A valid inhomogeneous cell-based smoothed finite element model for the transient characteristics of functionally graded magneto-electro-elastic structures

For the sake of surmounting defect of over-stiffness of finite element model (FEM) and accurately solving the transient response problems of structures comprise functionally graded magneto-electro-elastic (FGMEE) materials, we put forward an inhomogeneous cell-based smoothed finite element model (ICS-FEM) and a modified Newmark method. By employing the inhomogeneous gradient smoothing technique into FEM, the mass matrix M and the equivalent stiffness matrix K(eq )are derived, ICS-FEM that provides a stiffness coinciding with the actual condition is also obtained. Moreover, this model can be carried out with user-defined subroutines in the existing FEM software. Several numerical examples including cantilever beams, a layered FGMEE sensor and an FGMEE energy harvester are analyzed, which prove that ICS-FEM could achieve results with higher accuracy and reliability than FEM. ICS-FEM are applied to more complex structures such as FGMEE layered sensor and energy harvester. Therefore, such method to solve the transient characteristics of FGMEE structures can be a reference for the design of smart structures.