Edouard Diouf1, Jérémie Gaston Sambou2, and Alioune Ba3
1 Laboratoire de Mathématiques et Applications, Université de Ziguinchor, BP 523 Ziguinchor, Sénégal
2 Laboratory of Mathematics and Applications, University Assane Seck of Ziguinchor, BP 523, Senegal
3 Laboratory of Mathematics and Applications, University Assane Seck of Ziguinchor, BP 523, Senegal
Original language: English
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Abstract
In this study, we propose the analysis of a tubular structure undergoing expansion along the axis of the cylindrical material under internal pressure. Both kinematic and dynamic aspects are examined, leading to the derivation of an exact analytical solution using a system of partial differential equations. Simulation results demonstrate that the solution exhibits sinusoidal behavior in all cases. Minor variations result in incremental or decremental intervals, while significant changes in radius cause simultaneous increase and decrease intervals with trigonometric patterns. Additionally, we observe that the second component significantly influences the overall solution behavior compared to the first component.
Author Keywords: Kinematics of transformation, gradient tensor, Cauchy-Green tensor, isotropic elementaries invariants, incompressible transformation, equations of equilibrium, Bessel differential equations solutions.
