74 LAMINATED COMPOSITES 3.2.2 Stiffness Matrices for Selected Laminates For certain ply arrangements(layups),some of the couplings described do not occur,and the [A],[B],[D]matrices become simpler. Symmetrical laminate.In a symmetrical laminate the ply located at a position +z is identical to the ply at-z.Correspondingly,the stiffness matrix [O]of the ply at +z is identical to the stiffness matrix of the ply at-z: [@(z)=@1(-z) (3.24) By substituting these stiffnesses into Eq.(3.18),we find that the [B]matrix is zero: [B=0 (symmetrical). (3.25) Thus,for a symmetrical laminate there is no in-plane-out-of-plane coupling, and Eg.(3.21)reduces to N A A2 A16 A2 A22 h6 (3.26) A6 46 Mx Du D12 D16 M D12 Dn D (3.27)） D16 D26 D66 When the laminate is symmetrical,the compliance matrix is generally ex- pressed as C11 C12 16 a11 a12 a16 811 812 816 d d2 dis 012 22 d26 12 22 l26 822 d26 d2 d2 d26 16 C26 66 a16 126 66 816 d26 866 di6 ds d66 (3.28) where A12 a16 467 11 a12 A2 42 A26 a12 a22 26 (3.29) 16 a26 a66 A16 A26 A66 d d2 di6 D11 D12 d2 d D2 D22 D26 (3.30) d山6 6 d66 D16 D26 D6674 LAMINATED COMPOSITES 3.2.2 Stiffness Matrices for Selected Laminates For certain ply arrangements (layups), some of the couplings described do not occur, and the [A], [B], [D] matrices become simpler. Symmetrical laminate. In a symmetrical laminate the ply located at a position +z is identical to the ply at −z. Correspondingly, the stiffness matrix [Q] of the ply at +z is identical to the stiffness matrix of the ply at −z: [Q](z) = [Q](−z). (3.24) By substituting these stiffnesses into Eq. (3.18), we find that the [B] matrix is zero: [B] = 0 (symmetrical). (3.25) Thus, for a symmetrical laminate there is no in-plane–out-of-plane coupling, and Eq. (3.21) reduces to    Nx Ny Nxy    =    A11 A12 A16 A12 A22 A26 A16 A26 A66       o x o y γ o xy    (3.26)    Mx My Mxy    =    D11 D12 D16 D12 D22 D26 D16 D26 D66       κx κy κxy    . (3.27) When the laminate is symmetrical, the compliance matrix is generally ex￾pressed as    α11 α12 α16 α12 α22 α26 α16 α26 α66    =    a11 a12 a16 a12 a22 a26 a16 a26 a66       δ11 δ12 δ16 δ12 δ22 δ26 δ16 δ26 δ66    =    d11 d12 d16 d12 d22 d26 d16 d26 d66    , (3.28) where    a11 a12 a16 a12 a22 a26 a16 a26 a66    =     A11 A12 A16 A12 A22 A26 A16 A26 A66     −1 (3.29)    d11 d12 d16 d12 d22 d26 d16 d26 d66    =    D11 D12 D16 D12 D22 D26 D16 D26 D66    −1 . (3.30)