Geodesic
The first boundary value problem of elasticity theory for a~cylinder with $N$~cylindrical cavities
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 2, pp. 177-189

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An efficient method for the analytical-numerical solution to the non-axyally symmetric boundary value problem of elasticity theory for a multiconnected body in the form of a cylinder with $N$ cylindrical cavities is proposed. The solution is constructed as superposition of the exact basis solutions of the Lame equation for a cylinder in the coordinate systems assigned to the centers of the boundary surfaces of the body. The boundary conditions are exactly satisfied with the help of the apparatus of the generalized Fourier method. As a result, the original problem reduces to an infinite system of linear algebraic equations, which has a Fredholm operator in the Hilbert space $l_2$. The resolving system is numerically solved by the reduction. The rate of convergence of the reduction is investigated. The numerical analysis of stresses in the areas of their greatest concentration is carried out. The reliability of the results obtained is confirmed by comparing them for the two cases: a cylinder with sixteen and a cylinder with four cylindrical cavities. 
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     author = {A. G. Nikolaev and E. A. Tanchik},
     title = {The first boundary value problem of elasticity theory for a~cylinder with $N$~cylindrical cavities},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {177--189},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2015_18_2_a5/}
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A. G. Nikolaev; E. A. Tanchik. The first boundary value problem of elasticity theory for a~cylinder with $N$~cylindrical cavities. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 2, pp. 177-189. http://geodesic.mathdoc.fr/item/SJVM_2015_18_2_a5/