Some models for nanosized magnetoelectric bodies with surface effects

The dynamic problems for piezomagnetoelectric nanosized bodies with account for damping and surface effects are considered. For these problems, we propose the new mathematical model, which generalizes the models of the elastic medium with damping in sense of the Rayleigh approach and with surface effects for the cases of piezoelectric and magnetoelectric materials. For solving these problems, the finite element approximations are discussed. A set of effective finite element schemes is examined for finding numerical solutions of weak statements for transient, harmonic, modal and static problems within the framework of modeling the piezomagnetoelectric nanosized materials with surface effects.