In the three-dimensional statement, by the method of approximation of functions by discrete Fourier series, we perform the analysis of the dependence of the stress state of a hollow cylinder whose cross section has the form of joined concave semicorrugations subjected to the action of internal pressure under certain conditions imposed on the end faces on the thicknesses and curvatures of the cross sections of the cylinders caused by the changes in the number of semicorrugations. The results of the solution of the problem are presented in the form of the plots of distributions of the fields of displacements and stresses.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. K. Godunov, “On the numerical solution of boundary-value problems for systems of ordinary differential equations,” Usp. Mat. Nauk, 16, No. 3(99), 171–174 (1961).
Ya. M. Grigorenko, O. I. Bespalova, and G. P. Urusova, “Dynamic stability of the shell of revolution with corrugated shape of the generatrix,” Dop. Nats. Akad. Nauk Ukr., No. 10, 61–66 (2011).
Ya. M. Grigorenko and A. Ya. Grigorenko, “Static and dynamic problems for anisotropic inhomogeneous shells with variable parameters and their numerical solution (Review),” Prikl. Mekh., 49, No. 2, 3–70 (2013); English translation: Int. Appl. Mech., 49, No. 2, 123–197 (2013).
Ya. M. Grigorenko and L. S. Rozhok, “Stress state of hollow cylinders with convex corrugated cross sections,” Mat. Met. Fiz.-Mekh. Polya, 55, No. 4, 125–130 (2012); English translation : J. Math. Sci., 198, No. 2, 158–165 (2014).
Ya. M. Grigorenko and L. S. Rozhok, “Applying discrete Fourier series to solve problems of the stress state of hollow noncircular cylinders,” Prikl. Mekh., 50, No. 2, 3–26 (2014); English translation: Int. Appl. Mech., 50, No. 2, 105–127 (2014).
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, MсGraw-Hill, New York (1961).
N. P. Semenyuk and N. B. Zhukova, “Stability and postcritical behavior of corrugated cylindrical panels under external pressure,” Prikl. Mekh., 49, No. 6, 86–99 (2013); English translation: Int. Appl. Mech., 49, No. 6, 702–714 (2013).
S. P. Timoshenko, Course of the Theory of Elasticity, MсGraw-Hill, New York (1970).
D. I. Chernopiskii, “On stress-strain state in thick-walled cylindrical shells bounded by corrugated surfaces,” Probl. Prochn., 44, No. 1, 58–74 (2012); English translation: Strength Mater., 44, No. 1, 40–52 (2012).
D. Beben, “Field performance of corrugated steel plate road culvert under normal live-load conditions,” J. Perform. Constr. Facil., 27, No. 6, 807–817 (2013).
F.-B. Liu and Y.-C. Tsai, “An experimental and numerical investigation of fluid flow in a cross-corrugated channel,” Heat Mass Transfer, 46, No. 5, 585–593 (2010).
R. W. Hamming, Numerical Methods for Scientists and Engineers, McGraw-Hill, New York (1962).
Z. He, G. Liu, W. Jiang, Z. Huang, and D. Zhang, “Nonlinear dynamic responses of a corrugated shell structure under uniform load,” J. Eng. Mech., 140, No. 6, (2014), https://doi.org/10.1061/(ASCE)EM.1943-7889.0000717.
R. F. Janz, S. Ozpetek, L. E. Ginzton, and M. M. Laks, “Regional stress in a noncircular cylinder,” Biophys. J., 55, No. 1, 173–182 (1989).
L. Ma, L. Zhou, and S. Wan, “Study of the calculation method of lateral load distribution on a continuous composite box girder bridge with corrugated steel webs,” J. Highway Transp. Res. Dev. (English Edition), 8, No. 2, 42–46 (2014).
Z. Manko and D. Beben, “Research on steel shell of a road bridge made of corrugated plates during backfilling,” J. Bridge Eng., 10, No. 5, 592–603 (2005).
E. C. Preissner and J. R. Vinson, “Application of theorem of minimum potential energy to a complex structure. Part I: Twodimensional analysis,” Int. J. Solids Struct., 40, No. 5, 1089–1108 (2003).
K. Sakata and G. Ben, “Fabrication method and compressive properties of CFRP isogrid cylindrical shells,” Adv. Compos. Mater., 21, No. 5-6, 445–457 (2012).
K. P. Soldatos, “Mechanics of cylindrical shells with noncircular cross-section. A survey,” Appl. Mech. Rev., 52, No. 8, 237–274 (1999).
Author information
Authors and Affiliations
Additional information
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 58, No. 4, pp. 70–77, October–December, 2015.
Rights and permissions
About this article
Cite this article
Grigorenko, Y.М., Rozhok, L.S. Analysis of the Stress State of Hollow Cylinders with Concave Corrugated Cross Sections. J Math Sci 228, 80–89 (2018). https://doi.org/10.1007/s10958-017-3607-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-017-3607-x