3.2 STIFFNESS MATRICES OF THIN LAMINATES 73 Table 3.3.llustration of the coupling terms A2,D12 that may be present both in composite and in isotropic materials.When the element shown in the last column is zero,there is no coupling. Coupling No Coupling Element Extension-extension A2 Bending-bending M. D12 B;are the in-plane-out-of-plane coupling stiffnesses that relate the in-plane forces N,N,Ny to the curvatures K,Ky,Kxy and the moments M,My, Mry to the in-plane deformations∈，eg,y- Examination of the [A],[B],and [D]matrices shows that different types of couplings may occur as discussed below and illustrated in Tables 3.2 and 3.3. Extension-shear coupling.When the elements A6,A6 are not zero,in-plane normal forces N,N cause shear deformation and a twist force Ny causes elongations in the x and y directions. Bending-twist coupling.When the elements Di6,D26 are not zero,bending mo- ments M,My cause twist of the laminate Ky,and a twist moment Mry causes curvatures in the x-z and y-z planes. Extension-twist and bending-shear coupling.When the elements B6,B26 are not zero,in-plane normal forces N,Ny cause twist Kxy,and bending moments Mr, My result in shear deformation In-plane-out-of-plane coupling.When the elements B;are not zero,in-plane forces N,N,Ny cause out-of-plane deformations(curvatures)of the laminate, and moments M,My,My cause in-plane deformations in the x-y plane. The preceding four types of coupling are characteristic of composite materials and do not occur in homogeneous isotropic materials.The following two couplings occur in both composite and isotropic materials(Table 3.3): Extension-extension coupling.When the element A12 is not zero,a normal force N causes elongation in the y direction e,and a normal force N,causes elongation in the x direction e. Bending-bending coupling.When the element Di2 is not zero,a bending moment Mr causes curvature of the laminate in the y-z plane Ky,and a bending moment My causes curvature of the laminate in the x-z plane K.3.2 STIFFNESS MATRICES OF THIN LAMINATES 73 Table 3.3. Ilustration of the coupling terms A12, D12 that may be present both in composite and in isotropic materials. When the element shown in the last column is zero, there is no coupling. Coupling No Coupling Element Extension--extension Nx Nx Nx Nx A12 Bending--bending Mx Mx Mx Mx D12 Bi j are the in-plane–out-of-plane coupling stiffnesses that relate the in-plane forces Nx, Ny, Nxy to the curvatures κx, κy, κxy and the moments Mx, My, Mxy to the in-plane deformations o x , o y , γ o xy. Examination of the [A], [B], and [D] matrices shows that different types of couplings may occur as discussed below and illustrated in Tables 3.2 and 3.3. Extension–shear coupling. When the elements A16, A26 are not zero, in-plane normal forces Nx, Ny cause shear deformation γ o xy, and a twist force Nxy causes elongations in the x and y directions. Bending–twist coupling. When the elements D16, D26 are not zero, bending mo￾ments Mx, My cause twist of the laminate κxy, and a twist moment Mxy causes curvatures in the x–z and y–z planes. Extension–twist and bending–shear coupling. When the elements B16, B26 are not zero, in-plane normal forces Nx, Ny cause twist κxy, and bending moments Mx, My result in shear deformation γ o xy. In-plane–out-of-plane coupling. When the elements Bi j are not zero, in-plane forces Nx, Ny, Nxy cause out-of-plane deformations (curvatures) of the laminate, and moments Mx, My, Mxy cause in-plane deformations in the x–y plane. The preceding four types of coupling are characteristic of composite materials and do not occur in homogeneous isotropic materials. The following two couplings occur in both composite and isotropic materials (Table 3.3): Extension–extension coupling. When the element A12 is not zero, a normal force Nx causes elongation in the y direction o y , and a normal force Ny causes elongation in the x direction o x . Bending–bending coupling. When the element D12 is not zero, a bending moment Mx causes curvature of the laminate in the y–z plane κy, and a bending moment My causes curvature of the laminate in the x–z plane κx