Multi-physics zonal Galerkin free element method for static and dynamic responses of functionally graded magneto-electro-elastic structures

Abstract

Functionally graded magneto-electro-elastic (FGMEE) structures have been extensively applied in engineering applications, which are often in the multi-field coupling environment. Driven by the desire to identify and understand the complexities of coupled fields, the multi-physics zonal Galerkin free element method (MZG-FREM), which belongs to a weak-form meshless method, is proposed for static and transient responses of magneto-electro-elastic structure, which material properties vary along the thickness direction. Based on the thermodynamic potential function and generalized Hamilton variational principle, the equations for the FGMEE medium are derived. Through the zone technique, MZG-FREM processes a robust capability to handle the model with complex geometry and the results obtained by MZG-FREM are insensitive to irregularly distributed nodes. Besides, Galerkin method is introduced to set up the equation for each node to guarantee the stability and accuracy of the results. The effect of exponential factors on the responses of FGMEE structures is investigated by MZG-FREM with a modified Newmark scheme. The convergence, accuracy, and robustness of MZG-FREM are verified through numerical examples including FGMEE structure with complex geometry and FGMEE energy harvester composed of various materials. The proposed method MZG-FREM and obtained results can be effectively incorporated for the accurate design of FGMEE smart devices.