402 FINITE ELEMENT ANALYSIS By comparing Eqs.(9.19)and(9.23),we have Ju Jv 67 J26 =h[4-1 (9.24) J61 J62J66 Owing to the Poisson effect,the in-plane forces introduce a normal strain ea in the z direction.For a single layer this strain is (see Eq.2.133) Ox e2=3 23 S36 (9.25) Txy where ox,oy,and txy are the stresses in the plies.The average normal stress x across the laminate and the normal ply stress ox are illustrated in Figure 9.5 (bottom).The stresses in a single layer are (Eq.3.13) =[@ (9.26) Equations(9.25),(9.26),(9.23),and(9.18)give e2=323536]ohs[4 (9.27) By combining Eqs.(9.18)and(9.27),and by replacing the integral with a sum- mation,for the sublaminate we obtain Ks 石x 5g5356](k-2-1)@k)[4 (9.28) k=1 [U31J32J36] By comparing Eqs.(9.20)and (9.28),we have 1g=之Sg5k(a-a-@[4, (9.29)402 FINITE ELEMENT ANALYSIS By comparing Eqs. (9.19) and (9.23), we have    J11 J12 J16 J21 J22 J26 J61 J62 J66    = hs [A] −1 . (9.24) Owing to the Poisson effect, the in-plane forces introduce a normal strain z in the z direction. For a single layer this strain is (see Eq. 2.133) z = [S13 S23 S36]    σx σy τxy    , (9.25) where σx, σy, and τxy are the stresses in the plies. The average normal stress σ x across the laminate and the normal ply stress σx are illustrated in Figure 9.5 (bottom). The stresses in a single layer are (Eq. 3.13)    σx σy τxy    = [Q]    x y γxy    . (9.26) Equations (9.25), (9.26), (9.23), and (9.18) give z = [S13 S23 S36][Q]hs [A] −1    σ x σ y τ xy    . (9.27) By combining Eqs. (9.18) and (9.27), and by replacing the integral with a sum￾mation, for the sublaminate we obtain z = * Ks k=1 ([S13 S23 S36](zk − zk−1)[Q]k)[A] −1 % &' ( [J31 J32 J36]    σ x σ y τ xy    . (9.28) By comparing Eqs. (9.20) and (9.28), we have [J31 J32 J36] = * Ks k=1 ([S13 S23 S36]k (zk − zk−1)[Q]k)[A] −1 , (9.29)