Functionally graded cylindrical shell thermal instability based on improved Donnell equations

The thermal instability of cylindrical shells of functionally graded material is considered. The derivation of equations is based on first-order shell theory and the complete Sanders kinematic equations. The resulting equilibrium and the stability equations contain the rotations in the chi and theta directions and the transverse shear force in the theta direction, in addition to the conventional Donnell equations. When it is assumed that the material properties vary linearly through the thickness direction, the system of fundamental partial differential equations in terms of the displacement components is established. Instability analysis of functionally graded cylindrical shells under two types of thermal loads with simply supported boundary conditions is carried out. Results are obtained in analytical form. The results are validated with the known data in the literature.