Large Deformation Elastic Analysis of Pressurized FGM Thick Cylindrical Shells with Nonlinear Plane Elasticity Theory (NPET)

In the present study, the governing equation of pressurized axisymmetric thick cylinders made of Functionally Graded materials (FGMs) with large deformations is derived using the Nonlinear Plane Elasticity Theory (NPET). Because of large deformations along the radial direction and hence the 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 strain states using the perturbation technique. According to the equilibrium equation, boundary conditions and different end conditions of the cylinder: open ends and closed ends; radial, axial, and circumferential stresses and radial displacement in cylindrical shells are analytically calculated. To investigate the accuracy of the results obtained from the analytical solution, the numerical finite element modeling of the mentioned cylinder with ABAQUS software based on the nonlinear elasticity theory is done 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 load. The aim of this study is to provide a mathematical solution for the nonlinear analysis of large deformations of FGM cylinders.