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Analysis of Stress-Strain State of Multi-wave Shell on Parabolic Trapezoidal Plan

  • V. N. Ivanov
  • Timur Soibnazarovich ImomnazarovEmail author
  • Ismael Taha Farhan Farhan
  • Daou Tiekolo
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 113)

Abstract

The paper presents the calculation of stress-strain state of shell with carved middle surface (Krivoshapko and Ivanov in Encyclopedia of analytical surfaces. Springer International Publishing Switzerland, 752p, 2015 [1], Ivanov and Krivoshapko in Analytical methods of analyses of shells of non canonic form. RUDN, Moscow, 542p, 2010 [2], Ivanov and Rynkovskaya in MATEC web of conferences 95, 5p, 2017 [3]) with horizontal parabolic curve as directrix and multi-wave sine curve with axis in the plane of parabola as generatrix. We obtain the multi-wave parabolic sine shell on a curved trapezoidal plan (Fig. 1). There is a comparative calculation of two shells with different amplitudes of the sine generatrix—1 m and 0.5 directrix is a quadratic parabola—\(y = y_{0} - a \cdot x^{2}\), y0 = 11.5; a = −0.05 m−1; \(- 15 \le x \le 15\,(\text{m})\).

Keywords

Modelling multi-wave shells Parabolic trapezoidal plan Stress-strain state Shell with carved middle surface 

Notes

Acknowledgements

The publication was prepared with the support of the «RUDN University Program 5-100».

References

  1. 1.
    Krivoshapko SN, Ivanov VN (2015) Encyclopedia of analytical surfaces. Springer International Publishing Switzerland, 752pGoogle Scholar
  2. 2.
    Ivanov VN, Krivoshapko SN (2010) Analytical methods of analyses of shells of non canonic form. RUDN, Moscow, 542pGoogle Scholar
  3. 3.
    Ivanov V, Rynkovskaya M (2017) Analysis of thin-walled wavy shell of Monge type surface with parabola and sinusoid curves by variation-difference method. In: MATEC web of conferences 95, 12007, Art. № 12007, 5pGoogle Scholar
  4. 4.
    Ivanov VN, Rizvan M (2002) Geometry of Monge surfaces and construction of the shell. Structural mechanics of s and buildings. Construction: collection of science works, vol 11, ACB, pp 27–36 Google Scholar
  5. 5.
    Ivanov VN, Nasr Y (2000) Analyses of the shells of complex geometry by variation differential difference method. In: Collection of science works, vol 11, ACB, pp 25–34Google Scholar
  6. 6.
    Mesnil R, Santerre Y, Douthe C, Baverel O, Leger B (2015) Generating high node congruence in freeform structures with Monge’s surfaces. In: Proceedings of the international association for shell and spatial structures (IASS)Google Scholar
  7. 7.
    Ivanov VN, Mathieu G (2014) Some aspects of the geometry of surfaces with a system of flat coordinate lines. Int J Soft Comput Eng (IJSCE), pp 77–82Google Scholar
  8. 8.
    Lagu R (1986) A variational finite-difference method for analyzing channel waveguides with arbitrary index profiles. IEEE J Quant Electron 22(6):968–976CrossRefGoogle Scholar
  9. 9.
    Smit GD (1986) Numerical solution of partial differential equations by finite difference methods. In: Oxford applied mathematics and computing science series, 2nd edn. UK, 350pGoogle Scholar
  10. 10.
    Mitchell AR, Griffiths DF (1980) The finite difference method in partial differential equations. Wiley, 284p. 11. Curant R (1943) Variational methods for the solution of problems of equilibrium and vibrations. Bull Am Math Soc 49:1–23Google Scholar
  11. 11.
    Maksimyuk VA, Storozhuk EA, Chernyshenko IS (2012) Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review). Int Appl Mech 48(6):613–687MathSciNetCrossRefGoogle Scholar
  12. 12.
    Singh JP, Dey SS (1990) Variational finite difference method for free vibration of sector plates. J Sound Vib 136(1):91–104CrossRefGoogle Scholar
  13. 13.
    Curant R (1943) Variational methods for the solution of problems of equilibrium and vibrations. Bull Am Math Soc 49:1–23MathSciNetCrossRefGoogle Scholar
  14. 14.
    Reddy JN (2002) Energy principles and variational methods in applied mechanics. Willy. New Jersey, 542pGoogle Scholar
  15. 15.
    Andujar Moreno IR, Roset J, Kilar V (2014) Variational mechanics and stochastic methods applied to structural design, 173pGoogle Scholar
  16. 16.
    Aginam CH, Chidolue CA, Ezeagu CA (2012) Application of direct variational method in the analysis of isotropic thin rectangular plates. ARPN J Eng Appl Sci 7(9):1128–1138Google Scholar
  17. 17.
    Lanczos C, (1970) The variational principles of mechanics. University of Toronto Press, Canada, 418pGoogle Scholar
  18. 18.
    Argyris JH (1960) Energy theorems and structural analysis. Butterworths Scientific Publications, London, 85pGoogle Scholar
  19. 19.
    Lapidus L, Pinder GF (1982) Numerical solution of partial differential equations in science and engineering. Wiley-Interscience, New York, 677pGoogle Scholar
  20. 20.
    Wunderlich W, Pilkey W (2002) Mechanics of structures. Variational and computational methods. CRC Press, pp 852–877Google Scholar
  21. 21.
    Ivanov VN (2001) Variation principals and methods of analyses of the problems of theory of elasticity. RUDN, Moscow, 176pGoogle Scholar
  22. 22.
    Ivanov VN (2008) The base of the finite elements method and the variation-difference method. RUDN, Moscow, 170pGoogle Scholar
  23. 23.
    Ivanov VN, Kushnarenko IV (2013) The variational-difference method for the analyses of the shell with complex geometry. In: International association for shell and spatial structures proceedings of the IASS 2013 symposium “beyond the limits of man”, 6pGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • V. N. Ivanov
    • 1
  • Timur Soibnazarovich Imomnazarov
    • 1
    Email author
  • Ismael Taha Farhan Farhan
    • 1
  • Daou Tiekolo
    • 1
  1. 1.Department of Civil Engineering, Engineering AcademyPeoples’ Friendship University of Russia (RUDN University)MoscowRussian Federation

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