Abstract
A numerical-analytical method based on approximation of the sought solution by a system of basis functions is proposed to solve the boundary-value problem of axisymmetric deformation of articles made of a transversely isotropic material. An algorithm for constructing polynomial functions on the basis of invariant-group solutions is described.
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References
F. L. Matthews and R. D. Rawlings, Composite Materials. Engineering and Science, CRC Press, Boca Raton (2000).
N. M. Bodunov, G. V. Druzhinin, and I. M. Zakirov, “One algorithm for solving a three-dimensional problem of the elasticity theory for a transversely isotropic medium,” Izv. Vyssh. Ucheb. Zaved., Aviats. Tekh., No. 1, 18–21 (2007).
G. V. Druzhinin and N. M. Bodunov, “Approximate method for solving a two-dimensional problem of elasticity theory,” J. Appl. Mech. Tech. Phys., 40, No. 4, 712–718 (1999).
G. V. Druzhinin, “Construction of basis functions and their application to boundary-value problems of mechanics of continuous media,” J. Appl. Mech. Tech. Phys., 44, No. 6, 779–785 (2003).
G. V. Druzhinin, I. M. Zakirov, and N. M. Bodunov, Basis Functions in Approximate Solutions of Boundary-Value Problems [in Russian], Fen, Kazan’ (2000).
S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Solid [in Russian], Nauka, Moscow (1977).
M. A. Koltunov, Yu. N. Vasil’ev, and V. A. Chernykh, Elasticity and Strength of Cylindrical Bodies [in Russian], Vysshaya Shkola, Moscow (1975).
A. A. Babloyan, “One problem of axisymmetric deformation of a finite-length circular cylinder from a transversely isotropic body,” Dokl. Akad. Nauk ArmSSR, 32, No. 4, 189–195 (1961).
L. V. Ovsyannikov, Group Analysis of Differential Equations, Academic Press, New York (1982).
V. Novacki, “Stress functions in spatial problems of an elastic body with transverse isotropy,” Bul. Pol. Akad. Nauk (Otd. 4), No. 1, 23–34 (1954).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 6, pp. 81–89, November–December, 2009.
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Bodunov, N.M., Druzhinin, G.V. One solution of an axisymmetric problem of the elasticity theory for a transversely isotropic material. J Appl Mech Tech Phy 50, 982–988 (2009). https://doi.org/10.1007/s10808-009-0132-9
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DOI: https://doi.org/10.1007/s10808-009-0132-9