The adaptive hygrothermo–magneto–electro–elastic coupling improved enriched finite element method for functionally graded magneto–electro–elastic structures

Abstract

In this study, the hygrothermo–magneto–electro–elastic coupling improved enriched finite element method (HC-IEFEM) is proposed to analyze functionally graded magneto–electro–elastic (FG-MEE) structures. The static behavior of FG-MEE structures in the hygrothermal environment is studied. In the enriched finite element method (EFEM) enhanced by interpolation cover functions, the improved shape functions are added to solve the rank defect problem. Quadrilateral elements are used in the analysis of FG-MEE structures in this study. This improved method has proven to be relatively more efficient and resistant to mesh distortion than the traditional finite element method (FEM). Besides, the adaptive mesh refinement (AMR) scheme is used to refine the mesh in local areas to improve numerical calculation efficiency. Numerical examples show that the adaptive HC-IEFEM can achieve relatively high accuracy for analyzing FG-MEE structures. The proposed HC-IEFEM can obtain high accuracy in the hygrothermal environment using a relatively coarse mesh through the improved shape function and AMR scheme. Therefore, the significant potential is demonstrated in analyzing FG-MEE structures in the hygrothermal environment using the proposed adaptive HC-IEFEM.