Effect of Imperfections on Thermal Buckling of Functionally Graded Cylindrical Shells

m, n = number of half longitudinal and circumferential waves Ni j = force resultant T = temperature distribution u, v, w = axial, circumferential, radial displacement under load w∗ = equivalent initial radial deviation from cylindrical shape x , θ , z = axial, circumferential, radial coordinate direction γi j = shear strain i j = normal strain = temperature difference with respect to the reference temperature κi j = curvature of middle surface μ = imperfection parameter φ = Airy stress function