The inhomogeneous magneto-electro-elastic (MEE) coupling element-free Galerkin method (IMC-EFGM) is proposed for solving static behaviors of MEE structures. Plates made of homogeneous or inhomogeneous MEE materials are analyzed by IMC-EFGM, and the mechanical behaviors in different temperature fields are simulated. Displacement, magnetic potential and electric potential are studied using moving least squares (MLS) approximation. For inhomogeneous MEE materials, the constitutive equation in the MEE-thermal environment is first obtained by using Gibbs energy, and then used together with the Hamiltonian principle to determine the system governing equation. Since the MLS approximation does not satisfy the principle of Kronecker delta, the penalty function method is used to impose the natural boundary. The value of material properties at the point of integration is taken into account when calculating inhomogeneous materials. Compared with the analytical solution and finite element method (FEM), IMC-EFGM is straightforward and has greater precision than FEM. Some numerical examples are shown for the static FG-MEE plate with different hole shapes. Homogeneous MEE materials and inhomogeneous MEE materials are mainly used in intelligent structures and have good application perspectives. This research will promote the future use of inhomogeneous MEE materials.

提出了非均匀磁电弹性 (MEE) 耦合无元件伽辽金方法 (IMC-EFGM) 来解决 MEE 结构的静态行为。采用IMC-EFGM分析均质或非均质MEE材料制成的板材，模拟不同温度场下的力学行为。使用移动最小二乘法 (MLS) 近似来研究位移、磁势和电势。对于非均匀MEE材料，首先利用Gibbs能得到MEE-热环境下的本构方程，然后结合哈密顿原理确定系统控制方程。由于MLS逼近不满足Kronecker delta原理，因此采用惩罚函数法来施加自然边界。在计算非均质材料时，会考虑积分点处的材料属性值。与解析解法和有限元法 (FEM) 相比，IMC-EFGM 简单明了，并且比 FEM 具有更高的精度。给出了具有不同孔形状的静态 FG-MEE 板的一些数值示例。均质MEE材料和非均质MEE材料主要用于智能结构，具有良好的应用前景。这项研究将促进非均质 MEE 材料的未来使用。给出了具有不同孔形状的静态 FG-MEE 板的一些数值示例。均质MEE材料和非均质MEE材料主要用于智能结构，具有良好的应用前景。这项研究将促进非均质 MEE 材料的未来使用。给出了具有不同孔形状的静态 FG-MEE 板的一些数值示例。均质MEE材料和非均质MEE材料主要用于智能结构，具有良好的应用前景。这项研究将促进非均质 MEE 材料的未来使用。