Stresses in an elastic cylinder with cylindrical cavities forming a hexagonal structure

The boundary-value problem of the elasticity theory for a cylinder with cylindrical cavities forming a hexagonal structure is under consideration. The solution is constructed in the form of a superposition of accurate basic equations of the Lamé equations for a cylinder in the coordinate systems associated to the centers of the body surfaces. The boundary conditions of the problem are satisfied exactly with the help of the generalized Fourier method. The problem is reduced to an infinite system of linear algebraic equations with a Fredholm operator in the space $l_2$. The resolving system is solved numerically by the reduction method. The numerical analysis of stresses in the regions of their greatest concentration is carried out.