Calculator inputs
Enter laminate loads, strength allowables, and ply properties. Results appear above this form after submission.
Example data table
Sample carbon/epoxy style layup for testing the calculator interface and exports.
| Ply | Angle (°) | Thickness (mm) | E1 (MPa) | E2 (MPa) | G12 (MPa) | ν12 |
|---|---|---|---|---|---|---|
| 1 | 0 | 0.125 | 135000 | 10000 | 5000 | 0.30 |
| 2 | 45 | 0.125 | 135000 | 10000 | 5000 | 0.30 |
| 3 | -45 | 0.125 | 135000 | 10000 | 5000 | 0.30 |
| 4 | 90 | 0.125 | 135000 | 10000 | 5000 | 0.30 |
Formula used
The calculator applies classical laminate plate relations for orthotropic plies under plane stress. Each ply first uses the reduced stiffness matrix Q:
Q11 = E1 / (1 - ν12ν21) Q22 = E2 / (1 - ν12ν21) Q12 = ν12E2 / (1 - ν12ν21) Q66 = G12
The transformed stiffness matrix Q̅ is built from ply angle θ. Then the laminate stiffness terms are assembled through thickness coordinates z:
A = Σ(Q̅k · (zk - zk-1)) B = 1/2 · Σ(Q̅k · (zk² - zk-1²)) D = 1/3 · Σ(Q̅k · (zk³ - zk-1³))
Mid-plane strains and curvatures come from the ABD system:
{N, M} = [ A B ; B D ] · {ε0, κ}
Ply stresses are evaluated in material axes. Failure review includes Maximum Stress, Tsai-Hill, and Tsai-Wu style indices. A governing failure index above 1.0 indicates the submitted load state exceeds the chosen limits.
How to use this calculator
- Enter laminate force resultants Nx, Ny, and Nxy. Add bending resultants when curvature effects matter.
- Provide strength allowables Xt, Xc, Yt, Yc, and S in consistent stress units.
- List plies from bottom to top. Set each angle, thickness, E1, E2, G12, and ν12.
- Submit the form. The calculator solves the laminate ABD matrix and shows results above the form.
- Review equivalent laminate constants, per-ply stresses, failure indices, and the critical ply chart.
- Use the CSV button for spreadsheet review and the PDF button for a printable report.
FAQs
1) What does the laminate status mean?
It compares the largest calculated failure index against 1. A value at or below 1 passes this load case. A value above 1 suggests the selected strength limits are exceeded for at least one ply.
2) Why is the B matrix important?
The B matrix measures extension-bending coupling. When it is near zero, membrane loading causes much less unwanted curvature. Unsymmetric layups often produce larger B values and stronger coupling effects.
3) Should plies be entered bottom to top?
Yes. Stacking order changes the z positions, B matrix, D matrix, and ply stresses. Two laminates with identical angles but different order can show different curvatures and strength margins.
4) Can I use mixed materials in one laminate?
Yes. Each row accepts its own orthotropic constants, so hybrid laminates can be modeled. Keep units consistent across every ply and strength input to avoid misleading results.
5) What units should I use?
Use one consistent unit system. This page is arranged for MPa and millimeters, with membrane loads in N/mm and bending resultants in N. Consistency matters more than the specific system.
6) Why are Ex and Ey called equivalent values?
They are laminate-level engineering constants derived from the in-plane compliance of the full stack. They summarize the whole laminate response rather than the behavior of any single ply.
7) What does the reserve ratio show?
Reserve ratio is shown as 1 divided by the governing failure index. Values above 1 indicate spare capacity for this simplified comparison. Values below 1 indicate overload relative to the chosen criterion.
8) Does this replace detailed composite certification analysis?
No. It is a design-screening and study tool. Real projects may also need knockdown factors, environmental effects, progressive damage, manufacturing defects, test data, and certification-specific methods.