8.2 MATLAB Functions Used 155 H/2 -H/2 ah=20保-)= (8.19d) H/2 016dz= Q16(绿-录-1)=B16 (8.19e) 2 -H/2 k=1 Using the remaining two equations of the matrix(7.12),we obtain the general desired expressions as follows: N A=O(2k-2k-1) (8.20) k=1 0(绿-录-1)》 (8.21) k三1 MATLAB Example 8.2 Consider a graphite-reinforced polymer composite laminate with the elastic con- stants as given in Example 2.2.The laminate has total thickness of 0.500 mm and is stacked as a [0/90s laminate.The four layers are of equal thickness.Calculate the [A,[B],and [D]matrices for this laminate. Solution This example is solved using MATLAB.First,the reduced stiffness matrix [Q]for a typical layer using the MATLAB function ReducedStiffness as follows: >>Q=ReducedStiffness(155.0,12.10,0.248,4.40) 0= 155.7478 3.0153 3.0153 12.1584 0 0 0 4.4000 Next,the transformed reduced stiffness matrix is calculated for each layer using the MATLAB function Qbar as follows: >Qbar1 Qbar(Q,0) Qbar1 155.7478 3.0153 0 3.0153 12.1584 0 0 4.40008.2 MATLAB Functions Used 155 H/  2 −H/2 Q¯12 zdz = 1 2 N k=1 Q¯12  z2 k − z2 k−1  = B12 (8.19d) H/  2 −H/2 Q¯16 zdz = 1 2 N k=1 Q¯16  z2 k − z2 k−1  = B16 (8.19e) Using the remaining two equations of the matrix (7.12), we obtain the general desired expressions as follows: Aij = N k=1 Q¯ij (zk − zk−1) (8.20) Bij = 1 2 N k=1 Q¯ij  z2 k − z2 k−1  (8.21) MATLAB Example 8.2 Consider a graphite-reinforced polymer composite laminate with the elastic con￾stants as given in Example 2.2. The laminate has total thickness of 0.500 mm and is stacked as a [0/90]S laminate. The four layers are of equal thickness. Calculate the [A], [B], and [D] matrices for this laminate. Solution This example is solved using MATLAB. First, the reduced stiffness matrix [Q] for a typical layer using the MATLAB function ReducedStiffness as follows: >> Q = ReducedStiffness(155.0, 12.10, 0.248, 4.40) Q = 155.7478 3.0153 0 3.0153 12.1584 0 0 0 4.4000 Next, the transformed reduced stiffness matrix ! Q¯" is calculated for each layer using the MATLAB function Qbar as follows: >> Qbar1 = Qbar(Q,0) Qbar1 = 155.7478 3.0153 0 3.0153 12.1584 0 0 0 4.4000