Calculator
Example data
| Input type | E1 | E2 | G12 | ν12 | θ (deg) | Q̅11 | Q̅22 | Q̅12 | Q̅16 | Q̅26 | Q̅66 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Constants | 135 | 10 | 5 | 0.30 | 45 | 43.003 | 43.003 | 33.003 | 31.460 | 31.460 | 34.983 |
Example uses GPa as the units label and rounds to three decimals.
Formula used
For an orthotropic ply under plane stress, the reduced stiffness terms are:
ν21 = ν12 (E2/E1)Q11 = E1 / (1 − ν12ν21)Q22 = E2 / (1 − ν12ν21)Q12 = ν12 E2 / (1 − ν12ν21)Q66 = G12
Let m = cos(θ) and n = sin(θ). The transformed reduced stiffness (Q̅) terms are:
Q̅11 = Q11 m⁴ + 2(Q12 + 2Q66)m²n² + Q22 n⁴Q̅22 = Q11 n⁴ + 2(Q12 + 2Q66)m²n² + Q22 m⁴Q̅12 = (Q11 + Q22 − 4Q66)m²n² + Q12(m⁴ + n⁴)
Q̅16 = (Q11 − Q12 − 2Q66)m³n − (Q22 − Q12 − 2Q66)mn³Q̅26 = (Q11 − Q12 − 2Q66)mn³ − (Q22 − Q12 − 2Q66)m³nQ̅66 = (Q11 + Q22 − 2Q12 − 2Q66)m²n² + Q66(m⁴ + n⁴)
The Q̅ matrix in Voigt form is:
[ [Q̅11 Q̅12 Q̅16], [Q̅12 Q̅22 Q̅26], [Q̅16 Q̅26 Q̅66] ].
How to use this calculator
- Select an input method: engineering constants or Q entries.
- Enter the ply angle θ in degrees or radians.
- Fill the material inputs using one consistent unit system.
- Click Calculate to display Q and Q̅ matrices.
- Use CSV for spreadsheets, and PDF for sharing or printing.