9.2 MATLAB Functions Used 173 Next,substitute(9.13)into (9.8)to obtain the required expressions as follows: 瓦=A1AA22-A经 A22H (9.14a) E,= A11AA22-A12 (9.14b) Au A12 Dry=A22 (9.14c) Dyt A12 A11 (9.14d) ,= (9.14e) MATLAB Example 9.2 Consider a four-layer [0/90s graphite-reinforced polymer composite laminate with the elastic constants as given in Example 2.2.The laminate has total thickness of 0.800 mm.The four layers are of equal thickness.Use MATLAB to determine the five effective elastic constants 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: EDU>>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 [is calculated for each layer using the MATLAB function Qbar as follows: EDU>>Qbar1 Qbar(Q,0) Obar1 155.7478 3.0153 0 3.0153 12.1584 0 0 0 4.40009.2 MATLAB Functions Used 173 Next, substitute (9.13) into (9.8) to obtain the required expressions as follows: E¯x = A11AA22 − A2 12 A22H (9.14a) E¯y = A11AA22 − A2 12 A11H (9.14b) ν¯xy = A12 A22 (9.14c) ν¯yx = A12 A11 (9.14d) G¯xy = A66 H (9.14e) MATLAB Example 9.2 Consider a four-layer [0/90]S graphite-reinforced polymer composite laminate with the elastic constants as given in Example 2.2. The laminate has total thickness of 0.800 mm. The four layers are of equal thickness. Use MATLAB to determine the five effective elastic constants 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: EDU>> 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: EDU>> Qbar1 = Qbar(Q, 0) Qbar1 = 155.7478 3.0153 0 3.0153 12.1584 0 0 0 4.4000