Inhomogeneous Smoothed Finite Element Method For Dynamic Analysis Of Functionally Graded Piezoelectric Beam

With the development of science and production technology,the manufacture of functionally graded piezoelectric material(FGPM)has been realized successfully,and it is becoming the focus of the research because of its excellent electromechanical performance.However,it is hard to solve the dynamic problem of FGPM due to inhomogeneous and electromechanical performance characters.In the two-dimension solid mechanics,Cell-based smoothed finite element method transforms the surface integral of solution domain into line integral,reduces the requirements of grid quality,enhances the solving precision,and used to solve the statics problem of FGPM successfully.In practical use,it is necessary to master the dynamic characteristic of FGPM for effectively control the structure.This paper construct inhomogeneous Cell-based smoothed finite element method based on inhomogeneous finite element method and smooth gradient technology,and solve the dynamic problem of FGPM.This paper summarize the research progress of FGPM and smooth gradient technology,analyze the developing status,discover the existing problems in the related research at present,construct the inhomogeneous Cell-based smoothed finite element method based on homogeneous finite element method,fundamental principle of piezoelectric and smooth gradient technology.This method use the Gauss divergence theorem transform surface integral to line integral,do not need the derivation of shape function and high requirements of grid quality,solve it use the real material parameters in gauss integral points of FGPM.If so,it makes material parameters embody the gradient change in each element.This method can overcome the over stiff in stiffness matrix of inhomogeneous finite element method,improve the precision,drive the inhomogeneous Cell-based smoothed finite element method(ICS-FEM),study the modal and transient dynamic problems.In modal analysis condense the degree of freedom related to the potential,in transient dynamic analysis use Newmark method to solve the dynamic equilibrium equations,and compare with the solution results of ANSYS.The numerical simulation shows that inhomogeneous Cell-based smoothed finite element method has high precision.