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Stresses in an infinite circular cylinder with four cylindrical cavities. (Ukrainian, English) Zbl 1349.74018

Mat. Metody Fiz.-Mekh. Polya 57, No. 3, 132-142 (2014); translation in J. Math. Sci., New York 217, No. 3, 299-311 (2016).
In this paper, an analytical and numerical solution of non-axisymmetric boundary value problem of elasticity theory for a cylindrical body with four cylindrical cavities is obtained by the generalized Fourier method. The problem is reduced to an infinite system of linear algebraic equations whose operator is a Fredholm operator. The convergence of the reduction method for the solution of this system is investigated. Dependences of the stress tensor principal components on the geometric parameters are established.

MSC:

74A10 Stress
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74A45 Theories of fracture and damage
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