Unsteady deformation of anisotropic circular cylindrical shell


DOI: 10.34759/trd-2021-120-09

Аuthors

Lokteva N. A.1*, Serdyuk D. O.1**, Skopincev P. D.1***, Fedotenkov G. V.2****

1. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
2. ,

*e-mail: nlok@rambler.ru
**e-mail: d.serduk55@gmail.com
***e-mail: chgpashka@gmail.com
****e-mail: greghome@mail.ru

Abstract

The unsteady deformation of a thin, infinitely long circular cylindrical shell of constant thickness under the impact of a concentrated shock load distributed over an arbitrary region on its lateral surface is being studied. The shell material is assumed to be linearly elastic, anisotropic, and symmetrical about its middle surface. The Kirchhoff-Love model is employed to describe the shell motion. The motion of the shell is being considered in a cylindrical coordinate system associated with the axis of the cylindrical shell, and the sought-for function of the normal non-stationary deflection is constructed by connecting the Greenrsquo;s function with the function of the operating load using an integral operator of the convolution type in spatial variables and time. The Greenrsquo;s function for an anisotropic shell is a solution to a special problem of the impact of an instantaneous concentrated load on the shell, mathematically modeled by the Dirac delta functions. Expansions in exponential Fourier series, integral Laplace transform in time and integral Fourier transform in longitudinal coordinate are being used to construct the Greenrsquo;s function. The inverse integral Laplace transform is being performed analytically, and the original integral Fourier transform is being found using numerical methods for integrating rapidly oscillating functions. The integrals of the convolution of the Greenrsquo;s function with the load function are being taken with quadrature formulas using the rectangle method. As an example, the unsteady dynamics of cylindrical shell was sstudied under the impact of arbitrarily time-dependent concentrated load and load distributed over the finite area belonging to the lateral surface of the shell. Several options of symmetry of the elastic medium (isotropic, orthotropic and anisotropic) herewith were analyzed, which demonstrates calculated solution versatility both in terms of influence nature and shell material. For the considered symmetry options, the study of the unsteady vibrations propagation character, which allowed evaluating the solution adequacy, was conducted.The presented approach to constructing the unsteady deflection function while transition to the dimensional values opens opportunities for the analysis of the stress-strain state of the extended cylindrical shells with account for various options of the material anisotropy and law of distribution of the unsteady loading along both coordinates and time.

Keywords:

anisotropic cylindrical shell, unsteady dynamics, Green’s function, deflection function, generalized functions, integral transformations, quadrature formulas, normal displacement, Kirchhoff-Love shell

References

  1. Gorshkov A.G., Medvedskii A.L., Rabinskii L.N., Tarlakovskii D.V. Volny v sploshnykh sredakh (Waves in Continuous Media Study guide: for universities), Moscow, FIZMATLIT, 2004, 472 p.

  2. Bogdanovich A.E. Deformirovanie i prochnostrsquo; tsilindricheskikh kompozitnykh obolochek pri dinamicheskikh nagruzkakh (Deformation and Strength for Cylindrical Composite Shells under Dinamic Loads), Riga, 1985, 560 p.

  3. Bogdanovich A.E. Nelineinye zadachi dinamiki tsilindricheskikh kompozitnykh obolochek (Non-linear Problems of Dynamics of Cylindrical Composite Shells), Riga, Zinatne, 1987, 295 p.

  4. Koshkina T.B. Deformirovanie i prochnostrsquo; podkreplennykh kompozitnykh tsilindricheskikh obolochek pri dinamicheskikh szhimayushchikh nagruzkakh (Deformation and Strength of Orthotropic Cylindrical Shells Subjected to Dynamic Compressive Loads), Riga, Akademiya nauk Latviiskoi SSR, 1984, 180 p.

  5. Tarlakovskii D.V., Fedotenkov G.V. Two-Dimensional Nonstationary Contact of Elastic Cylindrical or Spherical Shells, Journal of Machinery Manufacture and Reliability, 2014, vol. 43, no. 2, pp. 145ndash;152. DOI: 10.3103/S105261881401017

  6. Tarlakovskii D.V., Fedotenkov G.V. Nonstationary 3D Motion of an elastic Spherical Shell, Mechanics of Solids, 2015, vol. 50, no. 2, pp. 208-217. DOI: 10.3103/S0025654415020107

  7. Mikhailova E.Yu., Tarlakovskii D.V., Fedotenkov G.V. The impact of liquid filled concentric spherical shells with a rigid wall, Shell Structures: Theory and Applications, 2017, vol. 4, pp. 305-308. DOI: 10.1201/9781315166605-68

  8. Mikhailova E.Yu., Tarlakovskii D.V., Fedotenkov G.V. Transient contact problem for liquid filled concentric spherical shells and a rigid barrier, Proceedings of the First International Conference on Theoretical, Applied and Experimental Mechanics, 2019, pp. 385-386. DOI: 10.1007/978-3-319-91989-8_92

  9. Fedotenkov G.V., Tarlakovsky D.V., Vahterova Y.A. Identification of non-stationary load upon timoshenko beam, Lobachevskii Journal of Mathematics, 2019, vol. 40, no. 4, pp. 439ndash;447. DOI: 10.1134/S1995080219040061

  10. Vakhterova Ya.A., Fedotenkov G.V. XII Vserossiiskii squot;ezd po fundamentalrsquo;nym problemam teoreticheskoi i prikladnoi mekhaniki: sbornik trudov. Ufa, Bashkirskii gosudarstvennyi universitet, 2019, vol. 3, pp. 878-880.

  11. Okonechnikov A.S., Tarlakovski D.V., Ulrsquo;yashina A.N., Fedotenkov G.V. Transient reaction of an elastic half-plane on a source of a concentrated boundary disturbance, IOP Conference Series: Materials Science and Engineering, 2016, vol. 158, no 1, pp. 012073. DOI:10.1088/1757-899X/158/1/012073

  12. Ivanov S.V., Mogilevich L.I., Popov V.S. Trudy MAI, 2019, no. 105. URL: http://trudymai.ru/eng/published.php?ID=104003

  13. Nushtaev D.V., Zhavoronok S.I., Klyshnikov K.Yu., Ovcharenko E.A. Trudy MAI, 2015, no. 82. URL: http://trudymai.ru/eng/published.php?ID=58589

  14. Karpov V.V., Semenov A.A., Kholod D.V. Trudy MAI, 2014, no. 76. URL: http://trudymai.ru/eng/published.php?ID=49970

  15. Zhigalko Yu.P., Sadykova M.M. Issledovaniya po teorii plastin i obolochek, 1990, no. 20, pp. 184-191.

  16. Morgachev K.S. Vestnik Samarskogo gosudarstvennogo tekhnicheskogo universiteta, 2007, vol. 15, no. 2, pp. 162-164.

  17. Drsquo;yachenko Yu.G. Nestatsionarnaya zadacha dinamiki plastin peremennogo secheniya v utochnennoi postanovke (Transient problem of dynamics of plates of variable cross-section in a refined formulation), authorrsquo;s abstract, Saratov, SGU, 2008, 19 p.

  18. Shevchenko V.P. Vetrov O.S. Trudy instituta prikladnoi matematiki i mekhaniki Natsionalrsquo;noi akademii nauk Ukrainy, 2011, vol. 22, pp. 207ndash;215.

  19. Nayfeh A.H., Chimenti D.E. Free Wave Propagation in Plates of General Anisotropic Media, Journal of applied mechanics-transactions of the ASME, 1989, vol. 56, no. 4, pp. 881 — 886. DOI: 10.1115/1.3176186

  20. Wahab M.A., Jabbour T., Davies P. Prediction of impact damage in composite sandwich plates, Materiaux amp; Techniques, 2019, vol. 107, no. 2. DOI: 10.1051/mattech/2019006

  21. Daros C.H. The dynamic fundamental solution and BEM formulation for laminated anisotropic Kirchhoff plates, Engineering analysis with boundary elements, 2015, vol. 54, no. 2, pp. 19 — 27. DOI: 10.1016/j.enganabound.2015.01.001

  22. Igumnov L.A., Markov I.P. A boundary element approach for 3d transient dynamic problems of moderately thick multilayered anisotropic elastic composite plates, Materials physics and mechanics, 2018, vol. 37, no. 1, pp. 79-83. DOI: 10.18720/MPM.3712018_11

  23. Sahli A., Boufeldja S., Kebdani S., Rahmani O. Failure analysis of anisotropic plates by the boundary element method, Journal of mechanics, 2014, vol. 30, no. 6, pp. 561-570. DOI: 10.1017/jmech.2014.65

  24. Starovoitov E.I., Leonenko D.V. Deformation of an Elastoplastic Three-Layer Circular Plate in a Temperature Field, Mechanics of Composite Materials, 2019, vol. 55, no. 4, pp. 503ndash;512. DOI: 10.1007/s11029-019-09829-6

  25. Ryazantseva M.Y., Starovoitov E.I. Static and Dynamic Models of Bending for Elastic Sandwich Plates, Structural Integrity, 2019, vol. 8, pp. 294ndash;297. DOI: 10.1007/978-3-030-21894-2_54

  26. Starovoitov E.I., Leonenko D.V., Tarlakovskii D.V. Thermoelastic Deformation of a Circular Sandwich Plate by Local Loads, Mechanics of Composite Materials, 2018, vol. 54, no. 3, pp. 299-312. DOI: 10.1007/s11029-018-9740-x

  27. Starovoitov E.I., Leonenko D.V. Vibrations of circular composite plates on an elastic foundation under the action of local loads, Mechanics of Composite Materials, 2016, vol. 52, no. 5, pp. 665ndash;672. DOI: 10.1007/s11029-016-9615-y

  28. Tarlakovskii D.V., Fedotenkov G.V. Obshchie sootnosheniya i variatsionnye printsipy matematicheskoi teorii uprugosti (General ratios and variation principles of mathematical theory of elasticity) Moscow, Izd-vo MAI-PRINT, 2009, 112 p.

  29. Mikhailova E.Yu., Tarlakovskii D.V., Fedotenkov G.V. Uprugie plastiny i pologie obolochki (Elastic Plates and Shallow Shells), Moscow, Izd-vo MAI, 2018, 92 p.

  30. Dech G. Rukovodstvo k prakticheskomu primeneniyu preobrazovaniya Laplasa i Z-preobrazovanii (Guide to the Practical application of Laplace and Z-transforms), Moscow, Izd-vo Nauka, 1971, 288 p.

  31. Bakhvalov N.S., Zhidkov N.P., Kobelrsquo;kov G.M. Chislennye metody (Numerical Methods), Moscow, Nauka, 1975, 630 p.

  32. Ashkenazi E.K. Anizotropiya drevesiny i drevesnykh materialov (Wood and Wood Materials Anisotropy), Moscow, Lesnaya promyshlennostrsquo;, 1978, 224 p.

  33. Igumnov L.A., Markov I.P., Pazin V.P. Vestnik Nizhegorodskogo universiteta im. N.I. Lobachevskogo, 2013, no. 1(3), pp. 115 — 119.


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