Three-dimensional polyhedral finite element method for the analysis of multi-directional functionally graded solid shells

Numerical models of three-dimensional (3D) shells made of multi-directional functionally graded material (FGM) are firstly proposed using the latest development of polyhedral finite element methods with arbitrary polyhedral elements (Poly-FEM). The shell is modelled as a solid structure and its static and dynamic responses are investigated. The effects of thickness of the shells are also studied. The material properties vary based on the power law with respect to directions of the structure. In addition, FGM in this study consists of two materials, which are ceramic and aluminium. The two latest developments of interpolation schemes over arbitrary polyhedral elements, namely polytopal composite scheme (PCEM) and consecutive interpolation scheme (CIPFEM), are used for analysing the models. After the verification studies, the results obtained from these schemes can verified with each other, which makes the results more reliable compared to those previously published in the literature. For static analysis, the displacement and normal stress are investigated, while the free vibration of the shell is investigated for dynamic models. Numbers of numerical examples are carried out to prove the efficiency of the proposed models.