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Layered Inhomogeneous Hollow Cylinders with Concave Corrugations Under Internal Pressure

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The stress problem for layered hollow inhomogeneous cylinders with concave semi-corrugations is solved in spatial statement, and their stress state is studied depending on the stiffness of the core layer. To solve the problem, the analytical methods of variable separation, approximation of functions by discrete Fourier series, and the numerical discrete-orthogonalization method are used. Numerical results are analyzed.

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References

  1. S. K. Godunov, “Numerical solution of boundary-value problems for systems of linear ordinary differential equations,” Usp. Mat. Nauk, 16, No. 3, 171–174 (1961).

    MathSciNet  Google Scholar 

  2. S. K. Golushko and Yu. V. Nemirovskii, Direct and Inverse Problems of the Mechanics of Elastic Composite Plates and Shells of Revolution [in Russian], Fizmatlit, Moscow (2008).

    Google Scholar 

  3. E. I. Grigolyuk and E. A. Kogan, Statics of Layered Elastic Shells [in Russian], NII Mekh. MGU, Moscow (1999).

    Google Scholar 

  4. Ya. M. Grigorenko and L. S. Rozhok, “Analysis of the stress state of hollow cylinders with concave corrugations,” Mat. Met. Fiz.-Mekh. Polya, 58, No. 4, 70–77 (2015).

    MATH  Google Scholar 

  5. V. O. Kaledin, S. M. Akul’chenko, A. B. Mitkevich, E. V. Reshetnikova, E. A. Sedova, and Yu. V. Shpakova, Modeling of Statics and Dynamics of Shell Structures Made of Composite Materials [in Russian], Fizmatlit, Moscow (2014).

    Google Scholar 

  6. S. G. Lekhnitskii, Theory of Elasticity of Anisotropic Body [in Russian], Nauka, Moscow (1977).

    MATH  Google Scholar 

  7. S. P. Timoshenko, A Course in the Theory of Elasticity [in Russian], Naukova Dumka, Kyiv (1972).

    Google Scholar 

  8. A. De Leo, A. Contento, and A. Di Egidio, “Parametric study of the distribution of the tensile stresses in pavilion structures constituted by four sectors of barrel shells,” Meccanica, 52, No. 10, 2293–2305 (2017).

    Article  MathSciNet  Google Scholar 

  9. A. Z. Galishin, A. A. Zolochevskii, and S. N. Sklepus, “Feasibility of shell models for determining the stress–strain state and creep damage of cylindrical shells,” Int. Appl. Mech., 53, No. 4, 398–406 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  10. A. Ya. Grigorenko, W. H. Muller, Ya. M. Grigorenko, and G. G. Vlaikov, Recent Developments in Anisotropic Heterogeneous Shell Theory: Applications of Refined and Three-Dimensional Theory, IIB, Springer (2016).

  11. K. Hatanaka, S. M. V. Rao, T. Saito, and T. Mizukaki, “Numerical investigations of shock oscillations ahead of a hemispherical shell in supersonic flow,” Shock Waves, 26, No. 3, 299–310 (2016).

    Article  ADS  Google Scholar 

  12. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, MG Graw-Hill, New York (1961).

    MATH  Google Scholar 

  13. H. W. Kwon, S. Y. Hong, and J. H. Song, “Vibrational energy flow analysis of coupled cylindrical thin shell structures,” J. Mech. Sci. Tech., 30, No. 6, 4049–4062 (2016).

    Article  Google Scholar 

  14. S. Malek and Chr. Williams, The Equilibrium of Corrugated Plates and Shells, Nexus Netw.J. (2017).

  15. A. V. Marchuk and S. V. Gnidash, “Analysis of the effect of local loads on thick-walled cylindrical shells with different boundary conditions,” Int. Appl. Mech., 52, No. 4, 368–377 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  16. S. Ya. Sajadi, M. H. Abolbashari, and M. Hosseini, “Geometrically nonlinear dynamic analysis of functionally graded thick hollow cylinders using total Lagrangian MLPG method,” Meccanica, 51, No. 3, 655–672 (2016).

    Article  MathSciNet  Google Scholar 

  17. E. A. Storozhuk and A. V. Yatsura, “Exact solutions of boundary-value problems for noncircular cylindrical shells,” Int. Appl. Mech., 52, No. 4, 386–397 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  18. L. Tokova, A. Yasinskyy, and C. C. Ma, “Effect of the layer inhomogeneity on the distribution of stresses and displacements in an elastic multilayer cylinder,” Acta Mech., 228, No. 8, 2865–2877 (2017).

    Article  MathSciNet  Google Scholar 

  19. G. Wrobel, M. Szymiczek, and J. Kaszmarczyk, “Influence of the structure and number of reinforcement layers on the stress state in the shells of tanks and pressure pipes,” Mech. Comp. Mat., 53, No. 2, 165–178 (2017).

    Article  Google Scholar 

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Correspondence to Ya. M. Grigorenko.

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Translated from Prikladnaya Mekhanika, Vol. 54, No. 5, pp. 47–54, September–October, 2018.

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Grigorenko, Y.M., Rozhok, L.S. Layered Inhomogeneous Hollow Cylinders with Concave Corrugations Under Internal Pressure. Int Appl Mech 54, 531–538 (2018). https://doi.org/10.1007/s10778-018-0905-z

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  • DOI: https://doi.org/10.1007/s10778-018-0905-z

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