The numerical analysis of FGM shells with enhanced finite elements

► A derivation of a six parameter shell (including drilling rotations) is proposed. ► Gauss integration is avoided by using special assumed strain fields. ► Effective elastic properties for FGM and multilayer structures are derived. ► A Fourier series approach is proposed for multilayer shells. ► Elastostatic analysis of FGM beam to shell connection is presented. Shell-like and beam structures made of Functionally Graded Materials (FGMs) show a gradual variation of material properties in one, two or three directions. In this paper an efficient low-order shell element with six nodal degrees of freedom (including the drill rotation) is presented, supplemented with a proper method for calculating effective elastic properties. This new FGM shell element is coupled with 3D FGM beam elements and combined elastostatic beam-shell structures are analyzed. The results indicate high a effectiveness and accuracy of the proposed approach.