The magneto-electro-elastic multi-physics coupling element free Galerkin method for smart structures in statics and dynamics problems

Abstract

To solve the problem of over-stiffness and the imprecise magneto-electro-elastic coupling effects of finite element model, we presented the element free Galerkin model to more accurately simulate the statics and dynamics behaviour of magneto-electro-elastic structures. In the element free Galerkin model, the moving least squares approximation was introduced into a magneto-electro-elastic multi-physical-field model. The element free Galerkin model can achieve a close-to-exact stiffness of the continuum structures which could automatically discrete nodes for complicated regions more readily and thus remarkably reduced the numerical errors. In addition, the Runge–Kutta method was presented for solving the motion equation of magneto-electro-elastic structures. Several numerical examples were investigated and exhibited that the element free Galerkin model could receive more accurate and reliable simulation results than the standard finite element model. Besides, the element free Galerkin model was employed to calculate transient responses of magneto-electro-elastic sensor and typical magneto-electro-elastic energy harvester. Therefore, the element free Galerkin model can be adopted to tackle the practical magneto-electro-elastic problems such as smart vibration transducers, magnetic field sensors, and energy harvester devices in intelligent magneto-electro-elastic structures systems.