| In recent years functionally graded material(FGM) have attracted considerable. FGM is a new material, which has continous change in component and structure from surface of the material to depth. By constructing a model based on the physical properties of the distribution across the thickness of piezoelectric functionally graded materials, we study the influence of microstructure parameter ( for example, component distribution factor, etc. ) of piezoelectric functionally gradient materials on the stress and displacement of rectangular plate by the modified classical lamination theory . 1. Problem description and basic equations A gradient model are presented, we study the physical properties of the distribution across the thickness of piezoelectric functionally graded material. Especially, we obtained the in-plane stresses and out-of-plane displacements by the modified CLT .The distribution of the volume fraction of filler phase , f (z),is chosen as follow : where z is the coordinate of each mid-plane, h FGM overall thickness,m FGM volume fraction exponent. Due to multiformity of preparation technics and the error between design to practicality, we introduce modify gene m . We obtain pFi j ( z)= C+D(z/h) , p = km (2) where Fi j is FGM physical parameter, C, D are constant of two PZT physical parameter, p practicality component distributing gene, m error modify gene ,k man-made component distributing gene. 2. Modified classical lamination theory(CLT) We study the influence of microstructure parameter ( for example, component distribution factor, etc. ) of piezoelectric functionally gradient materials on the stress and displacement of rectangular plate by the modified classical lamination theory . A piezoelectric laminate consists of n laminate , each being a piezoelectric material with specified electroelastic properties .The constitutive equation of a piezoelectric material inthe absence of temperature effects are given by where σij,εkl are the stress and stain tensor components , respectively, E m, the electric field vector component , C ijkl, the elastic stiffness tensor , and e mij, the piezoelectric coefficients .The electroelastic constants of each lamina may be computed from some micromechanical model . CLT assure a state of plane stress along the z -axis, where σz = σxz=σyz=0.The constitutive equations of a piezoelectric lamina ,Eq.(3),under applied electric field in the z -direction only ( E z),and under the assumption of plane stress along the z -axis ,reduce to It is noted here that Q ij , eij are the reduced stiffness constants and reduced piezoelectric constants , respectively .That are modified by the assumption of plane stress and where εx0 , εy0,εx0y are the in-plane strain components at mid-plane, z =0 , κx , κy,κxy are the curvatures of the plate. The electric field in each layer of multi layer FGM piezoelectric material can be obtained by considering the multi layers in a piezoelectric FGM as a series of condensers. We obtain electric field in each layer as ∑E i = Vdii=VTεiln =1 ( zl1? zl?1 )/εl , (i = 1,2...,n) (7) where Vt is the total voltage, d i the thickness of each capacitance or lamina in the piezoelectric FGM, εi the dielectric constant for each lamina . By Kirchhoff lamella theory and Eq.(4) , the resultant in-plane forces and bending moments are defined by {N M} n{ }(d zzdz)ihhii,,1 1∑∫= ?= σ(8) Carrying out the integration through the plate thickness of h ,the resultant forces and bending moments can then be written as...
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