In this article, an inhomogeneous cell-based smoothed finite element method (ICS-FEM) was proposed to overcome the over-stiffness of finite element method in calculating transient responses of functionally graded magneto-electro-elastic structures. The ICS-FEM equations were derived by introducing gradient smoothing technique into the standard finite element model; a close-to-exact system stiffness was also obtained. In addition, ICS-FEM could be carried out with user-defined sub-routines in the business software now available conveniently. In ICS-FEM, the parameters at Gaussian integration point were adopted directly in the creation of shape functions; the computation process is simplified, for the mapping procedure in standard finite element method is not required; this also gives permission to utilize poor quality elements and few mesh distortions during large deformation. Combining with the improved Newmark scheme, several numerical examples were used to prove the accuracy, convergence, and efficiency of ICS-FEM. Results showed that ICS-FEM could provide solutions with higher accuracy and reliability than finite element method in analyzing models with Rayleigh damping. Such method is also applied to complex structures such as typical micro-electro-mechanical system–based functionally graded magneto-electro-elastic energy harvester. Hence, ICS-FEM can be a powerful tool for transient problems of functionally graded magneto-electro-elastic models with damping which is of great value in designing intelligence structures.
The heterogeneous multiscale finite element method FE-HMM for the homogenization of linear elastic solids
