The method of homogeneous solutions in an axisymmetric problem of statics for a finite cylinder with homogeneous conditions on the ends

Using the property of Papkovich generalized orthogonality of eigenfunctions, we develop a method of satisfying the boundary conditions on the lateral surface of a cylinder. The stresses and displacements in a finite cylinder with homogeneous conditions on the ends are represented in terms of the axial displacement. The solution is constructed as an expansion in a series of eigenfunctions of the corresponding homogeneous boundary-value problem. We find a class of boundary conditions that admits a solution of the problem without reduction to an infinite system of algebraic equations. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 135–139.