152 8 Laminate Analysis-Part II (8.11) Nv AcGYu (8.12) M [D11 D12 D16 My D12 D22 D26 0 (8.13) My) D16 D26 D66」 4.Cross-Ply Laminates-A laminate is a cross-ply laminate if every layer has its fibers oriented at either 0 or 90.In this case,the components A16,A26,Bi6, B26,Di6,and D26 are all zero. 8.2 MATLAB Functions Used The three MATLAB functions used in this chapter to calculate the [A],[B],and [D] matrices are: Amatrir(A,Qbar,z1,22)-This function calculates the [A]matrix for a laminate consisting of N layers where each layer k(k 1,2,3,...,N)has a transformed reduced stiffness matrix [There are four input arguments to this function. This function assembles the desired matrix after each layer's effect is included in a separate call to this function.The parameters zl and 22 are zk-1 and zk,respectively, for layer k.The function returns the 3 x 3 matrix [A]. Bmatrir(B,Qbar,21,22)-This function calculates the [B]matrix for a laminate consisting of N layers where each layer k(k=1,2,3,...,N)has a transformed reduced stiffness matrix [There are four input arguments to this function. This function assembles the desired matrix after each layer's effect is included in a separate call to this function.The parameters z1 and 22 are zk-1 and zk,respectively, for layer k.The function returns the 3 x 3 matrix [B]. Dmatrir(D,Qbar,z1,22)-This function calculates the [D]matrix for a laminate consisting of N layers where each layer k(k 1,2,3,...,N)has a transformed reduced stiffness matrix [There are four input arguments to this function. This function assembles the desired matrix after each layer's effect is included in a separate call to this function.The parameters z1 and 22 are zk-1 and zk,respectively, for layer k.The function returns the 3 x 3 matrix [D]. The following is a listing of the MATLAB source code for these functions: function y Amatrix(A,Qbar,z1,z2) %Amatrix This function returns the [A]matrix % after the layer k with stiffness [Qbar] % is assembled. % A -[A]matrix after layer k % is assembled. % Qbar -[Qbar]matrix for layer k % z1 -z(k-1)for layer k % z2 -z(k)for layer k152 8 Laminate Analysis – Part II  Nx Ny =  A11 A12 A12 A22   ε0 x ε0 y (8.11) Nxy = A66γ0 xy (8.12) ⎧ ⎪⎨ ⎪⎩ Mx My Mxy ⎫ ⎪⎬ ⎪⎭ = ⎡ ⎢ ⎣ D11 D12 D16 D12 D22 D26 D16 D26 D66 ⎤ ⎥ ⎦ ⎧ ⎪⎨ ⎪⎩ κ0 x κ0 y κ0 XY ⎫ ⎪⎬ ⎪⎭ (8.13) 4. Cross-Ply Laminates – A laminate is a cross-ply laminate if every layer has its fibers oriented at either 0◦ or 90◦. In this case, the components A16, A26, B16, B26, D16, and D26 are all zero. 8.2 MATLAB Functions Used The three MATLAB functions used in this chapter to calculate the [A], [B], and [D] matrices are: Amatrix(A, Qbar, z1, z2) – This function calculates the [A] matrix for a laminate consisting of N layers where each layer k (k = 1, 2, 3,... ,N) has a transformed reduced stiffness matrix ! Q¯"k . There are four input arguments to this function. This function assembles the desired matrix after each layer’s effect is included in a separate call to this function. The parameters z1 and z2 are zk−1 and zk, respectively, for layer k. The function returns the 3 × 3 matrix [A]. Bmatrix(B, Qbar, z1, z2) – This function calculates the [B] matrix for a laminate consisting of N layers where each layer k (k = 1, 2, 3,... ,N) has a transformed reduced stiffness matrix ! Q¯"k . There are four input arguments to this function. This function assembles the desired matrix after each layer’s effect is included in a separate call to this function. The parameters z1 and z2 are zk−1 and zk, respectively, for layer k. The function returns the 3 × 3 matrix [B]. Dmatrix(D, Qbar, z1, z2) – This function calculates the [D] matrix for a laminate consisting of N layers where each layer k (k = 1, 2, 3,... ,N) has a transformed reduced stiffness matrix ! Q¯"k . There are four input arguments to this function. This function assembles the desired matrix after each layer’s effect is included in a separate call to this function. The parameters z1 and z2 are zk−1 and zk, respectively, for layer k. The function returns the 3 × 3 matrix [D]. The following is a listing of the MATLAB source code for these functions: function y = Amatrix(A,Qbar,z1,z2) %Amatrix This function returns the [A] matrix % after the layer k with stiffness [Qbar] % is assembled. % A - [A] matrix after layer k % is assembled. % Qbar - [Qbar] matrix for layer k % z1 - z(k-1) for layer k % z2 - z(k) for layer k