9.4 SUBLAMINATE 399 Laminate Sublaminates FE Mesh plies sublaminates Figure 9.3:Thick laminate(left),sublaminates(middle),and the finite element mesh(right). is practical.Plate elements give inaccurate results.Three-dimensional elements require that the material be uniform throughout the element,and,hence,an ele- ment must contain a single layer or adjacent identical layers.This may result in a very large number of elements,making the numerical computation difficult and often infeasible. We can overcome these difficulties by dividing the laminate into sublaminates (Fig.9.3).Each layer in the sublaminate may be monoclinic,orthotropic,trans- versely isotropic,or isotropic.The thickness of each element is the same as the thickness of the corresponding sublaminate.The stiffness matrix [E]of such a sublaminate is defined by the relationship Ex =[ (9.14) 7y2 气xy The bar denotes average stresses and strains.It is convenient to represent this expression in terms of the compliance matrix [ J11 J12 J13 J14 J15 J16] x Jy J24 J25 J26 J31 J32 /33 J54 J35 J36 J41 J J 5 J4 (9.15) J51 J52 J53 J54 J55 56 J62 163 J64 165 J66 元y where [=]-1 (9.16)9.4 SUBLAMINATE 399 Laminate Sublaminates FE Mesh plies sublaminates Figure 9.3: Thick laminate (left), sublaminates (middle), and the finite element mesh (right). is practical. Plate elements give inaccurate results. Three-dimensional elements require that the material be uniform throughout the element, and, hence, an ele￾ment must contain a single layer or adjacent identical layers. This may result in a very large number of elements, making the numerical computation difficult and often infeasible. We can overcome these difficulties by dividing the laminate into sublaminates (Fig. 9.3). Each layer in the sublaminate may be monoclinic, orthotropic, trans￾versely isotropic, or isotropic. The thickness of each element is the same as the thickness of the corresponding sublaminate. The stiffness matrix [E] of such a sublaminate is defined by the relationship    σ x σ y σ z τ yz τ xz τ xy    = [E]    x  y z γ yz γ xz γ xy    . (9.14) The bar denotes average stresses and strains. It is convenient to represent this expression in terms of the compliance matrix [J ]    x  y z γ yz γ xz γ xy    =          J11 J12 J13 J14 J15 J16 J21 J22 J23 J24 J25 J26 J31 J32 J33 J34 J35 J36 J41 J42 J43 J44 J45 J46 J51 J52 J53 J54 J55 J56 J61 J62 J63 J64 J65 J66          % &' ( [J ]    σ x σ y σ z τ yz τ xz τ xy    , (9.15) where [E] = [J ] −1 . (9.16)