Research On Mechanical-Electro-Magnetic Coupling Isogeometric Finite Element Method For Magneto-Electro-Elastic Materials

Magneto-electro-elastic materials,as a new type of smart materials,have excellent mechanical-electro-magnetic coupling properties and are widely used in aerospace,mechanical manufacturing,electronic information,biomedical and other fields.However,the complex coupling mechanism and harsh operating environments make the deformation,damage,and failure mechanisms of magneto-electro-elastic materials still unclear.Therefore,accurately analyzing the mechanical properties of magnetoelectro-elastic materials under multi-physical field coupling is of great significance for the design and application of magneto-electro-elastic intelligent devices.Due to the complex multi-physical field coupling relationship,it is difficult to analyze magneto-electro-elastic materials using analytical methods and experimental testing.The finite element method has gained popularity in engineering due to the rapid development in science,technology,and the strong function of the calculator.It is an efficient way to handle issues involving several multi-physical field coupling problems.However,as the complexity of the problem increases,the pre-processing quality,solving accuracy,and efficiency of the finite element method need to be further improved.To solve these problems,Isogeometric Analysis(IGA)was proposed by the internationally renowned scholar Hughes,based on the geometric model for structural mechanical response analysis.IGA is based on the Non-Uniform Rational B-Splines(NURBS)basis function to construct the problem being solved on an accurate geometric description,and the NURBS basis function is also used as the shape function in the analysis model for solving.This approach tightly combines geometric modeling of the structure with mechanical analysis,greatly improving the accuracy and efficiency of solving.The IGA method is combined with the multi-physical field coupling finite element method in this work.The NURBS basis function is introduced to construct the displacement function,electric potential function,and magnetic potential function based on the spline theory of IGA,the fundamental equations,and boundary conditions of magneto-electro-elastic materials.We propose the Mechanical-Electro-Magnetic Coupling Isogeometric Finite Element Method(MEM-IGFEM)for magneto-electroelastic materials,derive the control equation of MEM-IGFEM,and study the mechanical response of magneto-electro-elastic materials under multi-physical field coupling conditions through typical examples such as magneto-electro-elastic cantilever beam and plate with a hole.The correctness,convergence,high accuracy,and high efficiency of the proposed algorithm are verified.The research shows that MEM-IGFEM has high accuracy and efficiency in analyzing mechanical-electro-magnetic multi-physical field coupling problems,providing guidance for the design and application of magneto-electro-elastic devices.