72 LAMINATED COMPOSITES The [a],[B],and [matrices are related to the [A],[B],and [D]matrices by 11 a12 C16 B11B12B16 A A2 A16 B11 B12B161 C12 a22026 21 22 f26 A2 2k6B2 B22 B26 C16 C26 C66 P61 B62 B66 6 A426A66 B16 B26 B66 11 P21 B61 611 612 616 B11 B12 B16 D11 D12 D16 P12 P22 P62 612 622 d26 B12 B22 B26 D12 D22 D26 16 B26 B66 d16 826 866 B16 B26 B66 D16 D26 D66 (3.23) 3.2.1 The Significance of the [A],[B],and [D]Stiffness Matrices The [A,B],and [D]matrices represent the stiffnesses of a laminate and describe the response of the laminate to in-plane forces and moments. Ai are the in-plane stiffnesses that relate the in-plane forces Nr,Ny,Nry to the in-plane deformations e Dij are the bending stiffnesses that relate the moments M,My,Mry to the curvatures Kx,Ky,Kxy. Table 3.2.llustration of the coupling terms A16,D6,B16,B11,B12,B66 for composite materials.When the element shown in the last column is zero,there is no coupling.(The coupling terms A26,D26,B26,B22 can be illustrated in a similar manner by applying a force Ny and a moment My in the y-z plane.) Coupling No Coupling Element Extension-shear A6 Bending-twist M D16 Extension-twist B16 In-plane-out-of-plane N Bi1 B12 N Bo672 LAMINATED COMPOSITES The [α], [β], and [δ] matrices are related to the [A], [B], and [D] matrices by          α11 α12 α16 β11 β12 β16 α12 α22 α26 β21 β22 β26 α16 α26 α66 β61 β62 β66 β11 β21 β61 δ11 δ12 δ16 β12 β22 β62 δ12 δ22 δ26 β16 β26 β66 δ16 δ26 δ66          =          A11 A12 A16 B11 B12 B16 A12 A22 A26 B12 B22 B26 A16 A26 A66 B16 B26 B66 B11 B12 B16 D11 D12 D16 B12 B22 B26 D12 D22 D26 B16 B26 B66 D16 D26 D66          −1 . (3.23) 3.2.1 The Significance of the [A], [B ], and [D ] Stiffness Matrices The [A], [B], and [D] matrices represent the stiffnesses of a laminate and describe the response of the laminate to in-plane forces and moments. Ai j are the in-plane stiffnesses that relate the in-plane forces Nx, Ny, Nxy to the in-plane deformations o x , o y , γ o xy. Di j are the bending stiffnesses that relate the moments Mx, My, Mxy to the curvatures κx, κy, κxy. Table 3.2. Ilustration of the coupling terms A16, D16, B16, B11, B12, B66 for composite materials. When the element shown in the last column is zero, there is no coupling. (The coupling terms A26, D26, B26, B22 can be illustrated in a similar manner by applying a force N y and a moment M y in the y–z plane.) Coupling No Coupling Element Extension--shear Nx Nx Nx Nx A16 Bending--twist Mx Mx Mx Mx D16 Extension--twist Nx Nx Nx Nx B16 In-plane--out-of-plane Nx Nx Nx Nx Nx Nx Nx Nx Nx Nx Nx Nx B11 B12 B66