178 SANDWICH PLATES Table 5.2.The stiffnesses and the Poisson ratios of isotropic solid plates and isotropic sandwich plates;R is defined in Eq.(3.46). Isotropic sandwich plate Isotropic Isotropic Quasi-isotropic solid plate facesheets facesheets Aiso 品 +内海 (+1b)R Diso El (P+(d2b++ 121-2 1-( E [t(d)+(d]R Q11+02+602-40 8R plate: [A]= (5.38) where Aiso and Diso are defined in Table 5.2. When the core is isotropic in the plane parallel to the facesheets from Eq.(2.40) we have C4s =0,C44=(C11-C12)/2,and the shear stiffnesses are(Eq.5.32) 1=2=5=CGi,c金 c 2 32=0. (5.39) The sandwich plate may also be treated as isotropic when the top and bottom facesheets are quasi-isotropic laminates(page 79)consisting of unidirectional plies made of the same material.For such sandwich plates the [B]matrix is negligible, the [A]and [D]matrices are approximated by Eq.(5.38)(with the terms Aiso and Diso defined in Table 5.2),and the elements of the shear stiffness matrix are given byEq.(5.39). 5.2 Deflection of Rectangular Sandwich Plates 5.2.1 Long Plates We consider a long rectangular sandwich plate whose length is large compared with its width (Ly>Lx).The long edges may be built-in,simply supported,or free,as shown in Figure 5.8.The sandwich plate is subjected to a transverse load p(per unit area).This load,as well as the edge supports,does not vary along the longitudinal y direction. The deflected surface of the sandwich plate may be assumed to be cylindrical at a considerable distance from the short ends (Fig.4.4).The generator of this cylindrical surface is parallel to the longitudinal y-axis of the plate,and hence the178 SANDWICH PLATES Table 5.2. The stiffnesses and the Poisson ratios of isotropic solid plates and isotropic sandwich plates; R is defined in Eq. (3.46). Isotropic sandwich plate Isotropic Isotropic Quasi-isotropic solid plate facesheets facesheets Aiso Eh 1−ν2 (tt + tb) Ef 1−(νf)2 (tt + tb)R Diso Eh3 12(1−ν2 ) (dt )2tt + (db)2tb + (tt)3 + (tb)3 12 1−(νf)2 Ef " tt (dt ) 2 + tb(db)2 # R νiso ν νf Q11 + Q22 + 6Q12 − 4Q66 8R plate: [A] = Aiso    1 νf νf 1 1−νf 2    [D] = Diso    1 νf νf 1 1−νf 2    , (5.38) where Aiso and Diso are defined in Table 5.2. When the core is isotropic in the plane parallel to the facesheets from Eq. (2.40) we have C45 = 0, C44 = (C11 − C12)/2, and the shear stiffnesses are (Eq. 5.32) S 11 = S 22 = S = d2 c Cc 11 − Cc 12 2 S 12 = 0. (5.39) The sandwich plate may also be treated as isotropic when the top and bottom facesheets are quasi-isotropic laminates (page 79) consisting of unidirectional plies made of the same material. For such sandwich plates the [B] matrix is negligible, the [A] and [D] matrices are approximated by Eq. (5.38) (with the terms Aiso and Diso defined in Table 5.2), and the elements of the shear stiffness matrix are given by Eq. (5.39). 5.2 Deflection of Rectangular Sandwich Plates 5.2.1 Long Plates We consider a long rectangular sandwich plate whose length is large compared with its width (Ly  Lx). The long edges may be built-in, simply supported, or free, as shown in Figure 5.8. The sandwich plate is subjected to a transverse load p (per unit area). This load, as well as the edge supports, does not vary along the longitudinal y direction. The deflected surface of the sandwich plate may be assumed to be cylindrical at a considerable distance from the short ends (Fig. 4.4). The generator of this cylindrical surface is parallel to the longitudinal y-axis of the plate, and hence the