Research On Multi-physics Coupling Stabilized Node-based Smoothed Radial Point Interpolation Method

As a new type of composite smart material,functionally graded magneto-electro-elastic(FGMEE)material has both the excellent properties of piezoelectric material and piezomagnetic material.The material properties change continuously along a certain direction in space,and the internal interface of the material is not obvious,which optimizes the stress distribution inside the material.FGMEE material has incomparable mechanical properties of the traditional layered composite materials,which reduces the performance difference between different materials and has excellent multi-physics coupling effect.Therefore,this material is widely used in high-tech fields such as information technology,aerospace technology and micro electro mechanical systems.In order to further exert the advantages of FGMEE material and make it show better performance in the service environment,numerical methods have become a necessary means to study its multi-physics coupling problems.Finite element method(FEM)is the most mature numerical method at present,however,the shortcomings of FEM including relying on the mesh,being too sensitive to mesh distortion and obtaining a small displacement solution seriously limit its application in inhomogeneous problems and multi-physics coupling problems.Therefore,developing new methods with high accuracy and efficiency to analyze the mechanical properties of FGMEE materials in multi-physics coupling environment has become a research hotspot for scientists.The main work of this paper is as follows:Firstly,for improving the accuracy of FEM in solving inhomogeneous multi-physics coupling problems,magneto-electro-elastic coupling node-based smoothed radial point interpolation method(NS-RPIM)is proposed by combing with G space theory,weakened weak(W~2)formulation and radial point interpolation method(RPIM).This method could soften the stiffness of the system and obtain the upper bound solution in energy norm.However,magneto-electro-elastic coupling NS-RPIM only satisfies the spatial stability,when solving problems such as free vibration and transient responses,this method has temporal instability.Thus,the magneto-electro-elastic coupling stabilized node-based smoothed radial point interpolation method(SNS-RPIM)is presented by introducing the stable term constructed based on the strain gradient,which eliminates the influence of stabilization parameters on the accuracy of the method.Comparing the calculation results of multi-physics coupling SNS-RPIM with the analytical solution,the correctness and high accuracy of the method are verified.Secondly,for solving the static problems of FGMEE structures under magneto-thermo-electro-elastic(MTEE)multi-physics coupling effects,the inhomogeneous MTEE multi-physics coupling SNS-RPIM is proposed based on the generalized equilibrium equations,generalized geometric equations and constitutive equations.Based on G space theory and W~2formulation,RPIM and the stable term constructed based on the strain gradient are introduced into FEM.Combining with the condensation operation,the displacement,electric potential and magnetic potential of FGMEE structures are calculated.The results are compared with those of FEM to prove the superiority of inhomogeneous MTEE multi-physics coupling SNS-RPIM in solving multi-physics coupling problems.The influences of empirical constants,exponential factor and thermal variation on the mechanical properties of FGMEE structures are also investigated.Thirdly,for the dynamic problems of FGMEE structures under MTEE multi-physics coupling effects,based on the generalized equilibrium equations,generalized geometric equations and constitutive equations of FGMEE material,and combining with MTEE multi-physics coupling effects,minimum potential energy principle and SNS-RPIM,the inhomogeneous MTEE multi-physics coupling SNS-RPIM dynamic analysis model is proposed.The free vibration and transient responses of FGMEE structures are solved by using subspace iteration method and Newmark method,respectively.The correctness and accuracy of the dynamic analysis model are verified by the numerical examples,the effects of different parameters on the natural frequency and transient responses are studied.Fourthly,for the static problems of FGMEE structures under hygrothermo-magneto-electro-elastic(HMEE)multi-physics coupling effects,the inhomogeneous HMEE multi-physics coupling SNS-RPIM is presented,which is based on the coupling relations among thermal,humid,mechanical,electric and magnetic fields,coupled constitutive equations of FGMEE material under hygrothermal loadings and SNS-RPIM.The system equations of FGMEE structures in hygrothermal environment are derived,the generalized displacement(displacement,electric potential and magnetic potential)is calculated by combining the condensation operation.The influences of exponential factor and hygrothermal loadings on the static characteristics of the structures are studied.Comparing the results with those of FEM,the correctness and high accuracy of the proposed method are proved.Finally,for the dynamic problems of FGMEE structures under HMEE multi-physics coupling effects,the inhomogeneous HMEE multi-physics coupling SNS-RPIM dynamic analysis model is presented.The model is constructed based on the HMEE multi-physics coupling effects,the basic equations of FGMEE material under hygrothermal loadings and SNS-RPIM.The motion equation of FGMEE structures in hygrothermal environment is derived.The free vibration and transient responses of FGMEE structures are solved by subspace iteration method and Newmark method,respectively.Comparing the inherent frequency and generalized displacement with the results of FEM,the high accuracy of the model in solving inhomogeneous HMEE multi-physics coupling dynamic problems is verified.The researches above show that the multi-physics coupling SNS-RPIM possesses high accuracy,high efficiency and stability in solving the static and dynamic problems of FGMEE structures in thermal/hygrothermal environment,this method has great advantages and great application prospects in solving inhomogeneous multi-physics coupling problems.