Buckling Analysis of Functionally Graded Cylindrical Shells Under Mechanical and Thermal Loads by Dynamic Relaxation Method

In this study, using the dynamic relaxation method, nonlinear mechanical and thermal buckling behaviors of functionally graded cylindrical shells were studied based on first-order shear deformation theory (FSDT). It was assumed that material properties of the constituent components of the FG shell vary continuously along the thickness direction based on simple power-law and Mori-Tanaka distribution methods separately. An axial compressive load and thermal gradient were applied to the shell incrementally so that in each load step the incremental form of governing equations were solved by the DR method combined with the finite difference (FD) discretization method to obtain the critical buckling load. After convergence of the code in the first increment, the latter load step was added to the former so that the program could be repeated again. Afterwards, the critical buckling load was achieved from the mechanical/ thermal load-displacement curves. In order to validate the present method, the results were compared with other papers and the Abaqus finite element results. Finally, the effects of different boundary conditions, grading index, rule of mixture, radius-to-thickness ratio and length-to-radius ratio were investigated on the mechanical and thermal buckling loads.