Research On Hygro-Magneto-Electro-Elastic Inhomogeneous Cell-based Smoothed Finite Element Method

Functionally graded magneto-electro-elastic(FGMEE)materials are new intelligent materials made by combining functional graded technique with magnetoelectro-elastic(MEE)structures.They have excellent mechanical properties and coupling properties of multiple physical fields,and are widely used in sensing technology,microelectromechanical technology,information technology,aerospace technology and other high-tech fields.The mechanical properties and coupling properties of such intelligent structures are easily affected by the moisture concentration in the environment.The finite element method(FEM)widely used to analyze such problems still has some defects,such as rigid stiffness matrix,small displacement solution and high demand for elements.These disadvantages limit the development of FEM in the study of inhomogeneous materials and multi-physical coupling problems.In order to improve the calculation accuracy of mechanical properties of FGMEE,a hygro-magneto-electro-elastic inhomogeneous cell-based smooth finite element(CSFEM)method was derived.Compared with FEM,CS-FEM is not dependent on the quality of the elements,and the results can be obtained even if there are distorted elements.CS-FEM will reduce the requirement for the continuity of the shape function and will "soften" the stiffness matrix,and the solution of displacement is closer to the real value.In this paper,the basic formulas of the CS-FEM are firstly derived.Then,combined with the corresponding statics equation and Newmark method in dynamics,the statics analysis and dynamics study of the FGMEE structures under the coupling of hygro-magneto-electro-elastic multiple physical fields are carried out.The displacement,electric potential,magnetic potential and natural frequency of the FGMEE structures are obtained,and the factors affecting the response of the structure are analyzed.Distorted elements are used to analyze the response of the structure,and the results are compared with those calculated by FEM.The results of CS-FEM are in good agreement with the exact solution,which verifies the correctness,stability and effectiveness of the proposed method.At the same time,the calculation results of the distorted elements are in good agreement with the reference solution,which shows the advantage of CS-FEM in dealing with the problem of distorted elements.The results of numerical examples show that CS-FEM has good accuracy and broad application prospect when dealing with the coupling problem of multiple physical fields,which provides data support for the design and manufacture of intelligent structures in humidity field.