Abstract
A method is proposed for the regularization of the calculation process in investigations of homogeneous solutions of three-dimensional problems of elasticity theory by the method of homogeneous solutions. A qualitative investigation is performed of a three-dimensional compression—tension problem with mixed boundary conditions. Questions are examined of the a priori finding of limit values of the unknowns in an infinite system of equations, of the behavior of the coefficients and the series convergence on the boundary as a function of properties of the functions.
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References
I. I. Vorovich, "Certain mathematical questions of plate and shell theory," Trudy, Sec. All-Union Congress on Theor. and Appl. Mech., Survey Reports [in Russian], No. 3, 116–136, Moscow (1966).
A. S. Kosmodamianskii and V. A. Shaldyrvan, Thick Multiconnected Plates [in Russian] Kiev (1980).
V. T. Grinchenko, Equilibrium and Steady Vibrations of Elastic Bodies of Finite Size [in Russian], Kiev (1978).
G. S. Bulanov and V. A. Shaldyrvan, "On improvement of convergence by the method of homogeneous solutions," Prikl. Mat. Mekh.,44, No. 5, 957–960 (1980).
A. I. Gomilko, V. T. Grinchenko, and V. V. Meleshko, "On the method of homogeneous solutions and superposition in static boundary value problems for an elastic strip," Prikl. Mekh.,22, No. 8, 84–93 (1986).
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Donetsk. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 9–13, 1990.
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Bulanov, G.S., Shaldyrvan, V.A. Acceleration of the convergence of the method of homogeneous solutions in three-dimensional problems of the theory of plates. J Math Sci 68, 632–635 (1994). https://doi.org/10.1007/BF01249394
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DOI: https://doi.org/10.1007/BF01249394