# The first boundary-value problem of the elasticity theory for a cylinder with *N* cylindrical cavities

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## Abstract

An effective method for the analytical-numerical solution to a nonaxisymmetric boundary-value problem of the elasticity theory for a multiconnected body in the form of a cylinder with *N* cylindrical cavities is proposed. The solution is constructed as a superposition of exact basis solutions of the Lame equation for a cylinder in coordinate systems fitted 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 method. The rate of convergence of the reduction method 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 two cases: a cylinder with sixteen cylindrical cavities and a cylinder with four cylindrical cavities.

### Keywords

boundary-value problem multiconnected body generalized Fourier method resolving system cylindrical boundary addition theorems## Preview

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