We develop a variational method of homogeneous solutions for the solution of axisymmetric elasticity problems for a semiinfinite cylinder with free lateral surface. We consider four types of boundary conditions imposed on the end of cylinder, namely, the conditions in stresses, in displacements, and two types of mixed conditions. The solution of the problems with the help of this method is reduced to the solution of infinite systems of linear algebraic equations. We perform the numerical analysis of convergence of the obtained solutions. We also consider an example of application of the proposed approach to the determination of stress concentration near the joint of the end of the cylinder with a perfectly rigid lateral surface.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 56, No. 1, pp. 145–155, January–March, 2013.
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Chekurin, V.F., Postolaki, L.I. Variational Method of Homogeneous Solutions in Axisymmetric Elasticity Problems for a Semiinfinite Cylinder. J Math Sci 201, 175–189 (2014). https://doi.org/10.1007/s10958-014-1982-0
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DOI: https://doi.org/10.1007/s10958-014-1982-0