An analytical solution of a hollow cylindrical
tube subjected to inflation

Edouard Diouf

doi:https://doi.org/10.14445/22315373/IJMTT-V66I9P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 9 | Year 2020 | Article Id. IJMTT-V66I9P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I9P503

An analytical solution of a hollow cylindrical tube subjected to inflation

Edouard Diouf

Citation :

Edouard Diouf, "An analytical solution of a hollow cylindrical tube subjected to inflation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 9, pp. 9-16, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I9P503

Abstract

In this paper, we have proposed as work, the study of a hollow tubular cylindrical structure which has as deformation an inflation in order to obtain an analytical solution of displacement and also to see solution components behaviors when the radius varies. A deformation kinematics governing this behavior has been given in order to be able to solve the problem analytically. From this resolution, we obtained from the kinematics principal components of the stress tensor, equilibrium equations and boundary conditions, the analytical solution of the displacement, a solution that has a complex component. The simulation of the real and imaginary parts of this component allowed us to see a different behavior between these two parts when the radius varies. This study showed us that the geometrical shapes that does not only modify the volume contributions, the porosity, the directions, the therml coating as well as the variation of the scalar products of the material vectors but also creates certain behaviors at the solution level when the radius varies.

Keywords

Tubular cylindrical material, Inflation, Navier equation, Analytical solution.

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