“…The deformation for the post-buckling is very complex and the displacement function should have more expansion terms. The displacement functions that satisfy boundary condition (39) are assumed as [ 46 , 47 ]: where N is the circumferential wave number, a mn , b mn , and c mn are the undetermined coefficients; m and n are selected as m = 1, 3, 5… and n = 0, 1, 2.…”