alamir

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Thank you all friends. Your information was very useful.
Furthermore, I hope to derive the equations of motion of a Kirchhoff plate,

starting with the displacements

u = u- z * diff ( w0 , x ),     v = v- z * diff ( w0 , y )     w = w0 

and strains

exx = diff ( u0 , x ) - z * diff ( w0 , x $2),     eyy = diff ( v0 , y ) - z * diff ( w0 , y $2),     exy = diff ( u0 , y ) +diff ( v0 , x ) - z * diff(diff ( w0 , y ),  x)   , exz = eyz = ezz =0

and constitutive relations

sigma1 = Q11 e1 +Q12 e2     sigma2 = Q12 e1 +Q22 e2     sigma6 = Q66 e6 ,     sigma3 = sigma4 = sigma5 = 0

using the principle of virtual work

int (D U , t = 0 .. T) = 0 ,     D U = the total differentiation of U

where,   D U = int int int [sigmaxx * D( exx )+ sigmayy * D ( eyy ) + 2 sigmaxy * D ( exy ) ] dzdxdy

finally, equating the coefficients of Du0 , Dv0 and Dw0 by 0

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