Question 11.S.P.3: A [25°]12 graphite-epoxy laminate is trimmed to in-plane dim...
A [25°]_{12} graphite-epoxy laminate is trimmed to in-plane dimensions of 300×150 mm and is mounted in an assembly that provides type S4 simple supports along all four edges. The laminate is then subjected to a uniform transverse load q(x,y) = 30 kPa. No in-plane loads are applied (i.e., N_{xx} = N_{yy} = N_{xy} = 0). Determine the maximum out-of-plane displacement based on a Ritz analysis and plot the out-of-plane displacement field. Use the properties listed for graphite-epoxy in Table 3 of Chap. 3, and assume each ply has a thickness of 0.125 mm.
| Table 3 Nominal Material Properties for Common Unidirectional Composites | |||
| Property | Glass/epoxy | Kevlar/epoxy | Graphite/epoxy |
| E_{11} | 55 GPa (8.0 Msi) | 100 GPa (15 Msi) | 170 GPa (25 Msi) |
| E_{22} | 16 GPa (2.3 Msi) | 6 GPa (0.90 Msi) | 10 GPa (1.5 Msi) |
| ν_{12} | 0.28 | 0.33 | 0.30 |
| G_{12} | 7.6 GPa (1.1 Msi) | 2.1 GPa (0.30 Msi) | 13 GPa (1.9 Msi) |
| σ_{11}^{fT} | 1050 MPa (150 ksi) | 1380 MPa (200 ksi) | 1500 MPa (218 ksi) |
| σ_{11}^{fC} | 690 MPa (100 ksi) | 280 MPa (40 ksi) | 1200 MPa (175 ksi) |
| σ_{22}^{yT} | 45 MPa (5.8 ksi) | 35 MPa (2.9 ksi) | 50 MPa (7.25 ksi) |
| σ_{22}^{yC} | 120 MPa (16 ksi) | 105 MPa (15 ksi) | 100 MPa (14.5 ksi) |
| σ_{22}^{fT} | 55 MPa (7.0 ksi) | 45 MPa (4.3 ksi) | 70 MPa (10 ksi) |
| σ_{22}^{fC} | 140 MPa (20 ksi) | 140 Msi (20 ksi) | 130 MPa (18.8 ksi) |
| τ_{12}^{y} | 40 MPa (4.4 ksi) | 40 MPa (4.0 ksi) | 75 MPa (10.9 ksi) |
| τ_{12}^{f} | 70 MPa (10 ksi) | 60 MPa (9 ksi) | 130 MPa (22 ksi) |
| α_{11} | 6.7 μ/m °C
(3.7 μin./in. °F) |
-3.6 μm/m °C
(-2.0 μin./in. °F) |
-0.9 μm/m °C
(-0.5 μin./in. °F) |
| α_{22} | 25 μ/m °C
(14 μin./in. °F) |
58 μm/m °C
(32 μin./in. °F) |
27 μm/m °C
(15 μin./in. °F) |
| β_{11} | 100 μm/m %M
(100 μin./in. %M) |
175 μm/m %M
(175 μin./in. %M) |
50 μm/m %M
(50 μin./in. %M) |
| β_{22} | 1200 μm/m %M
(1200 μin./in. %M) |
1700 μm/m %M
(1700 μin./in. %M) |
1200 μm/m %M
(1200 μin./in. %M) |
Note that the plate has an aspect ratio R = 150/300 = 2.0, as was the case for the laminates considered in Sample Problems 1 and 2. A rather unusual fiber angle of 25° has been selected for consideration in this problem because it results in high relative values of D_{16} and D_{26}, resulting in an interesting distortion of the predicted out-of-plane displacement field. Specifically, for this laminate:
D_{16}/D_{11} = 0.370 D_{16} /D_{22} = 2.21
D_{26} / D_{11} = 0.126 D_{26} / D_{22} = 0.755
These relative values of D_{16} and D_{26} are quite high, at least as compared to those exhibited by the [(±45/0)_{2}]_{s} laminate considered in Sample Problem 1.
A solution for this problem was obtained using program SYMM, using M=N=10. A maximum displacement of 16.1 mm is predicted to occur at the center of the plate. A contour plot of out-of-plane displacements is shown in Fig. 6. Distortion of the displacement field due to the generally ortho-tropic nature of the [25°]_{12} panel is obvious, especially when compared to the very slightly distorted pattern for a [(±45/0)_{2}]_{s} laminate, previously shown in Fig. 4.
