The effect of change in the curvature parameters of the stress state of concave corrugated hollow cylinders is studied. The change is attributed to variations in the radius of a moving circle and in the distance to its center. The problem is solved in spatial statement using analytical methods of separation of variables, approximation of functions by discrete Fourier series, and the numerical discrete-orthogonalization method. Results are presented in the form of plots demonstrating distributions of displacement and stress fields and are analyzed.
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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).
V. S. Hudramovich, “Modeling stress–strain state of shell structures of rocket and power engineering,” Tekhn. Mekh., No. 4, 97–104 (2013).
I. G. Emel’yanov, “Determining stress state of shell structures using discrete Fourier series,” Vych. Mekh. Splosh. Sred, 8, No. 3, 245–253 (2015).
V. O. Kaledin, S. M. Aul’chenko, A. B. Mitkevich, E. B. Reshetnikova, E. A. Sedova, and Yu. V. Shpakova, Modeling Statics and Dynamics of Shell Structures of Composite Materials [in Russian], Fizmatlit, Moscow, (2014).
A. A. Savelov, Plane Curves. Taxonomy, Properties, Application (Reference Guide) [in Russian], Fizmatlit, Moscow (1960).
I. P. Shats’kyi and A. B. Struk, “Stressed state of pipeline in zones of soil local fracture,” Strength of Materials, 41, No. 5 (2009).
V. I. Andreev, “Numerical-analytical solution of a two-dimensional problem for elastic radially inhomogeneous thick-walled cylinder,” Appl. Mech. Mater., 752–753, 642–647 (2015).
E. I. Bespalova and G. P. Urusova, “Vibrations of shells of revolution with branched meridian,” Int. Appl. Mech., 52, No. 1, 117–126 (2016).
Ya. M. Grigorenko and L. S. Rozhok, “Stress state of longitudinally corrugated hollow cylinders with different cross-sectional curvature,” Int. Appl. Mech., 52, No. 6, 581–586 (2016).
K. M. Dovbnya and N. A. Shevtsova, “Studies on the stress state of an orthotropic shell of arbitrary curvature with the through crack under bending loading,” Strength of Materials, 46, No. 3, 345–349 (2014).
R. W. Hamming, Numerical Methods for Scientists and Engineers, MG Graw-Hill, New York (1962).
E. I. Hart, V. S. Hudramovich, S. A. Ryabokon’, and E. V. Samarskaya, “Numerical simulation of stress-strain state for nonhomogeneous shell-type structures based on the finite-element method,” Model. Numer. Simul. Mater. Sci., 3, No. 4, 155–157 (2013).
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, MG Graw-Hill, New York (1961).
G. A. Popov, Yu. S. Protserov, and I. A. Gonchar, “Exact solution of some axisymmetric problems for elastic cylinders of finite length taking into account specific weight,” Int. Appl. Mech., 51, No. 4, 391–402 (2015).
S. P. Timoshenko, Theory of Elasticity, MG Graw-Hill, New York (1934).
M. Zheng, Y. Zhao, H. Teng, J. Hu, and L. Yu, “Elastic limit analysis for elliptical and circular tubes under lateral tension,” Arab J. Sci. Eng., 40, No. 6, 1727–1732 (2015).
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Translated from Prikladnaya Mekhanika, Vol. 54, No. 3, pp. 27–35, May–June, 2018.
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Grigorenko, Y.M., Rozhok, L.S. Effect of Change in the Curvature Parameters on the Stress State of Concave Corrugated Hollow Cylinders. Int Appl Mech 54, 266–273 (2018). https://doi.org/10.1007/s10778-018-0879-x
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DOI: https://doi.org/10.1007/s10778-018-0879-x