Buckling of axially compressed thin cylindrical shells with functionally graded middle layer

Buckling of a simply supported three-layer circular cylindrical shell under axial compressive load is studied. The inner and outer layers of the shell are comprised of the same homogeneous and isotropic material, and the middle layer is made of an isotropic functionally graded (FG) material whose Young's modulus varies either affinely or parabolically in the thickness direction from its value for the material of the inner layer to that of the outer layer. The solution is expressed in terms of trigonometric functions that identically satisfy displacement type boundary conditions at the edges. Buckling loads for different values of the geometric parameters and the variation in material parameters of the middle layer are computed. Numerical results show that buckling modes are symmetric in the circumferential coordinate, and the buckling load decreases with an increase in the radius to thickness ratio, and increases with an increase in the average value of Young's modulus of the middle layer. The increase in the length to radius ratio has no effect on the buckling load, and it increases the axial wave number of the buckled shapes.