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Generalized variational principles for buckling analysis of circular cylinders

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Abstract

A generalized variational principle and a parameterized generalized variational principle are obtained for large deformation analysis of circular cylinders by the semi-inverse method; all known variational principles in the literature are special cases of the obtained parameterized functional. In this approach, a trial functional is constructed with an energy-like integral involving an unknown function, which is identified step by step. The present paper provides a quite straightforward but rigorous tool to the construction of a variational principle for the shell or plate buckling.

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References

  1. Adamu, M.Y., Ogenyi, P.: New approach to parameterized homotopy perturbation method. Therm. Sci. 22(4), 1865–1870 (2018)

    Article  Google Scholar 

  2. Ain, Q.T., He, J.H.: On two-scale dimension and its applications. Therm. Sci. 23(3B), 1707–1712 (2019). https://doi.org/10.2298/TSCI190408138A

    Article  Google Scholar 

  3. Anjum, N., He, J.H.: Laplace transform: making the variational iteration method easier. Appl. Math. Lett. 92, 134–138 (2019)

    Article  MathSciNet  Google Scholar 

  4. Chien, W.Z.: Torsional rigidity of shells of revolution. Appl. Math. Mech. 11(5), 403–412 (1990)

    Article  Google Scholar 

  5. Dost, S., Tabarrok, B.: Some variational formulations for buckling analysis of circular cylinders. Int. J. Solids Struct. 20(4), 315–326 (1984)

    Article  MathSciNet  Google Scholar 

  6. Dost, S., Tabarrok, B.: Application of a mixed variational principle to buckling analysis of circular cylinders. Z. Angew. Math. Mech. 68(3), 131–137 (1988)

    Article  MathSciNet  Google Scholar 

  7. Gazzola, F., Wang, Y., Pavani, R.: Variational formulation of the Melan equation. Math. Methods Appl. Sci. 41(3), 943–951 (2018)

    Article  MathSciNet  Google Scholar 

  8. He, J.H.: Hybrid problems of determining unknown shape of bladings in compressible S2-flow in mixed-flow turbomachinery via variational technique. Aircr. Eng. Aerosp. Technol. 71(2), 154–159 (1999)

    Article  Google Scholar 

  9. He, J.H.: Inverse problems of determining the unknown shape of oscillating airfoils in compressible 2D unsteady flow via variational technique. Aircr. Eng. Aerosp. Technol. 72(1), 18–24 (2000)

    Article  Google Scholar 

  10. He, J.H.: Generalized Hellinger–Reissner principle. ASME J. Appl. Mech. 67(2), 326–331 (2000)

    Article  MathSciNet  Google Scholar 

  11. He, J.H.: Coupled variational principles of piezoelectricity. Int. J. Eng. Sci. 39(3), 323–341 (2001)

    Article  MathSciNet  Google Scholar 

  12. He, J.H.: Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 20, 1141–1199 (2006)

    Article  MathSciNet  Google Scholar 

  13. He, J.H.: A tutorial review on fractal space time and fractional calculus. Int. J. Theor. Phys. 53, 3698–718 (2014)

    Article  Google Scholar 

  14. He, J.H.: An alternative approach to establishment of a variational principle for the torsional problem of piezoelastic beams. Appl. Math. Lett. 52, 1–3 (2016)

    Article  MathSciNet  Google Scholar 

  15. He, J.H.: Hamilton’s principle for dynamical elasticity. Appl. Math. Lett. 72, 65–69 (2017)

    Article  MathSciNet  Google Scholar 

  16. He, J.H.: Generalized equilibrium equations for shell derived from a generalized variational principle. Appl. Math. Lett. 64, 94–100 (2017)

    Article  MathSciNet  Google Scholar 

  17. He, J.H.: Fractal calculus and its geometrical explanation. Results Phys. 10, 272–276 (2018)

    Article  Google Scholar 

  18. He, J.H.: A modified Li–He’s variational principle for plasma. Int. J. Numer. Methods Heat Fluid Flow (2019). https://doi.org/10.1108/HFF-06-2019-0523

  19. He, J.H., Ji, F.Y.: Taylor series solution for Lane-Emden equation. J. Math. Chem. 57(8), 1932–1934 (2019). https://doi.org/10.1007/s10910-019-01048-7

    Article  MathSciNet  MATH  Google Scholar 

  20. He, J.H., Ji, F.Y.: Two-scale mathematics and fractional calculus for thermodynamics. Therm. Sci. 23(4), 2131–2133 (2019). https://doi.org/10.2298/TSCI1904131H

    Article  Google Scholar 

  21. He, J.H.: The simplest approach to nonlinear oscillators. Results Phys. 15, 102546 (2019). https://doi.org/10.1016/j.rinp.2019.102546

    Article  Google Scholar 

  22. Li, X.X., Tian, D., He, C.H.: A fractal modification of the surface coverage model for an electrochemical arsenic sensor. Electrochim. Acta 296, 491–493 (2019)

    Article  Google Scholar 

  23. Liu, G.L.: Formulation of inverse problem of 2-D unsteady flow around oscillating airfoils by variational principles. Acta Aerodyn. Sin. 14(1), 1–6 (1996)

    MathSciNet  Google Scholar 

  24. Liu, Z.J., Adamu, M.Y., Suleiman, E., et al.: Hybridization of homotopy perturbation method and Laplace transformation for the partial differential equations. Therm. Sci. 21, 1843–1846 (2017)

    Article  Google Scholar 

  25. Liu, Z.R., Cu, G.Q., Wang, X.: Vibration characteristics of a tunnel structure based on soil-structure interaction. Int. J. Geomech. 14(4), 04014018 (2014)

    Article  Google Scholar 

  26. Tabarrok, B., Dost, S.: Some variational formulations for large deformation analysis of plates. Computer Methods Appl. Mech. Eng. 22(3), 279–288 (1980)

    Article  MathSciNet  Google Scholar 

  27. Wang, Q.L., Shi, X.Y., He, J.H.: Fractal calculus and its application to explanation of biomechanism of polar bear hairs. Fractals 26, 1850086 (2018)

    Article  Google Scholar 

  28. Wang, Y., An, J.Y., Wang, X.Q.: A variational formulation for anisotropic wave traveling in a porous medium. Fractals 27(4), 1950047 (2019)

    Article  MathSciNet  Google Scholar 

  29. Wang, Y., Deng, Q.G.: Fractal derivative model for tsunami travelling. Fractals 27(2), 1950017 (2019). https://doi.org/10.1142/S0218348X19500178

    Article  MathSciNet  Google Scholar 

  30. Washizu, K.: Variational Methods in Elasticity and Plasticity, 2nd edn. Pergamon Press, New York (1975)

    MATH  Google Scholar 

  31. Wu, Y., He, J.H.: A remark on Samuelson’s variational principle in economics. Appl. Math. Lett. 84, 143–147 (2018)

    Article  MathSciNet  Google Scholar 

  32. Wu, Y., He, J.H.: Homotopy perturbation method for nonlinear oscillators with coordinate dependent mass. Results Phys. 10, 270–271 (2018)

    Article  Google Scholar 

  33. Wu, Y.P., Lu, E., Zhang, S.: Study on bi-stable behaviors of un-stressed thin cylindrical shells based on the extremal principle. Struct. Eng. Mech. 68(3), 377–384 (2018)

    Google Scholar 

  34. Zhou, L., Huang, Y.: The elastic deflection and ultimate bearing capacity of cracked eccentric thin-walled columns. Struct. Eng. Mech. Int. l J. 19(4), 401–411 (2005)

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Science, Xi’an University of Architecture and Technology, Xi’an, People’s Republic of China

    Ji-Huan He

  2. National Engineering Laboratory for Modern Silk, College of Textile and Engineering, Soochow University, Suzhou, People’s Republic of China

    Ji-Huan He

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  1. Ji-Huan He
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He, JH. Generalized variational principles for buckling analysis of circular cylinders. Acta Mech 231, 899–906 (2020). https://doi.org/10.1007/s00707-019-02569-7

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  • DOI: https://doi.org/10.1007/s00707-019-02569-7

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