Abstract—The stress state of a finite circular elastic cylinder under its own proper weight is evaluated in this paper. The edges of the cylinder are fixed. The circular surface is free from stress. To solve this problem, the finite Fourier’s integral transformations were applied to the equilibrium equations and subjected boundary conditions. The stated problem was reduced to a one-dimensional vector boundary problem at the transformations’ domain with regard to the unknown displacement’s transformations. The apparatus of matrix differential calculations is used and the explicit solution of the vector boundary problem is constructed. These obtained formulas for the displacements have an unknown function which was found by solving the corresponding singular integral equation. The numerical results indicating the dependence of the cylinder’s stress state on its geometrical parameters and proper weight were derived.

Index Terms—Finite cylinder, integral transformations, proper weight, singular integral equation.

The authors are with Odesa Mechnikov University, str. Dvoryanskaya, 2, 65082, Odesa, Ukraine (email: vaysfeld@onu.edu.ua).

Cite: Filipchuk Anastasiia, Protserov Yuriy, Vaysfeld Natalya, "The Stress State of a Finite Elastic Cylinder under Its Proper Weight," International Journal of Applied Physics and Mathematics vol. 9, no. 1, pp. 65-71, 2019.