Stability Analysis of an Inflated, Axially Extended, Residually Stressed Circular Cylindrical Tube

Document Type : Research Paper

Authors
Andrey Melnikov 1
Jose Merodio 2
1 Department of Mathematics, Nazarbayev University, Kabanbay Batyr Ave. 53, Astana, 010000, Kazakhstan
2 Departamento de Matemática Aplicada a las TIC, ETS de Ingeniería de Sistemas Informáticos, Universidad Politécnica de Madrid, Madrid, 28031, Spain
10.22055/jacm.2023.42359.3915
Abstract
Residual stress may have an important influence on the mechanical response of residually stressed materials. This paper is concerned with the effects of residual stress on the stability of inflated, axially extended, residually stressed circular cylindrical tube. To this end, the theory of small incremental deformations superimposed on a large underlying finite deformation is used. Asymmetric and axisymmetric types of bifurcation are considered. It is found that for residual stress parameter γ of the same sign the effect of the residual stress is different depending on the type of bifurcation. For example, for asymmetric bifurcations with mode number m = 1 and with positive γ inclusion of residual stress makes the tube more stable, on the other hand, for axisymmetric bifurcations inclusion of residual stress, corresponding to positive residual stress parameter γ, leads to increase of instabilities. In all cases, residual stress with positive and negative residual stress parameter γ leads to a symmetric character of bifurcation curves.
Keywords
Nonlinear elasticity
Residual stresses
Incremental elastic deformations
Tube bifurcation
Subjects

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Journal of Applied and Computational Mechanics
Volume 9, Issue 3
Summer 2023
Pages 834-847