A [25°]_{12} graphite–epoxy laminate is trimmed to in-plane dimensions of 300 × 150 mm and 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 3.1, and assume each ply has a thickness of 0.125 mm.
TABLE 3.1
Typical Properties of Common Unidirectional Composites
| Property | Glass/ Epoxy | Kevlar/ Epoxy | Graphite/ Epoxy |
| E_{11} | 55 GPa | 100 GPa | 170 GPa |
| (8.0 Msi) | (15 Msi) | (25 Msi) | |
| E_{22} | 16 GPa | 6 GPa | 10 GPa |
| (2.3 Msi) | (0.90 Msi) | (1.5 Msi) | |
| ν_{12} | 0.28 | 0.33 | 0.3 |
| G_{12} | 7.6 GPa | 2.1 GPa | 13 GPa |
| (1.1 Msi) | (0.30 Msi) | (1.9 Msi) | |
| \sigma _{11}^{fT} | 1050 MPa | 1380 MPa | 1500 MPa |
| (150 ksi) | (200 ksi) | (218 ksi) | |
| \sigma _{11}^{fC} | 690 MPa | 280 MPa | 1200 MPa |
| (100 ksi) | (40 ksi) | (175 ksi) | |
| \sigma _{22}^{ff} | 45 MPa | 35 MPa | 50 MPa |
| (5.8 ksi) | (2.9 ksi) | (7.25 ksi) | |
| \sigma _{22}^{fC} | 120 MPa | 105 MPa | 100 MPa |
| (16 ksi) | (15 ksi) | (14.5 ksi) | |
| \tau ^f_{22} | 40 MPa | 40 MPa | 90 MPa |
| (4.4 ksi) | (4.0 ksi) | (13.1 ksi) | |
| \alpha _{11} | 6.7 μm/m−°C | −3.6 μm/m−°C | −0.9 μm/m−°C |
| (3.7 μin./in.\boxtimes °F) | (−2.0 μin./in.−°F) | (−0.5 μin./in.−°F) | |
| \alpha _{22} | 25 μm/m−°C | 58 μm/m−°C | 27 μm/m−°C |
| (14 μin./in.−°F) | (32 μin./in.−°F) | (15 μin./in.−°F) | |
| \beta _{11} | 100 μm/m−%M | 175 μm/m−%M | 50 μm/m−%M |
| (100 μin./in.−%M) | (175 μin./in.−%M) | (50 μin./in.−%M) | |
| \beta _{22} | 1200 μm/m−%M | 1700 μm/m−%M | 1200 μm/m−%M |
| (1200 μin./in.−%M) | (1700 μin./in.−%M) | (1200 μin./in.−%M) | |
| Ply | 0.125 mm | 0.125 mm | 0.125 mm |
| Thickness | (0.005 in.) | (0.005 in.) | (0.005 in.) |
