A Research of Analytical Solution on Tubular Structure which is Subjected to an Axis Expansion in Different Contributions

Abstract

In this research paper, we proposed a classical mechanical study of the behavior of a tubular structure which is subjected to an expansion following the axis of the material. The first part, is focused on kinematic and dynamic aspects, Gradient tensor, left Cauchy-Green tensor ant isotropic invariants are used to proceed to find an analytical exact logarithmic solution function of the radius, of the problem at the limits through a system of partial differential equations in equilibrium condition. The simulations show that in the case of a sinusoidal, logarithmic and exponential function of time, the solution has a strong dependence to the radius. As a results, sinusoidal function of time has a big influence in the shape of the solution graphic which is negative or positive depending to the value of the time and radius. But logarithmic and exponential contribution has not a big influence in the arc shape of the solution graphic but a great influence in the values and it remains positive whatever the value of the radius.