Dynamic Buckling of Functionally Graded Cylindrical Shells under Axial Loading

Based on the Donnell shell theory and classical shell theory, we established the dynamic buckling governing equation of functionally graded cylindrical shell under axial load using Hamilton principle.According to the expression of the radial displacement based on the circumferential continuity of cylindrical shell, we also obtained the dynamic buckling critical load expression and the buckling solution of functionally graded cylindrical shell under axial loading using the separation variable method.Using MATLAB, we performed the numerical analysis of functionally graded cylindrical shells, and discussed the influence of the diameter-thickness ratio, the gradient index, the number of circumferential mode and axial mode on the critical load of dynamic buckling.The results show that the critical load of cylindrical shells decreases with the increase of the critical length.The constraint conditions have effects on the critical load, and the critical load of the clamped edges is higher than that of the simple support.Moreover, the critical load of cylindrical shells grows as the modal number increases, indicating that the higher the critical load is, the easier the high-stage mode excites.The dynamic buckling modal diagram becomes more complicated as the modal number increases.