Research On Magneto-electro-elastic Multi-physical Coupling Cell-based Smoothed Finite Element Method

The rapid development of the computer technology has made numerical computation algorithms valuable in engineering design & analysis and necessary in solving technical and complicated engineering problems.Numerical computation has been widely applied into aerospace,mechanical engineering,electrical engineering,national defense and military,construction engineering,medicine,and bionic engineering.The currently mature and widely-used finite element method(FEM)is the most effective solving method and a major milestone in the development of numerical computation algorithms.However,FEM,which is displacement-based,is limited by the relatively 'hard' rigid matrix,relatively small displacement solution,low ability to deal with distorted meshes,and high requirement for mesh quality.In particular,FEM returns inaccurate or even wrong results when handling complicated problems of multi-physical-field coupling or heterogeneous materials.At present,the structures based on magneto-electro-elastic(MEE)/functionally-gradient MEE materials have been extensively used as the core units,and researchers on longer pay attention to only one property of materials.The science & technology development has diverted more attention to the cross-coupling effect of materials.In particular,the MEE coupling effect is a new prospect in the future.Due to the limitations of FEM in handling heterogeneous materials and MEE multi-physical-field coupling,researchers have diverted to the smoothed FEM,which overcomes the disadvantages of mesh-based FEM and outstands with computational easiness,high precision and high efficiency.How to deal with heterogeneous materials and MEE multi-physical-field coupling with the use of smoothed FEM has becomes a hotspot in the field of computational mechanics.To improve the solving precision of FEM and introduce gradient smoothing into the MEE multi-physical-field coupling FEM,we proposed an MEE coupling/MEE coupling heterogeneous Cell-based smoothed FEM,and together with the modified solving algorithm for corresponding kinetic equations,analyzed the free vibration and transient response of MEE/functionally-gradient MEE beams.Firstly,based on the basic theories of MEE materials and FEM,we introduced gradient smoothing into MEE coupling FEM and deduced the static equations of MEE coupling Cell-based smoothed FEM.Thereby,an MEE coupling Cell-based smoothed FEM was put forward and used to study the static mechanical responses of 2D MEE bodies.The calculated results compared with FEM and the analytic solutions validate the accuracy and effectiveness of the MEE coupling Cell-based smoothed FEM.Secondly,based on the MEE basic equation,virtual work principle and minimum potential energy principle,we deduced the free vibration equation of MEE bodies and proposed an MEE Cell-based smoothed FEM for free vibration analysis.Then based on free vibration analysis and the degree-of-freedom coacervation principle,we deduced the expressions of electric potential and magnetic potential,and analyzed how the mechanical parameters,electric parameters and magnetic parameters of an MEE body would affect the systematic inherent frequency.The accuracy and feasibility of the Cell-based smoothed FEM in MEE body free vibration analysis were validated by numerical cases.Thirdly,starting from the basic equations of functionally-gradient MEE materials and according to the principles of virtual work and minimum potential energy,we deduced the free vibration equations of functionally gradient MEE beams,extended the mechanic-electric coupling heterogeneous smoothed FEM into MEE coupling problems,and proposed an MEE coupling heterogeneous Cell-based smoothed FEM for free vibration analysis of functionally-gradient MEE beams.With the degree-of-freedom coacervation method,we deduced the expressions of inherent frequencies of functionally-gradient MEE structures under MEE effects,studied how the mechanical parameters,electric parameters and magnetic parameters of functionally-gradient MEE bodies would affect the systematic free frequencies,and analyzed the free vibration of functionally-gradient MEE beams under different exponential factors and mesh divisions.The accuracy and effectiveness of the MEE coupling heterogeneous Cell-based smoothed FEM were validated with numerical cases.Fourthly,based on the control equations,boundary conditions and initial conditions of MEE materials and together with MEE coupling Cell-based smoothed FEM,the degree-of-freedom coacervation principle and the Wilson-? method,we put forward an improved Wilson-? method to solve the MEE coupling Cell-based smoothed FEM motion equations,and studied its stability.The temporal changes of displacement,electric potential and magnetic potential of MEE beams under harmonic loading were investigated and compared with FEM.The accuracy,effectiveness and stability of this method were validated through numerical cases.Finally,based on the control equations,boundary conditions and initial conditions of functionally-gradient MEE materials and together with the MEE coupling heterogeneous Cell-based smoothed FEM and the Newmark method,we put forward an improved Newmark method to solved the motion equations of the functionally-gradient MEE coupling dynamic system,and determined the acceleration,speed,displacement,potential and magnetic potential of this system.The stability of this method was also evaluated,and it was applied into solve the instant response of functionally-gradient MEE beams.The temporal changes of generalized displacement of functionally-gradient MEE beams under harmonic loading were investigated and compared with FEM.The accuracy,effectiveness and stability of this method were validated.The above analyses prove the high precision,efficiency and prospects of the MEE multi-physical-field coupling Cell-based smoothed FEM in handling MEE multi-physical-field coupling and heterogeneous materials.