Dynamic analysis of the three-phase magneto-electro-elastic (MEE) structures with the overlapping triangular finite elements

The conventional finite element method (FEM) usually fails to generate sufficiently fine numerical solutions in the analyses of Mageto-electro-elastic (MEE) structures in which three different types of physical fields are coupled together. To enhance the performance of the FEM in analyzing MEE structures, in this work a novel overlapping triangular finite element is introduced for dynamic analysis of MEE structures. In this new paradigm for finite element analysis, both local and global numerical approximations are used to construct the considered three-phase physical fields. The local numerical approximation is built by using the method of finite spheres (MFS) and the global numerical approximation is based on the traditional finite element interpolation. In the local numerical approximation, the polynomials or other specially-designed functions can be used as the nodal degrees of freedom. Free vibration and harmonic response analyses are carried out to show the abilities of the overlapping triangular elements in analyzing the three-phase MEE structures. It is demonstrated by the numerical solutions that the present overlapping triangular elements are much more effective to predict the dynamic behaviors of the MEE structures and more accurate solutions can be generated than the traditional FEM with the same mesh. Therefore, the present overlapping triangular elements embody great potential in analyzing various complicated MEE structures in practical engineering applications.