Steel Research, 2011, vol. 67, pp. 1506–1515. https://doi.org/10.1016/j.jcsr.2011.03.024
  16. Artem’eva A. A., Bazhenov V. G., Kazakov D. A., Kibets A. I., Nagornykh E. V. Large deformations and limiting states of elastoplastic shells of revolution under combined complex loadings. Journal of Applied Mathematics and Mechanics, 2015, vol. 79, iss. 4, pp. 394–402. https://doi.org/10.1016/j.jappmathmech.2016.01.010, EDN: XXBCDJ
  17. Bazhenov V. G., Zefirov S. V., Tsvetkova I. N. Numerical modeling of problems of non-stationary contact interaction of deformable structures. Prikladnyye problemy prochnosti i plastichnosti. Chislennoye modelirovaniye fiziko-mekhanicheskikh protsessov [Applied Problems of Strength and Plasticity. Numerical Modeling of Physical and Mechanical Processes. Interuniversity Collection]. Vol. 52. Moscow, Tovarishchestvo nauchnykh izdaniy KMK, 1995, pp. 154–160 (in Russian).
  18. Lomunov V. K. Elastic-plastic Buckling of Smooth, Composite and Reinforced Shells of Rotation Under Axial Impact. Diss. Cand. Sci. (Tech.). Gor’kiy, 1979 (in Russian).
  19. Yartsev V. P., Andrianov K. A., Ivanov D. V. Fiziko-mekhanicheskiye i tekhnologicheskiye osnovy primeneniya penopolistirola pri dopolnitel’nom uteplenii zdaniy i sooruzheniy [Physico-mechanical and Technological Basis for the Use of Polystyrene Foam for Additional Insulation of Buildings and Structures]. Tambov, Tambov State Technical University Publ., 2010. 120 p. (in Russian). EDN: QNPCOT
  20. Pleskachevskiy Yu. M., Leonenko D. V. Analysis of threeply round cylindrical shells natural frequency in elastic medium (environment). Topical Issues of Mechanical Engineering, 2012, vol. 1, pp. 244–246 (in Russian). EDN: YMDHKR
  21. Pasternak P. L. Osnovy novogo metoda rascheta fundamentov na uprugom osnovanii pri pomoshchi dvukh koeffitsiyentov posteli [Fundamentals of a new method for calculating foundations on an elastic foundation using two bed coefficients]. Moscow, Gosstroyizdat, 1954. 56 p. (in Russian).
  22. Bazhenov V. G., Zhegalov D. V., Pavlenkova Ye. V. Numerical and experimental study of elastoplastic tension-torsion processes in axisymmetric bodies under large deformations. Mechanics of Solids, 2011, vol. 46, iss. 2, pp. 204–212. https://doi.org/10.3103/S0025654411020087, EDN: OHUGKR
  23. Bazhenov V. G., Nagornykh E. V., Samsonova D. A. Investigation of the Winkler foundation model applicability for describing the contact interaction of elastoplastic shells with a core under external pressure. PNRPU Mechanics Bulletin, 2020, iss. 4, pp. 36-48 (in Russian). https://doi.org/10.15593/perm.mech/2020.4.04
Received: 
01.12.2023
Accepted: 
28.12.2023
Published: 
01.03.2024
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