9.4 SUBLAMINATE 407 Table 9.1.The equations used for calculating the nonzero elements of the [compliance matrix Equation numbers 「9.249.249.45 9.247 「J11.J16 9.249.249.45 9.24 9.299.299.46 9.29 9.53 9.53 61..J66 9.539.53 9.249.249.45 9.24 9.4.4 Step 4.The Stiffness Matrix By combining the results of the preceding three steps,we obtain the following strain-stress relationship: Ex J J12 J13 0 0 J167 石x J21 J22 J23 0 0 J26 J31 J32 J33 0 0 J36 (9.56) 0 0 0 J44 J45 0 0 0 0 J54 Jss Tx J61 J62 J63 0 0 J66 y V-E- where [is the compliance matrix of the sublaminate.The stiffness matrix is [E=U]1 (9.57) We note that both [J]and E]are symmetrical.The equations to be used for calculating the elements of [J]are summarized in Table 9.1. Under plane-stress condition,the strain-stress relationship is J12 J16 (9.58) J61 J62J66 Therefore,under plane-stress condition we need to determine only those elements that appear in this expression. 9.1 Example.Calculate the stiffness matrix of a sublaminate made of graphite epoxy unidirectional plies.The material properties are given in Table 3.6(page 81). The layup is [02/452/02/452 (Fig.9.8).The thickness of the sublaminate is hs= 0.0008m.9.4 SUBLAMINATE 407 Table 9.1. The equations used for calculating the nonzero elements of the [J ] compliance matrix Equation numbers     J11... J16 . . . ... . . . J61... J66     =⇒          9.24 9.24 9.45 − − 9.24 9.24 9.24 9.45 − − 9.24 9.29 9.29 9.46 − − 9.29 −−− 9.53 9.53 − −−− 9.53 9.53 − 9.24 9.24 9.45 − − 9.24          9.4.4 Step 4. The Stiffness Matrix By combining the results of the preceding three steps, we obtain the following strain–stress relationship:    x  y z γ yz γ xz γ xy    =          J11 J12 J13 0 0 J16 J21 J22 J23 0 0 J26 J31 J32 J33 0 0 J36 000 J44 J45 0 000 J54 J55 0 J61 J62 J63 0 0 J66          % &' ( [J ]=[E] −1    σ x σ y σ z τ yz τ xz τ xy    , (9.56) where [J ] is the compliance matrix of the sublaminate. The stiffness matrix is [E] = [J ] −1 . (9.57) We note that both [J ] and [E] are symmetrical. The equations to be used for calculating the elements of [J ] are summarized in Table 9.1. Under plane-stress condition, the strain–stress relationship is    x  y γ xy    =    J11 J12 J16 J21 J22 J26 J61 J62 J66       σ x σ y τ xy    . (9.58) Therefore, under plane–stress condition we need to determine only those elements that appear in this expression. 9.1 Example. Calculate the stiffness matrix [J ] of a sublaminate made of graphite epoxy unidirectional plies. The material properties are given in Table 3.6 (page 81). The layup is [02/452/02/452] (Fig. 9.8). The thickness of the sublaminate is hs = 0.0008 m