The effect of the changes in the curvature caused by variations in the radius of the epicycle and the distance to its center on the stress state of longitudinally corrugated hollow cylinders is studied using a three-dimensional problem statement, the variable separation method, discrete Fourier series, and the discrete-orthogonalization method. The results obtained are presented in the form of graphs of displacement and stress fields and analyzed
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. M. Kulikov and S. V. Plotnikova, “Solution of three-dimensional problems for thick elastic shells by the method of reference surfaces,” Mech. Solids, 49, No. 4, 403–412 (2014).
2. D. I. Chernopiskii, ”On the stress–strain state in thick-walled cylindrical shells bounded by corrugated surfaces,” Strength of Materials, 44, No. 1, 40–52 (2012).
3. Ya. M. Grigorenko and A. Ya. Grigorenko, ”Static and dynamic problems for anisotropic inhomogeneous shells with variable parameters and their numerical solution (review),” Int. Appl. Mech., 49, No. 2, 123–197 (2013).
Ya. M. Grigorenko and L. S. Rozhok, ”Applying discrete Fourier series to solve problems of the stress state of hollow noncircular cylinders,” Int. Appl. Mech., 50, No. 2, 105–127 (2014).
Ya. M. Grigorenko and L. S. Rozhok, “Stress state of hollow cylinders with convex corrugated cross sections,” J. Math. Sci., 198, No. 2, 158–165 (2014).
Liu Fung-Bao and Tsai Ying-Chi, ”An experimental and numerical investigation of fluid flow in a cross-corrugated channel,” Heat and Mass Transfer, 46, No. 5, 585–593 (2010).
R. W. Hamming, Numerical Methods for Scientists and Engineers, McGraw-Hill, New York (1962).
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).
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York (1961).
E. C. Preissner and J. R. Vinson, ”Application of theorem of minimum potential energy to a complex structure. Part 1: Two-dimensional 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. Comp. Mat., 22, No. 5–6, 445–457 (2012).
N. P. Semenyuk and N. B. Zhukova, “ Stability and postcritical behavior of corrugated cylindrical panels under external pressure,” Int. Appl. Mech., 49, No. 6, 702–714 (2013).
N. P. Semenyuk, N. B. Zhykova, and V. V. Ostapchuk, ”Stability of corrugated composite noncircular shells under external pressure,” Int. Appl. Mech., 43, No. 12, 1380–1389 (2007).
K. P. Soldatos, ”Mechanics of cylindrical shells with noncircular cross-section. A survey,” Appl. Mech. Rev., 52, No. 8, 237–274 (1999).
S. P. Timoshenko, Theory of Elasticity, McGraw-Hill, New York (1934).
L. P. Zheleznov, V. V. Kabanov, and D. V. Boiko, ”Nonlinear deformation and stability of discretely reinforced elliptical cylindrical shells under transverse bending and internal pressure,” Russian Aeronautics (Izv. Vuzov), 57, No. 2, 118–126 (2014).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Translated from Prikladnaya Mekhanika, Vol. 52, No. 1, pp. 78–85, January–February, 2016.
Rights and permissions
About this article
Cite this article
Grigorenko, Y.M., Rozhok, L.S. Influence of Curvature on the Stress State of Longitudinally Corrugated Hollow Cylinders. Int Appl Mech 52, 49–55 (2016). https://doi.org/10.1007/s10778-016-0731-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-016-0731-0