The stress state of longitudinally corrugated hollow cylinders made of orthotropic and isototropic materials is analyzed using a spatial problem statement, analytical variable separation and discrete Fourier series methods and numerical method of discrete orthogonalization. The results are presented as graphs and diagrams 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
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).
Ya. M. Grigorenko, A. T. Vasilenko, I. G. Emel’yanov, and others, Statics of Structural Members, Vol. 8 of the 12-volume series Mechanics of Composite Materials [in Russian], A.S.K., Kyiv (1999).
Ya. M. Grigorenko, G. G. Vlaikov, and A. Ya. Grigorenko, Numerical Analytic Solution of Shell Problems Based on Various Models [in Russian], Akademperiodika, Kyiv (2006).
I. G. Emel’yanov, “Using discrete Fourier series to determine the stress state of shell structures,” Vych. Mekh. Splosh. Sred, 8, No. 3, 245–253 (2015).
L. M. Fedorchenko and Y. O. Zhuk, “Analysis of the stress–strain state of an orthotropic cylindrical shell with different boundary conditions,” Visn. Kyivs’kogo Nats. Univ. im. Tarasa Shevchenko, Ser.: Fiz.-Mat. Nauky, No. 1, 49–52 (2015).
O. M. Khimich, O. A. Nikolaevska, and T. V. Chistyakova, “Some methods to increase the accuracy of computations,” Mat. Komp. Model., Ser.: Fiz.-Mat. Nauky, No. 15, 249–254 (2017).
O. M. Khimich, “Supercomputer technologies and mathematical modeling of complex systems,” Visn. NAN Ukrainy, No. 5, 69–72 (2018).
I. P. Shats’kyi and A. B. Struk, “Stressed state of pipeline in zones of soil local fracture,” Strength of Materials, 41, No. 5, 548–553 (2009).
Yu. Yu. Abrosov, V. A. Maximyuk, and I. S. Chernyshenko, “Influence of cross-sectional ellipticity on the deformation of a long cylindrical shell,” Int. App. Mech., 52, No. 5, 529–534 (2016).
V. K. Belov, L. P. Zheleznov, and T. S. Ognyanova, “Research on nonlinear deformation and stability of an advanced aircraft fuselage composite section under pure bending,” Russian Aeronautics, 60, No. 4, 514–522 (2017).
E. I. Bespalova, “Generalized method of finite integral transforms in static problems for anisotropic prisms,” Int. App. Mech., 54, No. 1, 41–55 (2018).
A. Ya. Grigorenko, M. Yu. Borisenko, E. V. Boichuk, and A. P. Prigoda, “Numerical determination of natural frequencies and modes of the vibrations of a thick-walled cylindrical shell,” Int. App. Mech., 54, No. 1, 75–84 (2018).
A. Ya, Grigorenko, Å. N. Pliska, G. V. Sorochenko, and N. N. Tormakhov, “Application of methods of numerical analysis for studying mechanical processes in biomechanics,” Int. App. Mech., 54, No. 3, 336–372 (2018).
Ya. M. Grigorenko, A. Ya. Grigorenko, and L. I. Zakhariichenko, “Analysis of the influence of the geometrical parameters of elliptic cylindrical shells with variable thickness on their stress–strain state,” Int. App. Mech., 54, No. 2, 155–162 (2018).
Ya. M. Grigorenko and L. S. Rozhok, “Stress state of longitudinally corrugated hollow cylinders with different cross-sectional curvature,” Int. App. Mech., 52, No. 6, 581–586 (2016).
Ya. M. Grigorenko and L. S. Rozhok, “Effect of change in the curvature parameters on the stress state of concave corrugated hollow cylinders,” Int. App. Mech., 54, No. 3, 266–273 (2018).
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).
R. W. Hamming, Numerical Methods for Scientists and Engineers, McGraw-Hill, New York (1962).
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw-Hill, New York (1961).
S. G. Lekhnitsky, Theory of an Anisotropic Body, MIR Publishers, Moscow (1981).
E. A. Storozhuk and A. V. Yatsura, “Analytical-numerical solution of static problems for noncircular cylindrical shells of variable thickness,” Int. App. Mech., 53, No. 3, 313–325 (2017).
E. A. Storozhuk and A. V. Yatsura, “Exact solutions of boundary-value problems for noncircular cylindrical shells,” Int. App. Mech., 52, No. 4, 386–397 (2016).
S. N. Thakur, Ch. Ray, and S. Chakraborty, “A new efficient higher-order shear deformation theory for a doubly curved laminated composite shell,” Acta Mechanica, 228, No. 1, 69–87 (2017).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika, Vol. 55, No. 5, pp. 110–120, September–October 2019.
Rights and permissions
About this article
Cite this article
Rozhok, L.S. Stress Analysis of Longitudinally Corrugated Hollow Orthotropic Cylinders. Int Appl Mech 55, 552–561 (2019). https://doi.org/10.1007/s10778-019-00977-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-019-00977-9