A Galerkin meshless framework for static and vibration analysis of magneto-electro-elastic structures in hygrothermal environment

The work performance of smart structures is easily affected by external environmental factors. A Galerkin meshless method, multi-physics zonal Galerkin free element method (MZG-FREM), is proposed for constructing a framework to evaluate the structural responses of magneto-electro-elastic (MEE) structures in the hygrothermal environment, aiming to fully understand the mechanism of coupling effect induced by multiphysical loading on deformation behavior. The advantage of this method is that through Galerkin format and the zonal technique, the proposed meshless scheme enables to achieve stable and accurate results for complex geometric models with high computational efficiency. Thermodynamic potential theory, in conjunction with Hamilton principle, is employed to derive the motion equations for MEE structure exposed in hygrothermal environment, and the formulations account for the dependence of the elastic stiffness coefficient on the hygrothermal environment. Besides, the natural frequency and vibration responses with Rayleigh damping are determined by the newly introduced condensation approach, and the parametric studies are performed to reveal the effects of boundary conditions, temperature variation, and moisture concentration on structural responses. Several 2D or 3D numerical illustrations are provided and compared with analytical or reference solutions to demonstrate the capability of the present method in handling hygro-thermo-magneto-electro-elastic (HTMEE) coupled problems. The results show the influence of hygrothermal environment on the vibration of the MEE structure, which can provide benchmark outcomes for design or further research.