Thermomechanical analysis of hyperelastic thick-walled cylindrical pressure vessels, analytical solutions and FEM

Abstract

In this investigation, employing the multiplicative decomposition of the deformation gradient, both analytically and numerically thermomechanical analysis of a hyperelastic thick-walled cylindrical pressure vessel are presented. The exp−exp energy density function due to its excellent agreement with experiments and including exponential terms for compressible and particularly incompressible materials is used to predict the hyperelastic response of elastomers. It is found that the radial and axial stresses are more sensitive to variation of the angular velocity than the hoop stress. Also, the variation of the axial stretch has the most significant effect on the axial and hoop stresses. Moreover, the behavior of the axial stress, for a constant axial stretch λ, depends on the value of λ whether it is larger than 1 or not, while in the inner radius of the vessel, the hoop stress has the same behavior for various values of the axial stretch. It is concluded that the positive temperature gradient leads to tensile radial stress and compressive hoop and axial stresses in the rotating cylinder, and the increase in the temperature gradient leads to increase in all stress components. The radial and hoop stresses through the wall-thickness are more sensitive to the temperature change than the thermal axial stress. Moreover, increasing the angular velocity makes the cylinder more unstable, while the stability increases with λ > 1. It is deduced that the more axial stretch in the inner radius of the pressure vessel, the more stable it is. It was shown that the comparison of the results of Finite Element and analytical method shows a good fit as a verification of the analytical solution. This analytical solution can be used either for parametric study (material or geometrical parameters) of the pressure vessels or for design and optimization that involve a large number of simulations where computational cost is a crucial parameter.