An analytical-numerical method of solving boundary-value static problems for transversally isotropic infinitely long noncircular cylindrical shells of variable thickness is formulated and developed. The system of basic equations is derived using the relations of the refined theory of deep shells with low shear stiffness. Expressions for internal power factors and generalized displacements of closed and open cylindrical shells with arbitrary cross-section acted upon by surface and linear forces are presented. The integrals appearing in these expressions are calculated with the method of trapezoids. The numerical results for a closed shell of elliptic cross-section under uniform internal pressure presented in the form of tables and plots are analyzed
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Ya. M. Grigorenko, V. D. Budak, and O. Ya. Grigorenko, Solution of Shell Problems Based on Discrete-Continuum Methods [in Ukrainian], Ilion, Nikolaev (2010).
Yu. Yu. Abrosov, V. A. Maksimyuk, and I. S. Chernyshenko, ”Influence of cross-sectional ellipticity on the deformation of a long cylindrical shell,” Int. Appl. Mech., 52, No. 5, 529–534 (2016).
Y. N. Chen and J. Kempner, ”Buckling of oval cylindrical shell under compression and asymmetric bending,” AIAA J., 14, No. 9, 1235–1240 (1976).
Ya. M. Grigorenko and L. V. Kharitonova, “Deformation of flexible noncircular cylindrical shells under concurrent loads of two types,” Int. Appl. Mech., 43, No. 7, 754–760 (2007).
A. N. Guz, E. A. Storozhuk, and I. S. Chernyshenko, ”Nonlinear two-dimensional static problems for thin shells with reinforced curvilinear holes,” Int. Appl. Mech., 45, No. 12, 1269–1300 (2009).
V. Karpov and A. Semenov, ”Strength and stability of orthotropic shells,” World. Appl. Sci. J., 30, No. 5, 617–623 (2014).
T. A. Kiseleva, Yu. V. Klochkov, and A. P. Nikolaev, ”Comparison of scalar and vector FEM forms in the case of an elliptic cylinder,” J. Comput. Math. Phys., 55, No. 3, 422–431 (2015).
I. V. Lutskaya, V. A. Maximyuk, E. A. Storozhuk, and I. S. Chernyshenko, ”Nonlinear elastic deformation of thin composite shells of discretely variable thickness,” Int. Appl. Mech., 52, No. 6, 616–623 (2016).
V. A. Maximyuk, E. A. Storozhuk, and I. S. Chernyshenko, ”Stress–strain state of flexible orthotropic cylindrical shells with a reinforced circular hole,” Int. Appl. Mech., 51, No. 4, 425–433 (2015).
F. Romano and D. Ramlet, “Noncircular rings under shear load,” J. Frank. Inst., 284, No. 5, 283–299 (1967).
K. P. Soldatos, ”Mechanics of cylindrical shells with non-circular cross-section: a survey,” Appl. Mech, Rev., 52, No. 8, 237–274 (1999).
E. A. Storozhuk and A. V. Yatsura, ”Exact solutions of boundary-value problems for noncircular cylindrical shells,” Int. Appl. Mech., 52, No. 4, 386–397 (2016).
R. C. Tennyson, M. Booton, and R. D. Caswell, ”Buckling of imperfect elliptical cylindrical shells under axial compression,” AIAA J., 9, No. 2, 250–255 (1971).
S. P. Timoshenko, Strength of Materials, Part 2. Advanced Theory and Problems, D. Van Nostrand Company, New York (1941).
F. Tornabene, N. Fantuzzi, M. Bacciocchi, and R. Dimitri, ”Free vibrations of composite oval and elliptic cylinders by the generalized differential quadrature method,” Thin-Walled Struct., 97, 114–129 (2015).
G. Yamada, T. Irie, and Y. Tagawa, ”Free vibration of non-circular cylindrical shells with variable circumferential profile,” J. Sound Vibr., 95, No. 1, 117–126 (1984).
W. C. Young and R. G. Budynas, Roark’s Formulas for Stress and Strain, McGraw-Hill, New York (2002).
L. P. Zheleznov, V. V. Kabanov, and D. V. Boiko, ”Nonlinear deformation and stability of oval cylindrical shells under pure bending and internal pressure,” J. Appl. Mech. Tech. Phys., 47, No. 3, 406–411 (2006).
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Translated from Prikladnaya Mekhanika, Vol. 53, No. 3, pp. 91–103, May–June, 2017.
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Storozhuk, E.A., Yatsura, A.V. Analytical-Numerical Solution of Static Problems for Noncircular Cylindrical Shells of Variable Thickness. Int Appl Mech 53, 313–325 (2017). https://doi.org/10.1007/s10778-017-0813-7
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DOI: https://doi.org/10.1007/s10778-017-0813-7