Buckling analysis of functionally graded cylindrical shells under mechanical and thermal loads by dynamic relaxation method

Document Type: Research Paper


Department of Mechanical Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran



Using dynamic relaxation method, nonlinear mechanical and thermal buckling behaviors of functionally graded cylindrical shells is studied based on first-order shear deformation theory (FSDT). It is 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. The axial compressive load and thermal gradient are applied to the shell incrementally so that in each load step the incremental form of governing equations are 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 is added to the former so that the program is repeated again. Then, the critical buckling load is achieved from the mechanical/ thermal load-displacement curves. In order to validate the present method, the results are compared with other papers and Abaqus finite element results. Finally, effects of different boundary conditions, grading index, rule of mixture, radius-to-thickness ratio and length-to-radius ratio are investigated on the mechanical and thermal buckling loads.