Nonlinear Buckling Analysis of Functionally Graded Cylindrical Shells under Mechanical Loads by Dynamic Relaxation Method

The main purpose of this study is to investigate nonlinear buckling analysis of Functionally Graded (FG) cylindrical shells under uniform axial compressive loads by dynamic relaxation (DR) method. The mechanical properties of shell vary continuously throughout the thickness direction according to the power-law، exponential function and the Mori-Tanaka distribution. The poisson’s ratio of the FG cylindrical shell is constant for power-law and exponential function. But in the Mori-Tanaka distribution variations of poisson''s ratio is determined as a function of the thickness direction. The incremental form of nonlinear formulations are based on first order shear deformation theory (FSDT) and large deflection von Karman equations. The DR method combined with the finite difference discretization technique is employed to solve the equilibrium equations. Some comparison study is carried out to compare the current solution with the results reported in the literature and the ones obtained by the Abaqus finite element software for the isotropic cylindrical shells. Finally، numerical results are presented for critical buckling load with various boundary conditions، grading indices، radius -to- thickness ratio، length -to- radius ratio and variation of poisson’s ratio.