Complete Solution of Pressurized Thick Cylinders with Large Deformation Using Nonlinear Plane Elasticity Theory

In this paper, governing equation of pressurized axisymmetric cylinders made of homogeneous and isotropic materials with large deformations is derived using the Nonlinear Plane Elasticity Theory (NPET). Because of large deformations along the radial direction and hence existence of nonlinear terms in kinematic equations, the governing equation is a nonlinear second-order equation with variable coefficients, which is solved in plane stress and plane stress states using perturbation theory. According to the equilibrium equation, boundary conditions and different end conditions of the cylinder; radial and circumferential normal stresses and radial displacement in cylindrical shells are calculated analytically. The effect of thickness, material and boundary conditions on stresses and displacement in cylindrical shell is studied by the results obtained from analytical solution. For investigating the accuracy of the results obtained from the analytical solution, the numerical finite element modeling of mentioned cylinder is done with ABAQUS software and the results of the two methods are compared. This research reveals that the obtained results by the mentioned analytical solution procedure have good accuracy for cylindrical shells under pressure loading.