Abstract
The approach to the solution of a three-dimensional boundary-value stress problem for elastic hollow inhomogeneous cylinders of corrugated elliptic cross-section is proposed. The boundary conditions make it possible to separate variables along the length at the cylinder ends. It is proposed to include additional functions into the resolving system of differential equations. These functions enable the variables to be separated along a directrix using discrete Fourier series. The boundary-value problem derived for the system of ordinary differential equations is solved by the stable numerical method of discrete orthogonalization over the cylinder thickness. Results in the form of plots and tables are presented.
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References
S.P. Timoshenko, Theory of Elasticity. New York: MG Graw-Hill (1934).
K.P. Soldatos, Mechanics of cylindrical shells with non-circular cross-section. A survey. Appl. Mech. Rev 52 (1999) 237-274
Ya.M. Grigorenko and L.S. Rozhok, On one approach to the solution of stress problems for noncircular hollow cylinders. Int. Appl. Mech. 38 (2002) 562-573
Ya.M. Grigorenko, A.T. Vasilenko and I.G. Emel’yanov, Statics of Sructural Elements of the Twelve – Volume Series Mechanics of Composites. Vol. 8. Kiev: “A.S.K.” (1999) 379 pp. (in Russian)
Ya.M. Grigorenko and A.M. Timonin, One approach to the numerical solution of two-dimensional problems of the theory of plates and shells with variable parameters. Soviet Appl. Mech. 23 (1987) 54-61
R.W. Hamming, Numerical Methods for Scientists and Engineers. New York: MG Graw-Hill (1962).
G.M. Fichtengol’ts, A Course of Differential and Integral Calculus. Vol. 3. Moscow-Leningrad: Gostechizdat (1949) 783 pp. (in Russian)
S.K. Godunov, Numerical solution of boundary-value problems for systems of linear ordinary differential equations. Uspekhi Mat. Nauk. 16 (1961) 171-174
Ya.M. Grigorenko, Isotropic and Anisotropic Laminated Shells of Variable Thickness. Kiev: Naukova Dumka (1973).
R. Bellman and R. Kalaba, Quasi-Linearization and Nonlinear Boundary-Value Problems. New York: Elsevier (1965).
I.S. Sokolnikoff and R.D. Specht, Mathematical Theory of Elasticity. New York: MG Graw-Hill (1946).
S.G. Lekhnitsky, Theory of an Anisotropic Body. Moscow: MIR Publishers (1981).
Ya.M. Grigorenko and L.S. Rozhok, Stress analysis of corrugated hollow cylinders. Int. Appl. Mech. 38 (2002) 1473-1481
Ya.M. Grigorenko and L.S. Rozhok, Discrete Fourier-series method in problems of bending of variable thickness rectangular plates. J. Engng. Math. 46 (2003) 269-280
Ya.M. Grigorenko and L.S. Rozhok, Solving the stress problem for hollow cylinders with corrugated elliptical cross section. Int. Appl. Mech. 40 (2004) 169-175
G.A. Korn and T.M. Korn, Mathematical Handbook for Scientists and Engineers. New York: MG Graw-Hill (1961).
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Grigorenko, Y.M., Rozhok, L.S. Equilibrium of Elastic Hollow Inhomogeneous Cylinders of Corrugated Elliptic Cross-Section. J Eng Math 54, 145–157 (2006). https://doi.org/10.1007/s10665-005-5572-5
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DOI: https://doi.org/10.1007/s10665-005-5572-5