Higher order theories for the buckling and post-buckling studies of shallow spherical shells made of functionally graded materials

For composite shallow spherical shells (including functionally graded materials) the buckling and post-buckling behaviour is strongly affected by the material characteristics of a shell wall constructions. Using a power series expansion for a parameter (z/h) different variants of 2-D shell formulations are discussed herein starting from the Love-Kirchhoff theory and finishing on the 9th order theory (stretching effects). The solutions are searched for with the use of the Bubnov-Galerkin method and the finite element analysis (the h- and p-approximations). Due to geometrical limits of shallowness shell theory the investigations can be carried out for structures having the moderate thickness - the h/R ratio should be less than 0.15.