Two approaches to the analysis of the stress–strain state of thick-walled cylindrical shells with different boundary conditions under local loads are proposed. These approaches involve the division of a thick shell into several coaxial shells. One approach uses polynomials to approximate the unknown functions in plan and over the thickness. In the other approach, the unknown functions are approximated by linear polynomials in plan, and their distribution over the thickness is found from the analytical solution of the corresponding system of differential equations. The stress–strain state of the shell in the area of local loading is analyzed for different boundary conditions. It is shown that the effect of the boundary conditions on the stress–strain state is very weak for shells of high curvature and strong for shells of low curvature
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Y. M. Grigorenko, A. T. Vasilenko, and N. D. Pankratova, Problems of Elasticity for Inhomogeneous Bodies [in Russian], Naukova Dumka, Kyiv (1991).
Y. M. Grigorenko, G. G. Vlaikov, and A. Ya. Grigorenko, Numerical Analytic Solution of Shell Problems Based on Various Models [in Russian], Akademperiodika, Kyiv (2006).
A. N. Guz, I. S. Chernyshenko, and K. I. Shnerenko, “Stress concentration near openings in composite shells,” Int. Appl. Mech., 37, No. 2, 139–181 (2001).
O. C. Zienkiewicz and K. Morgan, Finite Elements and Approximation, John Wiley & Sons, New York (1983).
H. Bakaiyan, H. Hosseini, and E. Ameri, “Analysis of multi-layered filament-wound composite pipes under combined interal pressure and thermo-mechanical loading wich thermal variations,” Compos. Struct., 88, 532–541 (2009).
A. Ya. Grigorenko and I. A. Loza, “Nonaxisymmetric waves in layered hollow cylinders with axially polarized piezoceramic layers,” Int. Appl. Mech., 50, No. 2, 150–158 (2014).
Y. M. Grigorenko and A. Y. 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).
Y. 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).
A. Hosine, D. Chapelle, M. L. Baubakar, et al., “Experimental and analytical investigation of the cylindsrical part of a metallic vessel reinforced by filament winding while submitted to internal pressure,” Int. J. Press. Vess. Piping, 86, 649–655 (2009).
A. V. Marchuk and V. G. Piskunov, “Statics, vibrations and stability of composite panels with gently curved orthorropic layers. 1. Statics and vibrations,” Mech. Comp. Mater., 35, No. 4, 285–292 (1999).
A. V. Marchuk and V. G. Piskunov, “Calculation of layered structures by semianalytic method of finite elements,” Mech. Comp. Mater., 33, No. 6, 553–556 (1997).
A. V. Marchuk, Y. L. Il’chenko, and S. V. Gnedash, “Analyzing the stress–strain state of thick cylindrical shells,” Int. Appl. Mech., 47, No. 4, 449–456 (2011).
C. A. Meyers and M. W. Hyer, “Response of elliptical composite cylinders to internal pressure loading,” Mech. Comp. Math. Struct., No. 4, 317–343 (1997).
A. K. Noor, W. S. Burton, and J. M. Peter, “Assessment of computational models for multilayered composite cylinders,” Int. J. Solids Struct., 27, No. 10, 1269–1286 (1991).
R. Nzengwa and B. H. Tagne Simo, “A two-dimensional model for linear elastic thick shells,” Int. J. Solids Struct., 36, No. 34, 5141–5176 (1999).
H. Y. Sheng and J. Q. Ye, “A three-dimensional state space finite element solution for laminated composite cylindrical shells,” Comp. Methods Appl. Mech. Eng., 192, 2441–2459 (2003).
A. I. Shuvalov and K. P. Soldatos, “On the successive approximation method for three-dimension analysis of radially ingomogeneous tubes with an arbitrary cylindrical anisotropy,” J. Sound. Vibr., 259, No. 1, 233–239 (2003).
K. P. Soldatos, “Mechanics of cylindrical shells with noncircular cross-section. A survey,” Appl. Mech. Rev., 52, No. 8, 237–274 (1999).
H. R. Yu, B. Liang, and L. Li, “Optimal design of cylindrical shells,” Struct. Optimiz., No. 4, 252–256 (1991).
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Translated from Prikladnaya Mekhanika, Vol. 52, No. 4, pp. 47–57, July–August, 2016.
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Marchuk, A.V., Gnidash, S.V. Analysis of the Effect of Local Loads on Thick-Walled Cylindrical Shells with Different Boundary Conditions. Int Appl Mech 52, 368–377 (2016). https://doi.org/10.1007/s10778-016-0761-7
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DOI: https://doi.org/10.1007/s10778-016-0761-7