Record number :

2558476

Title of article :

Axisymmetric Problem of the Elasticity Theory for the Radially Inhomogeneous Cylinder with a Fixed Lateral Surface

Author/Authors :

Akhmedov, Natiq K. Department of Mathematics and Statistics - Azerbaijan State University of Economics (UNEC), Baku, Azerbaijan

Pages :

13

From page :

598

To page :

610

Abstract :

By the method of the asymptotic integration of the equations of elasticity theory, the axisymmetric problem of elasticity
theory is studied for a radially inhomogeneous cylinder of small thickness. It is considered that the elasticity moduli are arbitrary
positive continuous functions of the radius of the cylinder. It is also assumed that the lateral surface of the cylinder is fixed, and
stresses are imposed at the end faces of the cylinder, which leave the cylinder in equilibrium. The analysis is carried out when the
cylinder thickness tends to zero. It is shown that solutions corresponding to the first and second iterative processes that
determine the internal stress-strain state of the radially inhomogeneous cylinder with a fixed surface do not exist. The third
iterative process defines solutions that have the boundary layer character equivalent to the Saint-Venant end effect on the theory
of inhomogeneous plates. The stresses determined by the third iterative process are localized at the ends of the cylinder and
decrease exponentially with distance from the ends. The asymptotic integration method is used to study the problem of torsion
of the radially inhomogeneous cylinder of small thickness. The nature of the stress-strain state is analyzed.

Keywords :

Radially inhomogeneous cylinder , Equilibrium equations , Matrix differential operator , Asymptotic method , Boundary layer , Papkovich spectral problem , Saint-Venant end effect

Journal title :

Journal of Applied and Computational Mechanics

Serial Year :

2021

Link To Document :