Force and moment resultants,[N,N,N]and [M,M,M l,respectively, are obtained by integration of the stresses in each layer over the laminate thickness,h, N h/2 Ox Ny dz (2.31) Ny -h2 Mx h/2 Ox My y zdz (2.32) Mxy] -h/2 where the subscript k represents the kth lamina in the laminate.Combination of Equations(2.24)with(2.30-2.32)leads to the following constitutive relation- ships among forces and moments and midplane strains and curvatures: Nx+NI+NM An A12 A16 B11 B12 B16 Kx Ny+Ny+NM A12 A22 A26 B12 B22 B26 Ky (2.33) Noy +Ny+NW A16 A26 A66」 B16 B26 B66 Ky」J M.+M+MM B11 B12 B6 D1 D12 D16 Kx My+M+MM B12 B22 B26 e9 D12 D22 D26 Ky (2.34) Mg+M码+M B16 B26 B66 D16 D26 D66] Ky」 where the ABand D are called extensional stiffnesses,coupling stiffnesses, and bending stiffnesses,respectively [1-61,given by A-立a-) (2.35a) =∑O,公-】 (2.35b) ©2003 by CRC Press LLCForce and moment resultants, [Nx, Ny, Nxy] and [Mx, My, Mxy], respectively, are obtained by integration of the stresses in each layer over the laminate thickness, h, (2.31) (2.32) where the subscript k represents the kth lamina in the laminate. Combination of Equations (2.24) with (2.30–2.32) leads to the following constitutive relation￾ships among forces and moments and midplane strains and curvatures: (2.33) (2.34) where the Aij, Bij, and Dij are called extensional stiffnesses, coupling stiffnesses, and bending stiffnesses, respectively [1–6], given by (2.35a) (2.35b) x y xy k x y xy h N h N N dz             =             − ∫ σ σ τ 2 2 x y xy h/2 h/2 k x y xy M M M zdz             =             − ∫ σ σ τ NNN NNN NNN AAA AAA AAA BBB BBB B B x xT x M y yT y M xy xyT xy M 11 12 16 12 22 26 16 26 66 x 0 y 0 xy 0 11 12 16 12 22 26 16 26 + + + + + +             =                         + ε ε γ 66 x y B xy                       κ κ κ x xT x M y yT y M xy xyT xy M 11 12 16 12 22 26 16 26 66 x 0 y 0 xy 0 11 12 16 12 22 26 16 26 66 MMM MMM MMM BBB BBB BBB DDD DDD D D + + + + + +             =                         + ε ε γ D x y xy                       κ κ κ ij ij k k k k N A = ( ) Q zz ( ) − − = ∑ 1 1 ij ij k k k k N B = ( ) Q zz ( ) − − = ∑ 1 2 2 1 2 1 TX001_ch02_Frame Page 21 Saturday, September 21, 2002 4:48 AM © 2003 by CRC Press LLC