Geometrically non-linear static analysis of functionally graded material shells with a discrete double directors shell element

A general shell model, including both theories of thin and thick shells, Kirchhoff-Love and Reissner-Mindlin undergoing finite rotations is presented. Based on Higher-order shear theory, where the fiber is cubic plane, the developed model does not need any transverse shear coefficients. The implementation is applicable to the analysis of isotropic and functionally graded shells undergoing fully geometrically nonlinear mechanical response. Material properties of the shells are assumed to be graded in the thickness direction according to a simple power-law and sigmoid distribution. The accuracy and overall robustness of the developed shell element are illustrated through the solution of several non trivial benchmark problems taken from the literature. The effect of the material distribution on the deflections and stresses is analyzed.