ply nk K-1 mid-plane flexed configuration before bending Figure 12.3 Bending of the Laminate facilitated by using the user friendly aspect of the program,allowing rapid return of the solution. 12.1.4 Flexure Behavior In the previous paragraph,we have limited discussion to loadings consisting of Ne N and To applying in the midplane of the laminate.We will now examine the cases that can cause deformation outside of the plane of the laminate.The laminate considered is-as before-supposed to have midplane symmetry. 12.1.4.1 Displacement Fields Hypothesis:Assume that a line perpendicular to the midplane of laminate before deformation (see Figure 12.3)remains perpendicular to the mid- plane surface after deformation. ■ Consequence:If one denotes as before uo and vo the components of the displacement in the midplane and wo as the displacement out of the plane (see Figure 12.3),the displacement of any point at a position z in the laminate (in the nondeformed configuration)can be written as Owo u=h。-z0x o v=v。-z而 (12.11) w Wo One can then deduce the nonzero strains: wo Ex Eox-Z- 3 2wo 号，=eoy-2 (12.12) 2 Yg=Yay-z× a'wo dxdy 2003 by CRC Press LLCfacilitated by using the user friendly aspect of the program, allowing rapid return of the solution. 12.1.4 Flexure Behavior In the previous paragraph, we have limited discussion to loadings consisting of Nx, Ny, and Txy applying in the midplane of the laminate. We will now examine the cases that can cause deformation outside of the plane of the laminate. The laminate considered is—as before—supposed to have midplane symmetry. 12.1.4.1 Displacement Fields
Hypothesis: Assume that a line perpendicular to the midplane of laminate before deformation (see Figure 12.3) remains perpendicular to the mid￾plane surface after deformation.
Consequence: If one denotes as before uo and vo the components of the displacement in the midplane and wo as the displacement out of the plane (see Figure 12.3), the displacement of any point at a position z in the laminate (in the nondeformed configuration) can be written as (12.11) One can then deduce the nonzero strains: (12.12) Figure 12.3 Bending of the Laminate u uo z ∂w0 ∂x = – --------- v v o z ∂w0 ∂y = – --------- w w = o Ó Ô Ô Ì Ô Ô Ï ex e ox z ∂ 2 w0 ∂x2 = – ------------ e y e oy z ∂2 w0 ∂y 2 = – ------------ g xy g oxy z ¥ 2 ∂2 w0 ∂x∂y = – ------------ Ó Ô Ô Ô Ô Ì Ô Ô Ô Ô Ï TX846_Frame_C12 Page 244 Monday, November 18, 2002 12:27 PM © 2003 by CRC Press LLC