Open Access
Issue
ESAIM: M2AN
Volume 59, Number 2, March-April 2025
Page(s) 1023 - 1042
DOI https://doi.org/10.1051/m2an/2025016
Published online 02 April 2025
  1. J. Ball, Stability theory for an extensible beam. J. Diff. Equ. 14 (1973) 399–418. [Google Scholar]
  2. S. Bernstein, Sur une classe d’équations fonctionnelles aux dérivées partielles. Bull. Acad. Sci. URSS. Sér. Math. [Izv. Akad. Nauk SSSR Ser. Mat.] 14 1 (1940) 17–26. [Google Scholar]
  3. D. Chapelle and K.J. Bathe, The Finite Element Analysis of Shells – Fundamentals, 2nd edition. Springer-Verlag, Berlin, Heidelberg (2011). [Google Scholar]
  4. M. Chipot, Elements of Nonlinear Analysis. Birkh¨auser Verlag, Basel (2000). [Google Scholar]
  5. M. Chipot, Remarks on some class of non-local elliptic problems, in Recent Advances of Elliptic and Parabolic Issues. World Scientific (2006) 79–102. [Google Scholar]
  6. H.B. Dwight, Tables of Integrals and Other Mathematical Data, 4th edition. The Macmillan Co., New York (1961). [Google Scholar]
  7. B. Feng and A. Soufyane, Memory-type boundary control of a laminated Timoshenko beam. Math. Mech. Solids 25 (2020) 1568–1588. [MathSciNet] [Google Scholar]
  8. N. Jacobson, Basic Algebra. I, 2nd edition. W.H. Freeman and Company, New York (1985). [Google Scholar]
  9. N. Kachakhidze, Julia code for “The solution method and its accuracy for a nonlinear Timoshenko axisymmetric shell model” (2024). https://github.com/nika3966/timoshenko_shell. [Google Scholar]
  10. N. Kachakhidze, N. Khomeriki, I. Peradze and Z. Tsiklauri, Chipot’s method for Kirchhoff’s one-dimensional static equation. Numer. Algor. 73 (2016) 1091–1106. [Google Scholar]
  11. L.S. Kharasova, Solvability of one problem for differential equations of shell theory of Timoshenko type. Int. J. Eng. Res. Tech. (IJET) 13 (2020) 5328–5334. [Google Scholar]
  12. G. Kirchhoff, Vorlesungen über Mathematische Physik: Mechanik. Teubner, Leipzig (1876). [Google Scholar]
  13. J.E. Lagnese and J.-L. Lions, Modelling Analysis and Control of Thin Plates. Springer-Verlag, Berlin, Heidelberg (1990). [Google Scholar]
  14. L.P. Lebedev, I.I. Vorovich and M.J. Cloud, Functional Analysis in Mechanics. Springer, New York, NY (2013). [Google Scholar]
  15. S.G. Mikhlin, The Numerical Performance of Variational Methods. Wolters-Noordhoff Publishing, Groningen (1971). [Google Scholar]
  16. J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables. Reprint of the 1970 original, Classics in Applied Mathematics. Vol. 30. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2000). [Google Scholar]
  17. G. Papukashvili, I. Peradze and Z. Tsiklauri, On a stage of a numerical algorithm for Timoshenko type nonlinear equation. Proc. A. Razmadze Math. Inst. 158 (2012) 67–77. [MathSciNet] [Google Scholar]
  18. J. Peradze, Densifying operator for one system of equations and its solvability. Proc. Tbilisi State Univ. 300 (1990) 88–100. [Google Scholar]
  19. J. Peradze, An approximate algorithm for a Kirchhoff wave equation. SIAM J. Numer. Anal. 47 (2009) 2243–2268. [Google Scholar]
  20. J. Peradze, A numerical algorithm for a Kirchhoff-type nonlinear static beam. J. Appl. Math. 2009 (2009). DOI: 10.1155/2009/818269. [Google Scholar]
  21. J. Peradze, On the convergence of an iteration method in Timoshenko’s theory of plates, in Shell-like Structures Nonclassical Theories and Applications. Springer-Verlag, Berlin, Heidelberg (2011) 83–90. [Google Scholar]
  22. J. Peradze, On an iteration method of finding a solution of a nonlinear equilibrium problem for Timoshenko’s plate. Z. Angew. Math. Mech. 91 (2011) 993–1001. [Google Scholar]
  23. J. Peradze and V. Odisharia, A numerical algorithm for a one-dimensional nonlinear Timoshenko system. Int. J. Appl. Math. Inf. 2 (2008) 67–75. [Google Scholar]
  24. S.N. Timergaliev, Method of integral equations for studying the solvability of boundary value problems for the system of nonlinear differential equations of the theory of Timoshenko type shallow inhomogeneous shells. Part. Diff. Equ. 55 (2019) 243–259. [Google Scholar]
  25. S.P. Timoshenko, On the correction for shear of the differential equation for transverse vibration of prismatic bar. Philos. Mag. 41 (1921) 744–746. [Google Scholar]
  26. S.P. Timoshenko and S. Woinowsky-Kriger, Theory of Plates and Shells, 2nd edition. McGraw-Hill Book Company, New York (1969). [Google Scholar]
  27. E. Ventsel and T. Krauthammer, Thin Plates and Shells. Marcel Dekker, Inc., New York (2001). [Google Scholar]
  28. V.Z. Vlasov, General Theory of Shells and its Application in Engineering. NASA TTF-99, Washington (1964). [Google Scholar]
  29. A.S. Volmir, The Nonlinear Dynamics of Plates and Shells. Foreign Technology Division, Wright-Patterson AFB, Dayton (1974). [Google Scholar]
  30. A.S. Volmir, The Shells on the Flow of Fluid and Gas, Problems of Hydroelasticity. Nauka, Moscow (1979). [Google Scholar]
  31. I.I. Vorovich, On the existence of solutions in the nonlinear theory of shells. Izv. Akad. Nauk SSSR. Ser. Mat. 19 (1955) 173–186. [MathSciNet] [Google Scholar]
  32. I.I. Vorovich, On some direct methods in the nonlinear theory of vibrations of curved shells. Izv. Akad. Nauk SSSR. Ser. Mat. 21 (1957) 747–784. [MathSciNet] [Google Scholar]
  33. I.I. Vorovich, Nonlinear Theory of Shallow Shells. Applied Mathematical Sciences. Vol. 133 Springer-Verlag, New York (1999). [Google Scholar]
  34. S. Woinowsky-Krieger, The effect of an axial force on the vibration of hinged bars. J. Appl. Mech. 17 (1950) 35–36. [MathSciNet] [Google Scholar]
  35. A.I. Zemlyanukhin, A.V. Bochkarev, L.I. Mogilevich and E.G. Tindova, Axisymmetric longitudinal-bending waves in a cylindrical shell interacting with a non-linear elastic medium. Model. Simul. Eng. 2016 (2016). DOI: 10.1155/2016/6596231. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you