Study Of A Novel Multi-physical Field Coupling Smoothed Finite Element Method

Magneto-electro-elastic(MEE)composite materials are ideal materials for fabricating intelligent devices that possess unique multi-physical field coupling(MP)properties.It can not only rapidly convert mechanical,electrical,magnetic,thermal and chemical energy,but satisfy the needs of modern science and technology to high integration,ultra-miniaturization,high-density integration development.The mechanical properties of MEE intelligence devices which work in the hygrothermal environment are strongly affected by environment temperature and humidity.Accurate prediction of static and dynamic characteristics of MEE intelligent devices in temperature and humidity environment can effectively avoid the failure of MEE intelligent devices,and improve the reliability,accuracy and service life of intelligent devices.The experimental technology and theoretical research of MEE are gradually improved,however,the numerical calculation of the multi-physical field coupling issues still needs further researches.Although the finite element method(FEM)is the most wildly used numerical calculation method,the stiffness matrix of FEM is so rigid that the displacement results have low bound property and stress results are inaccuracy;the demands on the element quality are high,and the distorted element will bring interruption to the analysis process;the computational efficiency is lower,and the element meshing process will waste too much time.Hence,to establish the multi-physical field coupling numerical calculation method with high efficiency and precision can not only direct the design and manufacture of MEE intelligent devices,but also promote the industrialization of MEE materials.In this paper,we introduce the smooth gradient technique into the multi-physical field coupling finite element method(MP-FEM),and propose the magneto-electro-elastic-thermo multi-physical field coupling cell-based smoothed finite element method(MPCS-FEM),the magneto-electro-elastic-thermo-moisture MPCS-FEM and the inhomogeneous magneto-electro-elastic-thermo-moisture multi-physical field coupling cell-based smoothed finite element method(IMPCS-FEM).The static and dynamic properties of MEE and functionally graded MEE(FGMEE)materials in steady temperature environment,steady hygrothermal environment and transient hygrothermal environment were further investigated.Firstly,based on the magneto-electro-elastic-thermo MP fundamental equations and boundary conditions,in combination with the natural variation principle,the gradient smoothing technology was brought into FEM,the magneto-electro-elastic-thermo MPCS-FEM was proposed,and the magneto-electro-elastic-thermo MPCS-FEM function was derived.Through the investigation of the static properties of MEE beam and MEE bi-layered beam in steady temperature environment,the accuracy,efficiency and convergence of magneto-electro-elastic-thermo MPCS-FEM were verified.Secondly,based on the fundamental equations of magneto-electro-elastic-thermo MP problems,boundary conditions and initial conditions,natural variation principle and gradient smoothing technology,and in combination with the magneto-electro-elastic-thermo MPCS-FEM,the magneto-electro-elastic-thermo MPCS-FEM which focuses on the research of dynamic properties of MEE devices in steady temperature environment was proposed.With the help of subspace iteration method and Newmark method,the free vibration and transient properties of MEE structures in steady temperature environment were investigated,and the correctness and effectiveness of the proposed method were verified.Thirdly,based on the magneto-electro-elastic-thermo-moisture MP fundamental equations and boundary conditions,in combination with the natural variation principle,the gradient smoothing technology was introduced into FEM,the magneto-electro-elastic-thermo-moisture MPCS-FEM was proposed and the magneto-electro-elastic-thermo-moisture MPCS-FEM equation was derived.Through the investigation of the static properties of MEE structures(MEE beam,MEE bi-layered beam and MEE beam with holes)in hygrothermal environment,the high precision,efficiency and convergence of the magneto-electro-elastic-thermo-moisture MPCS-FEM were verified.Fourthly,based on the magneto-electro-elastic-thermo-moisture MP theory and gradient smoothing technology,in combination with the magneto-electro-elastic-thermo-moisture MPCS-FEM,the magneto-electro-elastic-thermo-moisture MPCS-FEM was proposed which focuses on the research of dynamic properties of MEE devices in hygrothermal environment,and the dynamic equation of magneto-electro-elastic-thermo-moisture MPCS-FEM was derived.With the help of subspace iteration method and Newmark method,the free vibration and transient properties of structure were studied.The dynamic properties of MEE trapezoidal beam,MEE beam with holes and MEE sensor in transient hygrothermal environment were investigated,and the correctness and effectiveness of the proposed method were verified.Finally,based on the FGMEE materials fundamental equations,boundary conditions and initial conditions,natural variation principle and gradient smoothing technology in a magneto-electro-elastic-thermo-moisture coupling field,and in combination with the magneto-electro-elastic-thermo-moisture MPCS-FEM,the inhomogeneous magneto-electro-elastic-thermo-moisture IMPCS-FEM was proposed and the dynamic equation inhomogeneous magneto-electro-elastic-thermo-moisture IMPCS-FEM was derived.The influence of gradient factors,geometrical configurations and boundary conditions on the dynamic properties of FGMEE structures was analyzed through ideal numerical examples.The correctness and effectiveness of the proposed method were verified.It can be known that,the MPCS-FEM can effectively analyze magneto-electro-elastic-thermo and magneto-electro-elastic-thermo-moisture MP issues with high precision,high efficiency,strong stability,simple process and low element quality requirements.It has a good prospect and value in the design and application of MEE intelligent devices.The numerical calculation results provide important theory basis and data support for the practical application of MEE materials.