Research On The Mechanical-Electric-Magnetic Inhomogeneous Element-Free Galerkin Method For Non-Uniform Magneto-Electro-Elastic Materials Under Thermal Stress

Functionally graded magneto-electro-elastic(FG-MEE)materials are a new type of smart material,in which the material properties such as mechanical,electrical,and magnetic properties vary continuously along a specific direction.This material not only has high sensitivity to mechanical,electrical,and magnetic parameters,but also has characteristics of non-uniformity and adjustability.Therefore,FG-MEE materials have a wide range of applications in high-precision fields,such as sensors,actuators,memory chips,and highperformance batteries.Since FG-MEE materials are often subjected to complex service environments,such as thermal stress,mechanical loads,electric fields,and magnetic fields,the mechanical properties of FG-MEE materials directly determine the safety,reliability,and service life of related components.To further enhance the breadth and depth of FG-MEE material applications,it is necessary to analyze the mechanical properties of FG-MEE materials under thermal stress.Currently,the finite element method(FEM)is the most widely used numerical method for solving such problems,but it has certain limitations in dealing with functionally graded materials and multi-field coupling problems.Therefore,developing a high-precision numerical analysis method to analyze the multi-field coupling mechanical properties of FG-MEE materials has become a research hotspot for scientists and researchers worldwide.To improve the computational accuracy of solving the multi-field coupling problem of FGMEE materials,an inhomogeneous magneto-electro-elastic coupling element-free Galerkin method(IMC-EFGM)is proposed based on the basic equations and boundary conditions of FG-MEE materials,using the least squares approximation method to construct displacement,electric potential,and magnetic potential shape functions,and incorporating the Galerkin weak form and penalty function method to handle boundary conditions.Firstly,the generalized shape functions of IMC-EFGM are constructed based on the generalized equilibrium equation,generalized geometry equation,constitutive equation,and boundary conditions of FG-MEE materials under thermal stress,using the moving least squares approximation principle.Then,the control equation of FG-MEE materials under thermal stress is derived using the Galerkin weak form and penalty function method,and the static response of magneto-electro-elastic structures under thermal stress is solved.The numerical examples demonstrate the correctness and high accuracy of the proposed method.Secondly,the dynamic problem of FG-MEE structures under thermal stress is studied,and the dynamic control equation of FG-MEE structures is derived based on the basic equations of elastic mechanics,the moving least squares approximation principle,the Galerkin weak form,and the penalty function method.The equivalent natural frequency and transient response of FGMEE structures are obtained using the subspace iteration method and Newmark method,respectively,and the correctness and high accuracy of the IMC-EFGM in solving the dynamic response of FG-MEE structures under thermal stress are verified by numerical examples.IMC-EFGM can achieve high computational accuracy in solving the static and dynamic mechanical problems of FG-MEE structures under thermal stress,and has higher computational efficiency than FEM.IMC-EFGM has broad application prospects in solving the mechanical response problems of FGMEE materials under thermal stress,which will promote the significant improvement of the mechanical performance of related components.