The stress–strain state of open and closed variable-thickness elliptic cylindrical shells is studied. To solve the problem, the Mushtari–Donell–Vlasov shell model and numerical-analytical approach based on the spline-collocation and discrete-orthogonalization methods are used. Various types of boundary conditions and variable loadings are considered. The influence of the type of variable loading and thickness on the distribution of displacements and stresses in the shells is analyzed.
Similar content being viewed by others
References
Yu. S. Zav’yalov, Yu. I. Kvasov, and V. L. Miroshnichenko, Spline-Function Methods [in Russian], Nauka, Moscow (1980).
Kh. M. Mushtari, “Some generalizations of the theory of thin shells with application to problems of the stability of elastic equilibrium.” Prikl. Mat. Mekh., 2, No. 14, 439–456 (1939).
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, 123–193 (2013).
Ya. M. Grigorenko, A. Ya. Grigorenko, and L. I. Zakhariichenko, “Stress–strain solutions for circumferentially corrugated elliptic cylindrical shells,” Int. Appl. Mech., 42, No. 9, 1021–1028 (2006).
Ya. M. Grigorenko and N. N. Kryukov, “Solution of problems of the theory of plates and shells with spline function (survey),” Int. Appl. Mech., 31, No. 9, 413–434 (1995).
A. Ya. Grigorenko, W. H. Muller, Ya. M. Grigorenko, and G. G. Vlaikov, Recent Developments in Anisotropic Heterogeneous Shell Theory, Springer, Berlin (2016).
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, 102–127 (2014).
Ya. M. Grigorenko and L. I. Zakhariichenko, “Solution of the problem of the stress state of noncircular cylindrical shells of variable thickness,” Int. Appl. Mech., 34, No. 12, 1196–1206 (1998).
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, MG Graw-Hill, New York (1961).
K. P. Soldatos, “Mechanics of cylindrical shells with noncircular cross-section. A survey,” Appl. Mech. Rev., 52, No. 8, 237–274 (1999).
K. K. Viswanathan, K. S. Kim, J. H. Lee, H. S. Koh, and J. B. Lee, “Free vibration of multi-layer circular cylindrical shell with cross-ply walls, including shear deformation by using spline function method,” J. Mech. Sci. Technol., 22, No. 11, 2062–2075 (2008).
V. Z. Vlasov, General Theory of Shells and its Applications in Engineering, NASA TTF-99, Washington (1964).
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. VUZ), 57, No. 2, 118–126 (2014).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika, Vol. 54, No. 2, pp. 42–50, March–April, 2018.
Rights and permissions
About this article
Cite this article
Grigorenko, Y.M., Grigorenko, A.Y. & Zakhariichenko, L.I. Analysis of Influence of the Geometrical Parameters of Elliptic Cylindrical Shells with Variable Thickness on their Stress-Strain State. Int Appl Mech 54, 155–162 (2018). https://doi.org/10.1007/s10778-018-0867-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-018-0867-1